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+{"cells":[{"cell_type":"markdown","source":"TMA4320, spring 2022: Industrial mathematics project","metadata":{"tags":[],"cell_id":"984561f5dddb47ed833bb90a02f8d2b6","is_collapsed":false,"formattedRanges":[],"deepnote_app_coordinates":{"h":2,"w":8,"x":0,"y":1},"deepnote_cell_type":"text-cell-p"}},{"cell_type":"markdown","source":"Group: 1881","metadata":{"tags":[],"cell_id":"7a730eecc13c43ca98b7765f17cc3bcc","is_collapsed":false,"formattedRanges":[],"deepnote_app_coordinates":{"h":2,"w":8,"x":0,"y":4},"deepnote_cell_type":"text-cell-p"}},{"cell_type":"markdown","source":"# Dimensionality reduction and noise removal of face images with Non-Negative Matrix Factorization","metadata":{"tags":[],"cell_id":"4c6dce0491ae428b9d264d3882e648d5","is_collapsed":false,"formattedRanges":[],"deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":7},"deepnote_cell_type":"text-cell-h1"}},{"cell_type":"markdown","source":"Non-negative matrix factorization (NMF) is designed to extract alternative structures inherent in a given dataset. The method has a vast variety of applications, a few of which will be examined in this project. Digital images can be represented as matrices of which the elements represent each discernible pixel constituating the complete image. As was first discovered by Daniel D. Lee and H. Sebastian Seung, the inherit non-negativity of the NMF-method is a particularly powerful property when it comes to representing digital images, because colours are handily represented as positive numbers. In this project said property will be used in order to decompose the famous Cryptopunk-dataset - an algoritmically generated dataset consisting of characters randomly generated as sums of special features, i.e. hair, glasses, plain faces, etc. The factorization method will be conducted in according to the Lee and Seung's multiplicative update rule for NMF, and NMF will hereafter implicitly refer to this method, however other NMF-algorithms, such as Sequential NMF and Exact NMF, do exist. \n\nIn a broad scheme of things the NMF works in the way that it decomposes an arbitrary, non-negative, non-zero matrix $A$ into two matrices $W$ and $H$, such that $WH \\approx A$. In this way, the size of the rows and the size of the columns of $W$ and $H$, respectively, are fixed, equalling the size of the constituating matrix $A$. However, the size of the rows and the size of the columns of $W$ and $H$, respectively, are free to have any arbitrary positive whole number value. The consequence of changing this value, which will be called \"d\" or the \"$\\text{rank}$\" of the reconstruction, has great consequence for $\\textbf{I)}$ the size of the dataset, and $\\textbf{II)}$ the resemblance between the original and the reconstructed matrix. For:\n\n$\\textbf{I)}$: The rank (d) of the factorization should generally be chosen to be smaller than $n$ and $m$, so that $nd + md < nm$, i.e. so that the size of $W$ plus the size of $H$ is less than the size of $A$, making the factorization a compression of $A$. \n\n$\\textbf{II)}$: In some cases datasets can be polluted with noise or other errors. In such cases an imperfect reconstruction, meaning a reconstruction where $WH = A_{\\text{rec}} \\neq A_{\\text{original}}$, can be advantageous, and used to remove such unwanted irregularities. Noise reduction from a polluted dataset will further be examined in this project, as static noise is manually added to the Cryptopunk-dataset.\n\nThe discreprency between the original matrix and the reconstructed matrix can be measured as a norm of the difference between the two matrices. In this project the Frobenius norm, being an extension of the eucledian norm for higher dimensions, is used to calculate this norm, and \"norm\" will hereafter implicitly refer to the Frobenius norm.\n\nThe code in this project is written in Python 3.7.X and is run in notebook-format, however it is compatible with later versions of Python. Modelling is concluded using matrices, matrix-operations and special algorithms. The imported libraries are numpy, used for generating random numbers and speeding up the code, os, used for importing the Cryptopunk dataset, cv2, used for formatting said dataset, as well as matplotlib.pyplot used for formatted plotting. Numpy is also used for seeding the random numbers used in this project. In order to keep the number of global variables as low as possible, dedicated plotting functions without input nor output will be utilized, and these functions will therefore not have any content description, unlike other functional functions.","metadata":{"tags":[],"cell_id":"84cf9085aa4244f69faa763ccc23904d","deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":13},"deepnote_cell_type":"markdown"}},{"cell_type":"code","source":"\"\"\" Imported libraries \"\"\"\nimport numpy as np\nimport numpy.random as npr\nimport matplotlib.pyplot as plt\nimport os\n\n\"\"\" In order to make cv2 work: \"\"\"\n!apt update\n!apt install ffmpeg libsm6 libxext6 -y\n!pip install opencv-python\n!pip install --upgrade pip \nimport cv2\n\n\"\"\" Print options for numpy arrays, set to 3 decimals \"\"\"\nnp.set_printoptions(precision=3)\n\n\"\"\" Seeding \"\"\"\nnpr.seed(1)","metadata":{"tags":[],"cell_id":"90936e47e1dd421cbf2afeab298f3e73","source_hash":"4cf314c1","execution_start":1649447194005,"execution_millis":14714,"deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":19},"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"code"},"outputs":[{"name":"stdout","text":"Hit:1 http://security.debian.org/debian-security buster/updates InRelease\nHit:2 http://deb.debian.org/debian buster InRelease\nHit:3 http://deb.debian.org/debian buster-updates InRelease\n\n\n\n29 packages can be upgraded. Run 'apt list --upgradable' to see them.\n\n\n\nffmpeg is already the newest version (7:4.1.8-0+deb10u1).\nlibsm6 is already the newest version (2:1.2.3-1).\nlibxext6 is already the newest version (2:1.3.3-1+b2).\n0 upgraded, 0 newly installed, 0 to remove and 29 not upgraded.\nRequirement already satisfied: opencv-python in /root/venv/lib/python3.9/site-packages (4.5.5.64)\nRequirement already satisfied: numpy>=1.14.5 in /shared-libs/python3.9/py/lib/python3.9/site-packages (from opencv-python) (1.22.3)\nRequirement already satisfied: pip in /root/venv/lib/python3.9/site-packages (22.0.4)\n","output_type":"stream"}],"execution_count":null},{"cell_type":"markdown","source":"## Task 1","metadata":{"tags":[],"cell_id":"a7b7c41a15004239a72f284b212ca573","is_collapsed":false,"formattedRanges":[],"deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":25},"deepnote_cell_type":"text-cell-h2"}},{"cell_type":"markdown","source":"### Non-negativity of the update algorithm\n\nIn the following section some matrix-properties will be examined - and proven. In order to prove said properties, a couple of, rather obvious, results from the axioms for the real numbers must be stated and declared. These are: $\\textbf{I) The product}$ of two non-negative numbers is a non-negative number, $\\textbf{II) the sum}$ of two non-negative numbers is a non-negative number, and finally, because the tranposed-operator does not change values, only indices, $\\textbf{III) the transposed}$ matrix of a matrix with non-negative entries produces a transposed matrix, still exclusively containing non-negative elements.\n\nThe matrix multiplication between the matrices $A$ and $B$, resulting in the matrix $C$, is the sum of the product of the respective elements of the constituating matrices. In other words, the matrix multiplication between the matrices $A$ and $B$ equals the matrix $C$, s.t.:\n\n$$\nc_{ij} = \\sum_{k=1}^n a_{ik}b_{kj}.\n$$ \n\nBy I) and II), $c_{ij}$ must be a positive number if matrix $A$ and matrix $B$ are positive matrices. \n\n\nAn analogue argument can be ascertained for the Hadamard product and the Hadamard division, where the Hadamard product and division between two matrices consisting of non-negative elements also produces a matrix exclusively consisting of non-negative elements. The Hadamard product between the matrices $A$ and $B$ equals the matrix $C$, s.t.:\n\n$$\nc_{ij} = \\sum_{i=1}^n a_{ij} b_{ij}.\n$$\n\nBy I) and II), $c_{ij}$ must be a positive number if matrix $A$ and matrix $B$ are positive matrices. \n\n\nHence, for the iterates of the multiplicative update rule:\n\n$\\hspace{5mm}$\n\n$$\nH_{k+1} = H_k \\odot (W_k^T A) \\oslash (W_k^T W_k H_k),\n$$\n\nwhere $H_k$, $W_k$ and $A$, and by III) $W_K^T$, are matrices consisting only of non-negative elements. Since all matrices in the equation consist exclusively of non-negative elements, and since the operators in the equation produce non-negative matrices when the factors are non-negative, this implies that the right hand side, and by extension the left hand side must be non-negative. Hence all iterates of $H_k$ must be non-negative. Equally, for:\n\n$$\nW_{k+1} = W_k \\odot (A H_{k+1}^T) \\oslash (W_k H_k H_{k+1}^T),\n$$\n\nwhere $W_k$, $H_k$, $H_{k+1}$ and $A$, and by III) $H_{k+1}^T$, are matrices consisting only of non-negative elements. Since all matrices consist exclusively of non-negative elements, and since all associated operators produce non-negative matrices when the factors are non-negative, this implies that the right hand side, and by extension the left hand side must be non-negative. Hence all iterates of $W_k$ must be non-negative. QED.","metadata":{"tags":[],"cell_id":"f17872c70a384db3aba49461d2950aac","deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":31},"deepnote_cell_type":"markdown"}},{"cell_type":"markdown","source":"### Convergence and matrix of ones\n\nThe multiplicative update algorithm for the matrix $H$ is as follows:\n\n$$\nH_{k+1} = H_k \\odot (W_k^T A) \\oslash (W_k^T W_k H_k).\n$$\n\nIn order to prove that $H_{k+1} = H_k$ when $(W_k^T A) \\oslash (W_k^T W_k H_k)$ is a matrix of ones, it is necessary to examine the dimensions of the matrix quotient of the Hadamard division, i.e. $(W_k^T A) \\oslash (W_k^T W_k H_k)$. If the dimension of the resulting matrix is equal to the dimension of $H$, it is obvious that a Hadamard multiplication with $H$ will return the same $H$ if all the elements in the quotient are ones. \n\nThe multiplication between a matrix with size $m \\times d$ and a matrix with size $d \\times n$ yields a matrix of dimensions $m \\times n$, i.e. the same number of rows as the first matrix, and the same number of columns as the second matrix. The dimensions of the matrices in the update algorithm are:\n\n$$ \nA: m \\times n \n$$\n$$ \nW: m \\times d \n$$\n$$\nH: d \\times n\n$$\n\nThis means that $W^T$ is a $d \\times m$ matrix. The matrix product $W_k^T A$, hence, is a multiplication of a $(d \\times n)$-matrix with an $(m \\times n)$-matrix, which produces a $(d \\times n)$-matrix. For the product between $W_k^T W_k H_k$, it is split into two products. The first, $W_k^T W_k$, produces a $(d \\times d)$-matrix. This $(d \\times d)$-matrix is then multiplied with the $(d \\times n)$-matrix, $H$, to finally produce a $(d \\times n)$-matrix. The Hadamard quotient $(W_k^T A) \\oslash (W_k^T W_k H_k)$ is then an elementwise division of two $(d \\times n)$-matrices, which produces a $(d \\times n)$-matrix, with the same dimensions as $H$. If this matrix contains only ones, an elementwise multiplication with $H$ must mean that all the elements in $H$ are multiplied by $1$. The product of this Hadamard multiplication is therefore $H$, and for the update algorithm, this means that when the Hadamard quotient $(W_k^T A) \\oslash (W_k^T W_k H_k)$, returns a matrix of ones, the algorithm has converged to a fixed point, so that $H_k = H_{k+1}$. \n\nIf the matrix product between $WH$ is equal to $A$, then the Hadamard quotient is simply a matrix divided elementwise by itself. This means that every element in the quotient are equal to 1, and the update algorithm has therefore converged.\n","metadata":{"tags":[],"cell_id":"d0deee6777084505be7069b217b637f5","deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":37},"deepnote_cell_type":"markdown"}},{"cell_type":"markdown","source":"### Zero-matrix\n\nMultiplying two numbers that are equal to zero is trivial, however dividing a number by zero will render the quotient undefined. If an initial matrix is a matrix consisting of only zero-elements a zero over zero-case will occur and the operation will produce a quotient containing undefined elements. This is a problem. In addition, it is crucial to have at least one non-negative, non-zero element in order to get the algorithm running, because when all elements are zero, every product will return zeros and the algorithm will have converged before it even began, i.e. doing nothing.\n\nIn order to fix this issue, which is necessary because matrix entries may be zero, a machine epsilon (machin error), $\\delta$ can be added, so that division by zero then becomes division by $\\delta$, which a computer can handle. The value of the machine epsilon should be as little as possible in order not to pollute the algorithm, but high enough, so that the precision of the computer can handle them. An implementation should take into consideration the bit-size of the computer, being the floating-point number precision, and use this value as a guideline to the value of $\\delta$. Hence, for a $64$-bit computer the $\\delta$-value should be somewhere around $2^{-52} \\approx 10^{-15}$, and for $32$-bit, the $\\delta$-value should be somewhere around $2^{-23} \\approx 10^{-7}$.","metadata":{"tags":[],"cell_id":"076c61f149f54d869aea21fe62bcac21","deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":43},"deepnote_cell_type":"markdown"}},{"cell_type":"markdown","source":"Throughout the rest of task 1, the following four matrices are investigated:\n\n$$ A_1 = \\begin{bmatrix} 1 & 0 \\\\ 0 & 1 \\end{bmatrix}, \\quad A_2 = \\begin{bmatrix} 1 & 2 \\\\ 1 & 1 \\\\ 1 & 2 \\end{bmatrix}, \\quad A_3 = \\begin{bmatrix} 2 & 1 & 1 \\\\ 2 & 1 & 1 \\\\ 1 & 1 & 2 \\end{bmatrix}, \\quad A_4 = \\begin{bmatrix} 2 & 1 & 0 \\\\ 1 & 2 & 3 \\\\ 0 & 3 & 3 \\end{bmatrix} $$.","metadata":{"tags":[],"cell_id":"b8d289394009462cbe1abfd3837ebb9d","deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":49},"deepnote_cell_type":"markdown"}},{"cell_type":"code","source":"def NMF(V, d, maxIterations, H = None, W = None, seed = None):\n    \"\"\"\n    Multiplicative update algorithm in according to Lee and Seung's update rule.\n    Input:\n        V:               Numpy array, Matrix (M x N) which is factorized.\n        d:               Integer, Number of columns in W and rows in H.\n        maxIterations:   Integer, Maximum number of iterations of the multiplicative update algorithm.\n    Return:\n        W:               Numpy array, Factorized matrix (M x d). \n        H:               Numpy array, Factorized matrix (d x N).\n        normsList:       Numpy array, array containing the norm for every iteration.\n    \"\"\"\n    \n    \"\"\" Setting the machine error \"\"\"\n    import struct; numberBits = 8 * struct.calcsize(\"P\")\n    if numberBits >= 64:\n        machineError = 1E-15 # 64 bit precision\n    else:\n        machineError = 1E-7  # 32 bit precision is = 1E-7\n\n    M, N = V.shape\n\n    \"\"\" Random initialization of W and H \"\"\"\n    if seed != None:\n        np.random.seed(seed)\n    if W is None:\n        W = np.random.rand(M, d) * np.sqrt(np.mean(V) / d)\n    if H is None:\n        H = np.random.rand(d, N) * np.sqrt(np.mean(V) / d)\n\n    normsList = np.zeros(maxIterations)\n\n    \"\"\" The multiplicative update algorithm \"\"\"\n    for n in range(maxIterations):\n        H_next = H * (W.T @ V)        /   (W.T @ W @ H + machineError)\n        W_next = W * (V @ H_next.T)   /   (W @ H_next @ H_next.T + machineError)\n\n        H = H_next\n        W = W_next\n        \n        normsList[n] = np.linalg.norm(V - W @ H, 'fro')\n\n\n    assert not np.min(H) < 0 or not np.min(W) < 0, \"Negative numbers in NMF\"\n\n    return W, H, normsList","metadata":{"tags":[],"cell_id":"fe25b1ada8f54f9ea4ad0cafcf7fcee8","source_hash":"724746da","execution_start":1649447208733,"execution_millis":5,"deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":55},"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"code"},"outputs":[],"execution_count":null},{"cell_type":"code","source":"def ex1d():\n\n    A1 = np.array([[1, 0], [0, 1]])\n    A2 = np.array([[1, 2], [1, 1], [1, 2]])\n    d = 1\n    maxIterations = 1000\n\n    seeds = [1,2,3]\n    matrixLabel = ['A1', 'A2']\n    i = 0    # For plot titles\n\n    print(\"------------------------------------------------------------------\")\n    print(\"------------------------------------------------------------------\")\n    print(\"------------------------------------------------------------------\\n\")\n    \n    for A in [A1, A2]:\n        print(f\"A = {matrixLabel[i]}: \\n\", A, '\\n')\n\n        for seed in seeds:\n            print(f\"------ Seed = {seed} ------\")\n            W, H = NMF(A, d, maxIterations, seed = seed)[0], NMF(A, d, maxIterations, seed = seed)[1]\n            norm = np.linalg.norm(A - W @ H, 'fro')\n\n            print(\"H:  \\n\", H, '\\n')\n            print(\"W:  \\n\", W, '\\n')\n            print(\"WH: \\n\", W @ H, '\\n')\n            print(\"Norm: \", f\"{norm:1.3f}\", '\\n')          \n\n        print(\"------------------------------------------------------------------\")\n        print(\"------------------------------------------------------------------\")\n        print(\"------------------------------------------------------------------\\n\")\n        i += 1\n\n    \"\"\" Find rank of matrices, used in discussion \"\"\"\n    eigValsA1 = np.around(np.linalg.eig(A1)[0], 8)\n    eigValsA2 = np.around(np.linalg.svd(A2)[1], 8)\n\n    print(r\"Singular values (eigenvalues) of A_1: \", eigValsA1)\n    print(r\"Singular values of A_2: \", eigValsA2)\n\n    print(\"Rank of A1: \", len(eigValsA1[eigValsA1 != 0]))\n    print(\"Rank of A2: \", len(eigValsA2[eigValsA2 != 0]))\nex1d();","metadata":{"tags":[],"cell_id":"dc928a91db49404cac1821f0a5c4f8fb","source_hash":"73c89f0f","execution_start":1649447208976,"execution_millis":795,"deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":61},"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"code"},"outputs":[{"name":"stdout","text":"------------------------------------------------------------------\n------------------------------------------------------------------\n------------------------------------------------------------------\n\nA = A1: \n [[1 0]\n [0 1]] \n\n------ Seed = 1 ------\nH:  \n [[0.851 1.47 ]] \n\nW:  \n [[0.295]\n [0.509]] \n\nWH: \n [[0.251 0.434]\n [0.434 0.749]] \n\nNorm:  1.000 \n\n------ Seed = 2 ------\nH:  \n [[3.232 0.192]] \n\nW:  \n [[0.308]\n [0.018]] \n\nWH: \n [[0.996 0.059]\n [0.059 0.004]] \n\nNorm:  1.000 \n\n------ Seed = 3 ------\nH:  \n [[0.968 1.244]] \n\nW:  \n [[0.389]\n [0.501]] \n\nWH: \n [[0.377 0.485]\n [0.485 0.623]] \n\nNorm:  1.000 \n\n------------------------------------------------------------------\n------------------------------------------------------------------\n------------------------------------------------------------------\n\nA = A2: \n [[1 2]\n [1 1]\n [1 2]] \n\n------ Seed = 1 ------\nH:  \n [[1.194 2.109]] \n\nW:  \n [[0.921]\n [0.562]\n [0.921]] \n\nWH: \n [[1.1   1.943]\n [0.671 1.186]\n [1.1   1.943]] \n\nNorm:  0.411 \n\n------ Seed = 2 ------\nH:  \n [[1.94  3.427]] \n\nW:  \n [[0.567]\n [0.346]\n [0.567]] \n\nWH: \n [[1.1   1.943]\n [0.671 1.186]\n [1.1   1.943]] \n\nNorm:  0.411 \n\n------ Seed = 3 ------\nH:  \n [[1.369 2.419]] \n\nW:  \n [[0.803]\n [0.49 ]\n [0.803]] \n\nWH: \n [[1.1   1.943]\n [0.671 1.186]\n [1.1   1.943]] \n\nNorm:  0.411 \n\n------------------------------------------------------------------\n------------------------------------------------------------------\n------------------------------------------------------------------\n\nSingular values (eigenvalues) of A_1:  [1. 1.]\nSingular values of A_2:  [3.44  0.411]\nRank of A1:  2\nRank of A2:  2\n","output_type":"stream"}],"execution_count":null},{"cell_type":"code","source":"def ex1e():\n    A1 = np.array([[1, 0], [0, 1]])\n    A2 = np.array([[1, 2], [1, 1], [1, 2]])\n    d = 2\n    \n    maxIterationsList = [10, 100, 1000]\n    seeds = [1,2,3]\n\n    print(\"------------------------------------------------------------------\")\n    print(\"------------------------------------------------------------------\")\n    print(\"------------------------------------------------------------------\\n\")\n\n    matrixLabel = ['A1', 'A2']\n    i = 0    # For plot titles\n\n    for A in [A1, A2]:\n        print(f\"A = {matrixLabel[i]}: \\n\", A, '\\n')\n        for maxIterations in maxIterationsList:\n            print(\"------------------------------------------------------------------\")\n            print(\" Max iterations = \", maxIterations)\n            print(\"------------------------------------------------------------------ \\n\")\n            for seed in seeds:\n                print(f\"------ Seed = {seed} ------\")\n                W, H = NMF(A, d, maxIterations, seed = seed)[0], NMF(A, d, maxIterations, seed = seed)[1]\n                norm = np.linalg.norm(A - W @ H, 'fro')\n                #norm = A W @ H\n\n                print(\"H: \\n\", H, '\\n')\n                print(\"W: \\n\", W, '\\n')\n                print(\"WH: \\n\", W @ H, '\\n')\n                print(\"Norm: \", f\"{norm:1.3}\", '\\n')\n        \n        print(\"------------------------------------------------------------------\")\n        print(\"------------------------------------------------------------------\")\n        print(\"------------------------------------------------------------------\\n\")\n        i += 1\n\n    \"\"\" Check rank of matrices, for discussion \"\"\"\n    eigValsA1 = np.around(np.linalg.eig(A1)[0], 8)\n    eigValsA2 = np.around(np.linalg.svd(A2)[1], 8)\n\n    print(r\"Singular values (eigenvalues) of A_1: \", eigValsA1)\n    print(r\"Singular values of A_2: \", eigValsA2)\n\n    print(\"Rank of A1: \", len(eigValsA1[eigValsA1 != 0]))\n    print(\"Rank of A2: \", len(eigValsA2[eigValsA2 != 0]))\nex1e()","metadata":{"tags":[],"cell_id":"28a433db55bb45b2b63e9f790ec7a72e","source_hash":"63a9d785","execution_start":1649447209894,"execution_millis":1682,"deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":67},"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"code"},"outputs":[{"name":"stdout","text":"------------------------------------------------------------------\n------------------------------------------------------------------\n------------------------------------------------------------------\n\nA = A1: \n [[1 0]\n [0 1]] \n\n------------------------------------------------------------------\n Max iterations =  10\n------------------------------------------------------------------ \n\n------ Seed = 1 ------\nH: \n [[2.632e+00 0.000e+00]\n [1.573e-03 2.193e+00]] \n\nW: \n [[3.800e-01 2.022e-04]\n [0.000e+00 4.561e-01]] \n\nWH: \n [[1.000e+00 4.434e-04]\n [7.175e-04 1.000e+00]] \n\nNorm:  0.000843 \n\n------ Seed = 2 ------\nH: \n [[2.117e+00 3.276e-04]\n [0.000e+00 3.441e+00]] \n\nW: \n [[4.724e-01 0.000e+00]\n [4.518e-05 2.906e-01]] \n\nWH: \n [[1.000e+00 1.548e-04]\n [9.564e-05 1.000e+00]] \n\nNorm:  0.000182 \n\n------ Seed = 3 ------\nH: \n [[2.913e+000 5.378e-004]\n [4.239e-117 1.016e+000]] \n\nW: \n [[3.433e-001 1.105e-186]\n [3.917e-005 9.838e-001]] \n\nWH: \n [[1.000e+00 1.846e-04]\n [1.141e-04 1.000e+00]] \n\nNorm:  0.000217 \n\n------------------------------------------------------------------\n Max iterations =  100\n------------------------------------------------------------------ \n\n------ Seed = 1 ------\nH: \n [[2.632 0.   ]\n [0.    2.193]] \n\nW: \n [[0.38  0.   ]\n [0.    0.456]] \n\nWH: \n [[1. 0.]\n [0. 1.]] \n\nNorm:  6.47e-16 \n\n------ Seed = 2 ------\nH: \n [[2.117 0.   ]\n [0.    3.441]] \n\nW: \n [[0.472 0.   ]\n [0.    0.291]] \n\nWH: \n [[1. 0.]\n [0. 1.]] \n\nNorm:  5.55e-16 \n\n------ Seed = 3 ------\nH: \n [[2.913 0.   ]\n [0.    1.016]] \n\nW: \n [[0.343 0.   ]\n [0.    0.984]] \n\nWH: \n [[1. 0.]\n [0. 1.]] \n\nNorm:  1.13e-15 \n\n------------------------------------------------------------------\n Max iterations =  1000\n------------------------------------------------------------------ \n\n------ Seed = 1 ------\nH: \n [[2.632 0.   ]\n [0.    2.193]] \n\nW: \n [[0.38  0.   ]\n [0.    0.456]] \n\nWH: \n [[1. 0.]\n [0. 1.]] \n\nNorm:  7.11e-16 \n\n------ Seed = 2 ------\nH: \n [[2.117 0.   ]\n [0.    3.441]] \n\nW: \n [[0.472 0.   ]\n [0.    0.291]] \n\nWH: \n [[1. 0.]\n [0. 1.]] \n\nNorm:  4.97e-16 \n\n------ Seed = 3 ------\nH: \n [[2.913 0.   ]\n [0.    1.016]] \n\nW: \n [[0.343 0.   ]\n [0.    0.984]] \n\nWH: \n [[1. 0.]\n [0. 1.]] \n\nNorm:  1.16e-15 \n\n------------------------------------------------------------------\n------------------------------------------------------------------\n------------------------------------------------------------------\n\nA = A2: \n [[1 2]\n [1 1]\n [1 2]] \n\n------------------------------------------------------------------\n Max iterations =  10\n------------------------------------------------------------------ \n\n------ Seed = 1 ------\nH: \n [[0.553 2.258]\n [2.079 2.621]] \n\nW: \n [[3.280e-01 4.530e-01]\n [9.370e-05 4.199e-01]\n [5.111e-01 3.289e-01]] \n\nWH: \n [[1.123 1.928]\n [0.873 1.101]\n [0.967 2.016]] \n\nNorm:  0.219 \n\n------ Seed = 2 ------\nH: \n [[1.424 3.327]\n [1.761 1.107]] \n\nW: \n [[0.596 0.044]\n [0.2   0.362]\n [0.503 0.23 ]] \n\nWH: \n [[0.928 2.033]\n [0.922 1.066]\n [1.122 1.928]] \n\nNorm:  0.192 \n\n------ Seed = 3 ------\nH: \n [[1.369 0.91 ]\n [0.497 2.107]] \n\nW: \n [[0.479 0.737]\n [0.583 0.253]\n [0.502 0.721]] \n\nWH: \n [[1.022 1.989]\n [0.924 1.065]\n [1.045 1.976]] \n\nNorm:  0.115 \n\n------------------------------------------------------------------\n Max iterations =  100\n------------------------------------------------------------------ \n\n------ Seed = 1 ------\nH: \n [[0.365 2.573]\n [2.3   2.3  ]] \n\nW: \n [[4.529e-01 3.629e-01]\n [4.400e-05 4.348e-01]\n [4.529e-01 3.629e-01]] \n\nWH: \n [[1. 2.]\n [1. 1.]\n [1. 2.]] \n\nNorm:  1.28e-05 \n\n------ Seed = 2 ------\nH: \n [[1.47  3.357]\n [1.716 1.014]] \n\nW: \n [[0.568 0.094]\n [0.164 0.442]\n [0.565 0.101]] \n\nWH: \n [[0.996 2.002]\n [1.    1.   ]\n [1.004 1.998]] \n\nNorm:  0.00596 \n\n------ Seed = 3 ------\nH: \n [[1.421 0.868]\n [0.451 2.142]] \n\nW: \n [[0.467 0.744]\n [0.637 0.208]\n [0.467 0.744]] \n\nWH: \n [[1. 2.]\n [1. 1.]\n [1. 2.]] \n\nNorm:  2.33e-09 \n\n------------------------------------------------------------------\n Max iterations =  1000\n------------------------------------------------------------------ \n\n------ Seed = 1 ------\nH: \n [[0.365 2.573]\n [2.3   2.3  ]] \n\nW: \n [[4.529e-01 3.629e-01]\n [4.400e-05 4.348e-01]\n [4.529e-01 3.629e-01]] \n\nWH: \n [[1. 2.]\n [1. 1.]\n [1. 2.]] \n\nNorm:  8.31e-16 \n\n------ Seed = 2 ------\nH: \n [[1.47  3.357]\n [1.715 1.014]] \n\nW: \n [[0.566 0.098]\n [0.164 0.442]\n [0.566 0.098]] \n\nWH: \n [[1. 2.]\n [1. 1.]\n [1. 2.]] \n\nNorm:  1.23e-15 \n\n------ Seed = 3 ------\nH: \n [[1.421 0.868]\n [0.451 2.142]] \n\nW: \n [[0.467 0.744]\n [0.637 0.208]\n [0.467 0.744]] \n\nWH: \n [[1. 2.]\n [1. 1.]\n [1. 2.]] \n\nNorm:  1.31e-15 \n\n------------------------------------------------------------------\n------------------------------------------------------------------\n------------------------------------------------------------------\n\nSingular values (eigenvalues) of A_1:  [1. 1.]\nSingular values of A_2:  [3.44  0.411]\nRank of A1:  2\nRank of A2:  2\n","output_type":"stream"}],"execution_count":null},{"cell_type":"markdown","source":"NMF is performed for matrices $A_1$ and $A_2$, with three different seeds in order to explore whether the algorithm returns different results for different initializations. It is clear to see that the elements in $W$ and $H$ change for different seeds for both matrices. For $A_1$, even the matrix product $WH$ vary, meaning that convergence does not imply a unique solution, $WH$. For $A_2$, however, the NMF returns the same matrix $WH$ for each seed, meaning that the solution might be unique. This means that the norm only has a global minimum, not any locals, so that it converges to the same minimum for every initialization. \n\nFor both matrices, the norm converges to the same value for all three initializations, so this quantity is unique for a rank 1 approximation for both matrices.\n\nNMF for $A_1$ and $A_2$ yield different results with regards to the norm. The NMF is conducted using $d=1$, i.e. a rank 1 approximation. Matrix $A_1$ is recreated with a resulting norm of 1, while matrix $A_2$ is recreated with a resulting norm of 0.41. To understand why $A_2$ is reconstructed with higher precision, despite it having more elements than $A_1$, it is necessary to examine the singular values of the different matrices. $A_1$ has two singular values (equal to eigenvalues since the matrix is square), both 1. This means that both singular vectors (eigenvectors) are equally important in constructing the matrix. A rank 1 approximation, meaning that $W$ contains at most one basis vector, is therefore not sufficient to give a good reconstruction of $A_1$. $A_2$ also has two singular values, one equal to 3.44 and one equal to 0.41. Since one is much larger than the other, more information of the matrix is contained in the subspace spanned by a singular vector associated with the larger singular value. Therefore, a rank 1 approximation produces a better reconstruction for $A_2$ than for $A_1$. ","metadata":{"tags":[],"cell_id":"b470dfead1d2445b9c4898a498ca5dca","deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":73},"deepnote_cell_type":"markdown"}},{"cell_type":"markdown","source":"For $d=2$, the norm converges to (practically) zero for both matrices given enough iterations (~$10^{-15}$ is the machine zero). This is to be expected, as both matrices is of rank 2. However, different seeds return different $W$ and $H$, so the initialization might influnce the rate at which the algorithm converges.","metadata":{"tags":[],"cell_id":"4799b8b8da7e4a9baec468cfe0ee5587","deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":79},"deepnote_cell_type":"markdown"}},{"cell_type":"code","source":"def ex1f():\n    A3 = np.array([[2, 1, 1], [2, 1, 1], [1, 1, 2]])\n    A4 = np.array([[2, 1, 0], [1, 2, 3], [0, 3, 3]])\n\n    eigValsA3 = np.around(np.linalg.eig(A3)[0], 8)\n    eigValsA4 = np.around(np.linalg.eig(A4)[0], 8)\n\n    eigVecsA3 = np.linalg.eig(A3)[1]\n    eigVecsA4 = np.linalg.eig(A4)[1]\n\n    print(f\"Eigenvalues of A3: \\n {eigValsA3} \\n\")\n    print(\"Rank of A3: \\n      \", len(eigValsA3[eigValsA3 != 0]), '\\n')\n    print(f\"Eigenvectors of A3: \\n {eigVecsA3}\", '\\n')\n\n    print(f\"Eigenvalues of A4: \\n {eigValsA4}, \\n\")\n    print(\"Rank of A4: \\n      \", len(eigValsA4[eigValsA4 != 0]), '\\n')\n    print(f\"Eigenvectors of A4: \\n {eigVecsA4}\")  \nex1f()","metadata":{"tags":[],"cell_id":"50728ea9e20b4b37bea5f4aed47bb44b","source_hash":"5cb68295","execution_start":1649447211471,"execution_millis":110,"deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":85},"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"code"},"outputs":[{"name":"stdout","text":"Eigenvalues of A3: \n [ 4.  1. -0.] \n\nRank of A3: \n       2 \n\nEigenvectors of A3: \n [[ 0.577  0.408  0.302]\n [ 0.577  0.408 -0.905]\n [ 0.577 -0.816  0.302]] \n\nEigenvalues of A4: \n [-0.758  2.099  5.659], \n\nRank of A4: \n       3 \n\nEigenvectors of A4: \n [[-0.273 -0.945  0.178]\n [ 0.752 -0.094  0.653]\n [-0.6    0.312  0.736]]\n","output_type":"stream"}],"execution_count":null},{"cell_type":"markdown","source":"Matrix $A_3$ has 2 non-zero eigenvalues, hence it is of rank 2, and $A_4$ has 3 non-zero eigenvalues, so it is of rank 3.\n\nAs discussed in the project description, a rank $d$ matrix is in general expected to be perfectly recreated by an NMF with $d$ components. Although this does not always hold true, and we cannot say with certainty when it does, the rank does gives some indication of which $d$ is required in the NMF to yield a perfect reconstruction, where the norm converges to zero. Fundamentally, the rank of a matrix tells us how many linearly independent vectors are needed to construct the matrix by linear combinations of (singular) vectors. In the case of NMF, the rank of the matrix therefore gives some indication of how many basis vectors are needed in $W$ to reconstruct the original matrix.\n\nWe found that $A_3$ is a rank $2$ matrix, while $A_4$ is of rank $3$. It is therefore to be expected that the NMF yields better approximations for $d=2$ than for $d=1$ for both matrices, and a perfect reconstruction for $A_3$. For $d=3$, a perfect reconstruction is expected for both matrices, however, for $A_3$ it is unnecessary to further increase $d$ if the reconstruction is already perfect for $d=2$. For $d=2$ the norm will probably converge faster as it requires less operations and thus less computational power. \n\nIn addition to the rank, it is of interest to examine whether the matrices have negative eigenvalues or negative elements in its eigenvectors. As NMF is a method that enforces non-negativity on the matrices it attempts to reconstruct, it might fail if some key features of the matrices are represented by negative eigenvalues or negative elements in their eigenvectors, meaning the construction of the matrix by linear combinations of eigenvectors is not only additive but also subtractive. This will be further discussed in later sections when working with images, as it is easier to grasp the concept with a practical example at hand. We found that $A_4$ has four negative elements in its eigenvectors, as well as one negative eigenvalue. It is therefore a risk that a perfect reconstruction by NMF is not possible. ","metadata":{"tags":[],"cell_id":"da131e76cb02496bbd9aec9898241930","deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":91},"deepnote_cell_type":"markdown"}},{"cell_type":"code","source":"def ex1g():\n    A3 = np.array([[2, 1, 1], [2, 1, 1], [1, 1, 2]])\n    A4 = np.array([[2, 1, 0], [1, 2, 3], [0, 3, 3]])\n\n    dList = [1,2,3]\n\n    maxIterations = 1000\n    kArray = np.arange(0, maxIterations, 1)\n\n    plotTitles = ['A3', 'A4']\n    i = 0    # For plot titles\n\n    for A in [A3, A4]:\n        plt.figure(figsize=(10, 5))\n        plt.axes([0, 0, 1.4, 0.8])\n        for d in dList:\n            norm = NMF(A, d, maxIterations, seed = 4)[2]\n            plt.plot(kArray, norm, label = f'd = {d}') \n        plt.legend(fontsize = 14)\n        plt.title(f'A = {plotTitles[i]}', fontsize = 18)\n        plt.xlabel('Number of iterations, k', fontsize = 16)\n        plt.ylabel(r'$||A - W_k H_k||_F$', fontsize = 16)\n        plt.semilogy()\n        plt.grid()\n        plt.show()\n        i += 1\nex1g()","metadata":{"tags":[],"cell_id":"f8fe39d3a68845fc80aee2de4f4b96a3","source_hash":"8f7aeade","execution_start":1649447211493,"execution_millis":2654,"deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":97},"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"code"},"outputs":[{"data":{"text/plain":"<Figure size 720x360 with 1 Axes>","image/png":"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\n"},"metadata":{"needs_background":"light","image/png":{"width":1082,"height":358}},"output_type":"display_data"},{"data":{"text/plain":"<Figure 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\n"},"metadata":{"needs_background":"light","image/png":{"width":1077,"height":358}},"output_type":"display_data"}],"execution_count":null},{"cell_type":"markdown","source":"Above are plots showing how the norm changes as the number of iterations increases. Total number of iterations is set to 1000. It is clear from the plots that the norm is either stable or decreases as the number of iterations increases, so the update algorithm does seem to satisfy equation $(10)$ in the project description,\n\n$$\n||A - W_{k+1} H_{k+1}||_F \\leq ||A - W_k H_k ||_F.\n$$\n\nNote that the norm never really converges to true zero, but the machine epsilon, which is approximately $10^{-15}$ for a 64-bit computer. However, when commenting the plots, we say it converges to zero.\n\nThe plots are quite different for the two different matrices $A_3$ and $A_4$. The number of steps required for the algorithm to converge, that is, the number of steps before the norm reaches a local minimum, varies with $d$. For $d=1$, the norm converges, approximately instantaneously, for both matrices to around $1$ and $2$ respectively, meaning the NMF-factorization does not produce a very accurate representation of the original matrices. For $d=2$, the norm converges for both matrices, but while it goes to zero for $A_3$ very fast, it stabilizes at just less than $1$ for $A_4$. As discussed above, this is expected, as $A_3$ is a rank $2$ matrix. For $d=3$ for the $A_4$-factorization, it is unclear whether the norm converges to zero or not given enough iterations, since it converges so slowly. However, the norm does seem to approach som value close to $10^{-3}$ asymptotically. In that case, the $NMF$ does not yield a perfect recreation as expected. This might be due to the fact that the norm might have several local minimas, and the algorithm might get stuck in one such local minima instead of converging towards the global minima. Whether the algorithm does this or not might depend on the initialization of $W$ and $H$. A different seed in the $NMF$ might yield different results. The non-negativity constraint might also limit the approximation.\n\nA peculiar observation of the $A_4$ plot is the sudden crack in the graph for $d=2$ and $d=3$. This could be explained by imagining a topological surface, and the algorithm moving along this surface. Some places are steep, some are flat, some places there are deep valleys, corresponding to local minimas, while some places there are mountain tops, corresponding to local maxima. The algorithm, converging towards local minimas, does only realize steps that moves it to a point that is lower on the surface. On this surface, the algorithm could find itself located in a flat area where, no matter where it moves, the change in height is small. At some point, it might go from moving in a flat area to moving in a steep area, where the change of height in one step suddenly is big. This does not explain the cracks mathematically, but is a good analogue to think about how the algorithm moves and converges.","metadata":{"tags":[],"cell_id":"87e3829b265c4f59aeaa36391c5fa668","deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":103},"deepnote_cell_type":"markdown"}},{"cell_type":"markdown","source":"A weakness of NMF is, as mentioned, the enforcing of non-negativity which may cause a loss of important data, as key features for some matrix systems are represented by negative values. In practice, this means that a matrix might not be fully constructed by basisvectors that are added together - subtraction might also be necessary. The NMF cannot do this, it is an exclusively additive method, since the weights in $H$ which determines the linear combinations of the basisvectors in $W$ are always non-negative. Another weakness is the fact that the norm converges towards a local minimizer, not global, meaning the algorithm does not necessarily produce an optimal reconstruction of the original matrix for a given $d$. Note however that even local minimas are useful for many objectives. To examine whether any of these weaknesses might have played a role in the resulting plots above, it is appropriate to compare the results with results from a method that does not share the same weaknesses. \n\nThe SVD-method discussed in the project description has two, and probably more, important properties that separates it from NMF. One is, it does not require non-negativity. The other one is, a truncated SVD reconstruction of a matrix $A$ will always be the best possible reconstruction of $A$ with regards to the Frobenius norm. This means that for a specified $d$, the SVD algorithm is certain to find the global minimum of $||A - Ã||_F$, where $Ã$ is the truncated SVD reconstruction of rank $d$. \n\nBy comparing the convergence value of the norm for the two different methods, it will be clear whether the NMF has indeed found a best possible factorization of the original matrix, or if it $I)$ converges towards some local minmizer or $II)$ is limited by the non-negativity requirement. Only a comparison of the final value of the norm will be made, as it is the convergence value that is of interest here, not the rate at which it converges.","metadata":{"tags":[],"cell_id":"291036c492194627881b2fba97e2397b","deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":109},"deepnote_cell_type":"markdown"}},{"cell_type":"code","source":"def ex1g_SVDComparison():\n    \"\"\"\n    Function for \n    Input:\n        None.\n    Output: \n        None.\n    \"\"\"\n    A3 = np.array([[2, 1, 1], [2, 1, 1], [1, 1, 2]])\n    A4 = np.array([[2, 1, 0], [1, 2, 3], [0, 3, 3]])\n\n    dList = [1,2,3]\n\n    matrixLabel = ['A3', 'A4']\n    i = 0    # For matrix labels\n\n    for A in [A3, A4]:\n\n        for d in dList:\n\n            U, Sigma, VT = np.linalg.svd(A)\n\n            smat = np.diag(Sigma)\n\n            svd = U @ smat @ VT\n\n            norm = np.linalg.norm(A - svd, 'fro')\n\n            \"\"\" Reduce dimension to specified rank \"\"\"\n            rank = d\n            U_redusert = U[:, :rank]\n            smat_redusert = np.diag(Sigma[:rank])\n            VT_redusert = VT[:rank, :]\n            \n            svd_redusert = U_redusert @ smat_redusert @ VT_redusert\n\n            norm_redusert = np.linalg.norm(A - svd_redusert, 'fro')\n\n            #print(f'SVD for {matrixLabel[i]}, rank {d}:\\n', svd_redusert, '\\n')\n            print(f'Norm SVD for {matrixLabel[i]}, rank {d} approximation:', norm_redusert, '\\n')\n\n        i += 1\n\nex1g_SVDComparison()","metadata":{"tags":[],"cell_id":"a8ee8602af0f4dfaa8ab871c35fb407e","source_hash":"81dd8fc2","execution_start":1649447213732,"execution_millis":415,"deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":115},"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"code"},"outputs":[{"name":"stdout","text":"Norm SVD for A3, rank 1 approximation: 1.14841379830242 \n\nNorm SVD for A3, rank 2 approximation: 2.4525628233156873e-15 \n\nNorm SVD for A3, rank 3 approximation: 2.4525628233156873e-15 \n\nNorm SVD for A4, rank 1 approximation: 2.231680019120091 \n\nNorm SVD for A4, rank 2 approximation: 0.7577017654507557 \n\nNorm SVD for A4, rank 3 approximation: 5.0895131002843784e-15 \n\n","output_type":"stream"}],"execution_count":null},{"cell_type":"markdown","source":"For $A_3$, the NMF seems to produce the best possible reconstructions for all ranks, as the convergence value of the norm is the same as for the SVD. For $A_4$, the convergence value seems to be the same for rank 1 and 2, while for rank 3 it is zero for the SVD. It is difficult to see whether it converges to zero or not given enough iterations for NMF, but it is possible that either the non-negativity constraint or convergence towards a local minima has limited the NMF, compared to the SVD, for this rank. ","metadata":{"tags":[],"cell_id":"4ea2d66cd7d14f47b074631b0507c53c","deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":121},"deepnote_cell_type":"markdown"}},{"cell_type":"markdown","source":"## Task 2","metadata":{"tags":[],"cell_id":"67a22e3288fb4cbfb0893b935e8067e9","is_collapsed":false,"formattedRanges":[],"deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":127},"deepnote_cell_type":"text-cell-h2"}},{"cell_type":"markdown","source":"In the following section, the Cryptopunk dataset will be investigated through the lens of the NMF method. The methods ability to extract underlying features from a dataset, as well as yielding a representative reconstruction of the original data in a new, compressed dataset, will be tested experimentally. \n\nThe Cryptopunk dataset which will be examined consists of in total 10000 unique images. In this project, 500 of these will be randomly selected and represented in a 4-dimensional, numerical array. Experiments with NMF will be conducted on these randomly selected images.","metadata":{"tags":[],"cell_id":"8a0a894609e346a0a6f940d41d5aa404","deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":133},"deepnote_cell_type":"markdown"}},{"cell_type":"code","source":"def load_images(N):\n    \"\"\"\n    Loads images from cryptopunk dataset. Loading order is deterministic,\n    so for a certain N the exact same images will be loaded. \n    Input:\n        N:       integer, number of images to load\n    Output:\n        faces:   (24,24,4,N) numpy array containing images\n    \"\"\"\n\n    \"\"\" Allocate array to store images \"\"\"\n    faces = np.zeros((24,24,4,N))\n\n    \"\"\" Iteration variable \"\"\"\n    i = 0\n\n    \"\"\" Iterate over folders \"\"\"\n    for subdir, dirs, files in os.walk('./imgs'):\n\n        \"\"\" Iterate over files \"\"\"\n        for file in files:\n\n            \"\"\" Filepath to load from \"\"\"\n            filepath = subdir + os.sep + file\n\n            \"\"\" Make sure that the file is a .png \"\"\"\n            if filepath[-3:] == 'png':\n\n                \"\"\" Load the image \"\"\"\n                im = cv2.imread(filepath, cv2.IMREAD_UNCHANGED)\n\n                \"\"\" Convert it to RGBA and rescale pixels \"\"\"\n                faces[:,:,:,i] = cv2.cvtColor(im, cv2.COLOR_BGRA2RGBA)/255.0\n\n                i+=1\n            if i == N:\n                break\n    return faces\n\n\"\"\" Global variables to be used later \"\"\"\nmaxIterations = 1000\nN = 500                        # Number of faces to keep in final array\nfaces = load_images(10000)     # Load all 10000 images\nchoices = np.random.choice(faces.shape[-1], N, replace = False)\nfaces = faces[:,:,:,choices]  \n\nprint(\"The shape of faces: \", faces.shape) # Shape of faces","metadata":{"tags":[],"cell_id":"94b6f7e003d940bebd9906204594b622","source_hash":"b7b22aa5","execution_start":1649447213733,"execution_millis":40512,"deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":139},"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"code"},"outputs":[{"name":"stdout","text":"The shape of faces:  (24, 24, 4, 500)\n","output_type":"stream"}],"execution_count":null},{"cell_type":"code","source":"def plotimgs(imgs, d, nplot = 8, rescale = True, filename = None):\n    \"\"\"\n    Plots nplot * nplot images on an nplot x nplot grid. \n    Saves to given filename if filename is given\n    Can also rescale the RGB channels\n    Input:\n        imgs:      Numpy array, (24,24,4,N) or (24,24,3,N) array containing images, where N > nplot**2\n        nplot:     integer, nplot**2 images will be plotted\n        rescale:   bool\n        filename:  string, figure will be saved to this location. Should end with \".png\".\n    Output:\n        Plot of imgs.\n    \"\"\"\n    \"\"\" We will change some of the parameters of matplotlib, so we store the initial ones \"\"\"\n    oldparams = plt.rcParams['figure.figsize']\n\n    \"\"\" New params to make better plot. There definitely exists better ways of doing this \"\"\"\n    plt.rcParams['figure.figsize'] = (16, 16)\n    \n    \"\"\" Initialize subplots \"\"\"\n    fig, axes = plt.subplots(nplot,nplot)\n\n    \"\"\" Set background color \"\"\"\n    plt.gcf().set_facecolor(\"lightgray\")\n\n    \"\"\" Iterate over images \"\"\"\n    for idx in range(nplot**2):\n        \n        \"\"\" Indices \"\"\"\n        i = idx//nplot; j = idx%nplot\n\n        \"\"\" Remove axis \"\"\"\n        axes[i,j].axis('off')\n\n        \"\"\" Rescale RGB channels by dividing my maximal value \"\"\"\n        if rescale:\n            scaled_img = np.copy(imgs[:,:,:,idx])\n            scaled_img[:,:,:3] = scaled_img[:,:,:3]/np.max(scaled_img[:,:,:3])\n            axes[i,j].imshow(scaled_img)\n        else:\n            axes[i,j].imshow(imgs[:,:,:,idx])\n    \n    \"\"\" Tight layout so images will appear closer together \"\"\"\n    plt.tight_layout()\n\n    \"\"\" Save if filename is given \"\"\"\n    if filename is not None:\n        plt.savefig(filename)\n    if (d!= None):\n        fig.suptitle(f\"Dataset: {filename}, d = {d}\", fontsize = 32, x = 0.5, y = 1.05)\n    else:\n        fig.suptitle(f\"Dataset: {filename}\", fontsize = 32, x = 0.5, y = 1.05)\n\n    plt.show()\n\n    \"\"\" Return to old parameters \"\"\"\n    plt.rcParams['figure.figsize'] = oldparams\n\n\n# Example of plotting 8 times 8 images stored in \"faces\" and saving the output to a file named \"punks.png\"\nplotimgs(faces, d = None, nplot= 8, filename=\"64_CryptoPunks.png\")","metadata":{"tags":[],"cell_id":"6485b32722b046efb5ff8fa5eb7a3688","source_hash":"a0cdd63","execution_start":1649447254243,"execution_millis":3148,"deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":145},"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"code"},"outputs":[{"data":{"text/plain":"<Figure size 1152x1152 with 64 Axes>","image/png":"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\n"},"metadata":{"image/png":{"width":1142,"height":1213}},"output_type":"display_data"}],"execution_count":null},{"cell_type":"code","source":"def plotMeanImage(imgs):\n    \"\"\"\n    Loads image array \"faces\" with N = 500 images from Cryptopunk dataset. Loading order \n    is deterministic for certain seed.\n    Input:\n        imgs:   Numpy array, array of images from which the mean image is calculated\n    Output:\n        plot of the mean image, (24,24,4) numpy array mean image\n    \"\"\"\n    meanFace = np.mean(imgs, axis = -1)\n    fig, ax = plt.subplots(figsize=(8, 8))\n    plt.gcf().set_facecolor(\"lightgray\")\n    ax.set_title(\"Mean image\")\n    ax.imshow(meanFace)\n\n    \"\"\" Number of pixels with no opacity \"\"\"\n    print(\"Number of pixels with no opacity: \", len(np.argwhere(meanFace[:,:, 3] == 0.0)))\n\n    \"\"\" Finding the rank of the matrix by finding the number of non-zero singular values \"\"\"\n    facesRGB = faces[:,:,:3, :]\n    singVals = np.linalg.svd(facesRGB.reshape((np.prod(facesRGB.shape)//N, N)))[1]\n    print(\"Rank of matrix containing images: \", len(singVals[singVals > 1E-9]))\n\nplotMeanImage(faces)","metadata":{"tags":[],"cell_id":"8ba760c7263845d99520ed19ac6299a9","source_hash":"e8404234","execution_start":1649447257425,"execution_millis":1718,"deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":151},"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"code"},"outputs":[{"name":"stdout","text":"Number of pixels with no opacity:  166\nRank of matrix containing images:  373\n","output_type":"stream"},{"data":{"text/plain":"<Figure size 576x576 with 1 Axes>","image/png":"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\n"},"metadata":{"image/png":{"width":469,"height":482}},"output_type":"display_data"}],"execution_count":null},{"cell_type":"markdown","source":"In the above plot a representation of the average pixel occurence density of the dataset is depicted. Hence, darker colours resemble greater occurence, and brighter colours resemble lower occurence, i.e. white resemble no occurence. \n\n\nIf a pixel in the average image has an opacity equal to zero, it implies that all associated pixels in all of the $500$ images must have an opacity value equal to zero. This is because the only way that an average value can be equal to zero is that if all the values ​​used to calculate the average are equal to zero. \n\nThe mean image resembles a blurry face. Some pixels have high opacity, meaning these pixels contain features that are shared by more images. An example is the countour line of the face, which gives some indication of the average shape of the face for the $500$ images, and that most faces have the same position in the image. Examining the original images, it seems like all male faces share the same face shape, and the same for all female faces. This corresponds to a large number of pixels sharing the same values, and explains the high opacity contour line in the mean image. A resemblance of a mouth and two eyes are also apparent, meaning that for most of the images these features are contained in those high opacity pixels. The low opacity pixels surrounding the face tells us that some images include features outside of the average face shape, but these features are unique for one or a few images since the opacity is so low for these pixels.   \n\nFrom knowing the number of pixels with no opacity in the mean image, an upper bound estimate of the rank of the matrix containing all 500 images can be made. Each image is made up of $24 \\cdot 24 = 576$ pixels, and subtracting the number of no-opacity pixels in the mean image, which is 166, and then multiplying by the number of colour channels, 3, an upper bound for the rank is found to be $1230$. This estimate is found assuming all pixels with opacity in the mean image do have opacity in all separate $500$ images, which they most certainly do not. That is why it is an upper bound estimate, and a very rough one. \n\nThe actual rank can be found by finding the number of non-zero singular values. It is only of interest to find the rank of the matrix containing the three colour channels exclusively, as the opacity channel will be excluded from the NMF computation. In order to find the rank, the $(24 \\times 24 \\times 3 \\times 500)$-matrix must be reshaped to a two dimensional $([24 \\cdot 24 \\cdot 3] \\times 500)$-matrix. This is done in the code above, using built-in NumPy functions. The rank is found to be 373. Essentially, what this tells us, is that the column space in which the information about all 500 images are contained, is of dimension $373$, i.e. it is spanned by 373 linearly independent (singular) vectors. Hence, the rank gives a lower bound for which $d$ is necessary in order to reconstruct an original matrix with 100% precision through NMF, as $W$ must contain at least the same number of basis vectors in order to span the same column space.\n\nSince the rank is smaller than both the number of rows and columns in the original matrix, we know that all the information stored in the original matrix could be contained in a significantly smaller - compressed - dataset, as many of the singular vectors are linearly dependent and thus superfluous in the representation of the data. Compressing the dataset, i.e. represent the data in fewer elements, is exactly what NMF intends to do. However, as NMF requires non-negativity, it is unlikely that it is capable of yielding a 100% reconstruction for such a large dataset, no matter how large $d$ is chosen.","metadata":{"tags":[],"cell_id":"0bac14f67ceb46b5855bc142bd087f08","deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":157},"deepnote_cell_type":"markdown"}},{"cell_type":"code","source":"def NMFImages(V, d, maxIterations, H = None, W = None, seed = None):\n    \"\"\"\n    Multiplicative update algorithm in according to Lee and Seung's update rule.\n    Tailored to fit the cryptopunk dataset.\n    Input:\n        V:             input array containing images stored as(24,24,4,N)\n        d:             integer, Number of components we want to decompose V into\n        maxIterations: integer, maximum number of iterations\n        seed:          integer, random seed\n    Output:\n        W:             Numpy array, (m x d) array\n        H:             Numpt array, (d x n) array\n    \"\"\"\n\n    \"\"\" Setting the machine error \"\"\"\n    import struct; numberBits = 8 * struct.calcsize(\"P\")\n    if numberBits >= 64:\n        machineError = 1E-15\n    else:\n        machineError = 1E-7 # 32 bit precision is = 1E-7\n\n    \"\"\" Stores the opacity channel in 24 x 24 x N array \"\"\"\n    opacityMatrix = V[:,:, 3, :]   \n\n    \"\"\" Removes the opacity channel from V \"\"\"\n    imagesRGB = V[:,:,:3, :] \n    \n    \"\"\" Reshapes matrix to (1728 x N) shape \"\"\"\n    V = np.reshape(imagesRGB, (np.prod(imagesRGB.shape)//V.shape[3], V.shape[3])) \n\n    M = V.shape[0]\n    N = V.shape[1]\n\n    \"\"\" Random initialization of W and H \"\"\"\n    if seed != None:\n        np.random.seed(seed)\n    if W is None:\n        W = np.random.rand(M, d) * np.sqrt(np.mean(V) / d)\n    if H is None:\n        H = np.random.rand(d, N) * np.sqrt(np.mean(V) / d)\n    \n    normsList = np.zeros(maxIterations)\n\n    \"\"\" The multiplicative update algorithm \"\"\"\n    for n in range(maxIterations):\n        H_next = H * (W.T @ V)        /   (W.T @ W @ H + machineError)\n        W_next = W * (V @ H_next.T)   /   (W @ H_next @ H_next.T + machineError)\n\n        H = H_next\n        W = W_next\n\n        normsList[n] = np.linalg.norm(V - W @ H, 'fro')\n\n    assert not np.min(H) < 0 or not np.min(W) < 0, \"Negative numbers in NMF\"\n\n    return W, H, opacityMatrix, normsList\n\n\ndef ex2c():\n    dList = [4, 16, 64, 144]\n    WList = []\n    HList = []\n    for d in dList:\n        W, H, opacityMatrix, norm = NMFImages(faces, d, 1000)\n        WList.append(W); HList.append(H)\n        W_reshaped = np.reshape(W,(24,24,3,d))\n        plotimgs(W_reshaped, d, int(np.sqrt(d)), filename=f\"W_Columns_images.png\")\n    return W_reshaped, WList, HList, dList, opacityMatrix\n\n\"\"\" Global variables \"\"\"    \nW_reshaped, WList, HList, dList, opacityMatrix = ex2c()","metadata":{"tags":[],"cell_id":"21737f9b94b544a2b4064707fbba16de","source_hash":"b891cf76","execution_start":1649447258756,"execution_millis":227671,"deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":163},"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"code"},"outputs":[{"data":{"text/plain":"<Figure size 1152x1152 with 4 Axes>","image/png":"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\n"},"metadata":{"image/png":{"width":1139,"height":1213}},"output_type":"display_data"},{"data":{"text/plain":"<Figure size 1152x1152 with 16 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size 1152x1152 with 64 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\n"},"metadata":{"image/png":{"width":1142,"height":1213}},"output_type":"display_data"},{"data":{"text/plain":"<Figure 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2CAzZ86UTz/9NO4f44noP0V2fvevu+4657zk5eXJYYcdJkOHDpWcnBypq6uTLVu2yNKlS51w0kSZNWuW/Pvf/xaRnf3nhAkTJCMjQ1atWiWffPKJNDY2yoYNG+TSSy+VF198scVwm+3bt8sVV1whxcXFzkyj7t27y/bt2+Wjjz6SoqIiCQQC8utf/1pGjBgRdQbGZ599Jrfccosz4NS9e3c56qijpH///lJZWSlz5syR1atXy7XXXitHH310Qs9JPHZ9Zl988YXzbxMmTHBm2e06f9OmTWvVrDI09fDDD8v69eslPT1d7rrrrnbnups1a5a8++67IiLyy1/+Uvr27ZuIwwTQCRjcAZLUiBEjpEuXLs5f8b/++usmgztdunSR6667Tk477TTp0aNHs/vZuHGj3HDDDbJs2TL56quv5N1335WTTjpJbXPRRReJyM4ZQrsGd3b9WyyJen8RkWeeecYp33vvvXLyySc3u79AICCzZs1q8mNiV9sNN9zg/DC58MIL5eqrr24y/T4QCMiDDz4ozz//vJSVlcmvf/1rFTaz//77y/777y9vvvmmM7iz//77x3VOEi03N1dGjRolixYtEpGdgzj24E5xcbEz82DXTI2CggLZd999Zfny5TJv3jy5/PLLm+zbzMezO/LtrFixQq0sksiwr/r6ernlllucgZ0JEybIn//8Z2cwYZd33nlHbrvtNgkGg/LRRx/Jiy++KD/+8Y8TdhyJ8sILL0iXLl3kb3/7mxxyyCGqbf78+XLZZZdJMBiUt956S6qrq2XFihVy4YUXynXXXafCm66++mq5+OKLZdmyZVJaWir//e9/5dJLL4353jNmzBCRnaEBl156qZrddP3118stt9wiH374oUQiEXn88cflH//4R5N9JOL729E+/vhj8fl8csMNN8gFF1ygBh6vvPJKOf/882Xz5s2ydu1a+c1vfiPvvvuuTJ48Wf70pz+pH7fXXHON3HXXXfLaa69JJBKRf/7zn/L44483+56HHHKI/OxnP5NJkyY1O9AZDoedWSfhcFh+97vfydtvv93stjNmzHAGdtLS0uSOO+5oErZZUlIiv/rVr+T9998Xn88X83wkqv8U2dlP7QonHT16tDz++ONR839s3LixxdxgrfHcc89Jdna2PPDAA01mh61bt05+8YtfyIYNG2THjh1y9913y9/+9reY+3v99dclPT1d7rjjDjnzzDNV2/XXXy9XXHGFLFy4UOrr6+Wpp55qNndKTU2N3HHHHc7AzlFHHSW///3v1R9MbrjhBnn66aflL3/5S5PZYR3hpZdecgZ2MjMz5f7775djjjlGbbN27Vq58sorncGzRPnZz37W7kTCpl2heXuihQsXygsvvCAiIhdffHG7Z8xWVFTI7373OxHZOZh51llntfsYAXQeEioDScrn88k+++zj1Ldu3dpkm2HDhsmll14adWBFRGTQoEHyyCOPOA/or776asKOMZHvv+svvMOHD4/6w1Bk59KeP/zhD5t9IHr77bedsJLzzjtPbrzxxmbzKmRkZMgtt9zi/HV0/vz58s0330R9z8520EEHOeXmfgSZ4VrmA+2uwcBvv/22yXKoDQ0NzoCR/R6JYv5F3ufzqeTQ7TVt2jTZtGmTiIj07t1b/v73vzcZ2BEROfHEE+XGG2906k888cQeuzTsvffe22RgR2Tn53jKKaeIyM4wnPfff19++MMfyo033tgkb01+fr7ccsstTv2jjz6K673PPfdcueKKK5qErWVkZMgdd9zhfI++/PJLqampafL6RHx/O8N5550nF110UZPBk169esnVV1/t1N99910ZMGCAPPzww01mLfh8Prn55pudH+pffPFFs+dIZOeAyeTJk6POYPP7/XL++ec7A5AbNmyIOvDxz3/+0ylffvnlzebj6tGjhzzyyCPSo0cPiUQize5nl0T2n2Yo1iWXXBIzseugQYPkjDPOiHlsrRGJROS3v/1ts2F/Q4YMkUceecT53syaNUtWrFjR4j6vu+66JgM7IjtnJN11111OPdr37c0333QGzYYMGSIPPPBAk5mwPp9PLr74YjnrrLNa/KwSLRgMyr/+9S+nfssttzQZ2BERGTp0qPz973/fLasqpoKGhga57bbbJBwOy7Bhw5r9o0tr3XfffVJUVCRZWVly5513tjiIC2DPxswdIImZ4RTmDIjW6t27txx44IEyZ84cWbx4sTQ2NjbJ37M7xfP+u/Ky7MoB0xa7khNmZ2fLVVdd1eL2P/vZz+Tjjz8WkZ0P+dFCKVpjwIABCV+OedKkSfLkk0+KiDT7181dP/5ycnJUmNjEiRPl+eefl/r6evn222/VzK9vv/1WGhsbRWRneIA5kJgo5ipv+fn5CU2guyt5qsjOH7b2DyXTj3/8Y3n22Wdl69atUlRUJJ9//vkeke/FNHLkSDnqqKOith9xxBHy2muvOfUrr7wy6rYTJkyQgoICqayslJUrV0ooFIr5Yyw9PV2uuOKKqO1du3aVgw46SGbPni3hcFhWrFjR5LuSiO9vR8vIyJDLLrssarudOPaCCy6ImvspNzdXJk2aJDNnzpRwOCwrV65sNnwtXj/60Y+cv+5//fXXcvDBB6v2NWvWOAMxeXl5MWcVdunSRS644AL5y1/+EvM9E9l/hkIhp9xcTrbdaciQIc5gaHOGDh0qJ598svN9mjZtmtx0001Rt+/evXvMXFPDhg2T4cOHy+rVq6WsrEy2bdvWJCxmV8iMiMjPf/7zmPffK6+8Ul5//XV1Dne3uXPnOoNP/fv3b3Yga5e9995bTjrppITOLjrnnHMS2ie3Nznx7vK3v/1N1q1bJ36/X+666652P4d98sknTr6tK664IqH5AwF0DgZ3gCRm/pCorq6OuW0oFJLvv/9e1qxZI5WVlVJXV6f++rcr10MgEJBNmzbJsGHDEnqs7X3/fffdVxYtWiQbN26UBx98UK688krJycmJ+/3Ly8udv8COGzdOunTp0uJr9ttvP6dsJ6bdkxxwwAGSkZEhgUBAduzYIevWrVMPcbsGfMaNG6cGUA488EDx+XwSiURk3rx5anAn2myfRDJnL0T7UdwWjY2N8t133zn1lpKY+v1+OfbYY+W5554TkZ2rlOxpgzuHHXZYzPaBAwc65d69e8ccjPP5fDJgwACprKx0EkvHmjkxatSomLPvREQGDx7slEtLS5u0t/f72xlGjRoVM3dIQUGBdO3a1RlYb2nFP/MHZXFxcYvvX1ZWJsuXL5dt27ZJbW2tmlFmDuavW7euyWvNVe4OPvjgFs/1UUcdFXNwJ9H9p9n2yCOPyLBhw2T06NEt7jMRYg2S7nLMMcc4gzsLFy6Mue3kyZNbHJgePHiwrF69WkR2fj/MwZ2GhgZnIM7n88mUKVNi7qtXr14yevRoNbNyd1uwYIFTPuqoo1rMjXbssccmdHCnNSsoetW3337r3IPOPfdc2X///du1v8rKSicca+TIkZ0SNg4g8RjcAZKY+eM42syEqqoqeeKJJ+Stt95q9kdXtNckSqLe/+KLL3aWe3/66afllVdekUMPPVQOPPBAGTt2rIwcOTLmA/bKlSudwaS5c+c2u5R7LLsGn/ZEOTk5MnbsWCf0Ye7cuc7gTlFRkfPjzx6kKSwslL333ltWr14t8+bNU7M9zMGd3RGSJbJzRsEuiUyiu2XLFueHcJ8+feJK7mkuhb5hw4aEHUuitJSDxhwciydZprl9XV1dzMGdeJagbumzbO/3tzPEk/cnNzfXGWhpzWe0KxdUc7744gv5xz/+Id98801c4TfN9Zfr1693yvHMuhs8eLBkZmY6s/Vsie4/DznkEBk5cqQsW7ZMtmzZIueee67su+++csghh8j+++8v48aNazGRcVvFE/5phgU2N3hmiuc6ifX92LJli5Nrp2/fvnENnO2zzz4dOrhjXk/mwFw08WwDV2NjoxOO1b9/f7nuuuvavc/7779fduzY4SRl3pNXggQQP77JQBLbldxYRJpd8Wbz5s1yySWXNFkGuiXRHvBbK5Hvf8wxx8hdd90lDzzwgFRVVUlNTY18+OGH8uGHH4rIzgGOww47TE4//XT5wQ9+0OT1ZghQW8T6MbYnmDRpkjO4M2/ePDn77LNFpOWkyJMmTZLVq1c7y55nZWVJfX29Ch3bXTN3zAGFmpoaCQQCCfmBb34v4l21xdyuPSGOu0tL0/PNPArxTOU3t98VMtXW945nf+39/naG1v5/Z2Vlxb1ttHP+2GOPyaOPPhrnEe7UXKib+R2INXC3i9/vl4KCgqgzihLdf/r9fnn00Ufl1ltvlS+//FJEdg4grVy5Up599lkR2Rkedfzxx8u5554r3bt3b9f7m+I5H2Z/UF1dLZFIJGqukpY+d5s9YNfaz6o12yVKa4+R1bJa55FHHnEWPbj99tvbPZP1008/lbfeektEdubxMv94AcDbGNwBktSuvA27NPfX9V//+tfOwEr//v3l3HPPlQkTJsiAAQMkPz9fsrKynAfW3/zmNypPSSIk+v1PP/10OfbYY2X69Ony2WefycKFC52/CNfV1cmMGTNkxowZcthhh8mDDz6oHpDM/AT77LNPzKSuzYmVs2VPcNBBBzmrFJl5d3bNwMnOzm72r+0TJ06UF198URobG2XRokUyadIklW+nd+/eMnTo0N1yzGbo3a7ruaNCM9Dx2vP9TQVffPGFM7Dj8/nk+OOPl+OOO06GDx8uPXv2lKysLGfwc9OmTfKjH/2ow45td/SfPXv2lCeeeEIWLlwo77//vnz99ddODiiRnSsvPfbYY/Lvf/9b7r333mYT+CI1TJ8+XbZt25aw/R1//PF7zHLga9eudVYXO+mkk1oMwY3HriTegwcPjpl/DYD3MLgDJKnly5erPDv2MujfffedM5NjwIAB8sorr0hBQUHU/SUyFGt3vn9BQYGcffbZcvbZZ0skEpG1a9fKvHnz5MMPP5SvvvpKRETmzJkjd911l9x3333O68yZTT169Ei6+PPx48c7YRXFxcWyZs0aGTZsmDO4M378+GZnxRx44IFOee7cuTJp0qTdvgT6Lvvtt5+T2Fdk50pLiRjcMa+zeGccmGEjzc2Ci4f5l/1Yf+kX6fgksnuKtn5/U8F//vMfp3zzzTfLeeedF3XblnKsmaE98XwHwuGwmp1h25395/777+/kF6murpaFCxfKnDlz5H//+5+UlpZKTU2N3HjjjfLf//5Xhg8f3u73i+d8mP1Bfn7+bl1hqLWfVWu2S5TW9qmJDmN++eWXE7oU+ujRo/eYwZ3i4mJnQPPtt992EiC35LbbbpPbbrtNRHY+/z399NNO2/bt20VkZzid/WwYzbRp09Qf2BK98AOAxGApdCBJvfzyy045Pz+/yawMMx7/1FNPjTmwIiJOssdE6Yj39/l8MmzYMDnnnHPkySeflAceeMB5CJ8+fboKrzFniZgznpJFVlaWjB8/3qnPmzdPtm/f7uSPifaA16NHD+fc7BoIMh+id1e+HZGdoRlmctNXX321xRChePTv398ZyNq2bVtcP0bMpZnN5MCtYSatbSmH0NatW9v0HsmkNd/fVLCrz8zKypJzzjkn5rarVq2K2W5ewy1tK7LzR2CscNyO6j/z8/Pl8MMPl1tuuUXee+89GTdunIjsXIrbXA2uPeJZ2tz8f9zdKwwNGDDAyYeybdu2uP7QEc9nmkjm9RTP5x/POQYAtB4zd4AktHjxYvXXnR//+MdNZmW0lI/HtHz5ctm4cWOL72sm5Gtp+eTd8f4tmTp1qvz973+XtWvXSjgclvXr1zs/Dvr27StDhw6VtWvXSmlpqXz55ZdNlg9uLft8dLZJkyY5AzRz585VSTxj/fVu4sSJsmbNGlm0aJGUl5d3SL6dXS6++GJ5++23JRwOy6ZNm+Tpp5+WSy65pNX7qa2tdcJ4MjMzZdSoUc6KQR988IGTg6g54XBYZsyY4dTbukR1jx49nEHKdevWxZyFNGfOnDa9RzKL9f1NBbv6zNzc3BZzT+3KVRSNudLOl19+KXV1dTFXzJo5c2bM/e2O/rMlubm5cv755zvLkO/KSdJeH3/8sfzyl7+Muc1HH33klNu7alFLsrKyZOTIkbJ48WKJRCIya9YsOemkk6JuX1RUJEuXLt2tx2Qzz8HMmTPl5ptvjjmbyTx/iWDOSkk2PXr0iDvMcc6cOVJSUiIiO+9Tu1bgs0On493fihUrnIG4QYMGtfneB6DjMLgDJJnly5fL9ddf76wG1K1bN7nwwgubbGcmPTSXhbaFw2F54IEH4npvM29CRUVFzCSXu+P9W8tOdPmTn/xE7r33XhERue++++SFF16IO69Hc2E25nT6PWGWwUEHHeTk7Jg/f77zeWVnZ8f8kTxx4kR55ZVXJBAIyDPPPONcW/369VPLN+8Ou2ZuvPjiiyKyM7HkgAED4l76tqamRu666y6ZOnWqyslx8sknO4M7Tz75pJxwwglqsMv08ssvy5YtW0Rk5zLDLS1pHc2oUaOc0KKPPvoo6uDOli1bErpMcLJqbaJar+vatauUlJRIWVmZbN26NeoqTF999ZXMmjUr5r6GDRvmrEZVU1MjzzzzTNTcG1VVVc4SzLEkuv9srezs7Ha9fpd169bJ22+/HXUAZf369eqPJ63NL9QWJ5xwgjOo/sQTT8jUqVOjJvR+/PHHO/yPCZMnT5ZevXpJUVGRbN68WV577TU588wzm912zZo1cYcWYed3ddf3qiU/+9nPnMGd008/XU499dRmt4t3f48++qgzuHPAAQfE/ToAnYewLCBJbN26VR566CH56U9/Kjt27BCRnT9+Hn744WZnxkyYMMEpv/322/LJJ5802aayslJuvvlm+eqrr+J68Danp5t5WZqTyPffsmWLXHDBBTJ9+vSo4S6RSEReeOEF56+73bp1U6EEIiJnnHGGswzu6tWr5aKLLoo5xby+vl4+/PBDueiii5odoDLPx9dffx1XSNHmzZtl7Nixzn+tXUkslnHjxjk/gEpLS2X69OnOv8da+cec1bNrkEVk94ZkmW666SbnL4bBYFBuvvlmufvuu528Ac2prq6WZ599Vk444QR57733mrSffPLJzsDU1q1b5ZprrnEeik3vvfee/OlPf3Lql112WZtX7DIHl55//nlZuHBhk23WrVsnV1xxhdTU1LTpPbwoUd/fZGfmv7r99tubvUY+/fTTFmed7HLppZc65X/84x/NDiiWlpbKNddcI8XFxS3eAxLZf953333ywAMPxAzH3b59u5MkXkSfn13mzZun+tN4+Hw+ufvuu+XTTz9t0rZhwwa5+uqrnRC1KVOmdMiy3qeccor06tVLRHbOULrxxhub5FWKRCLy9NNPyyuvvBL3QJl5bnbN6myL9PR0NaPyj3/8Y7MDjOvWrZNrrrnGWdodAJBYzNwBPGL69OlqqnUgEJCqqiopKSmRJUuWyNq1a9USqv3795d77rkn6pTx4cOHy5QpU2TWrFkSCoXk6quvlsmTJ8uoUaMkLy9PNmzYILNmzZLKykoZPny4DB06tMWp/kcccYT873//ExGRO++8U+bPny977bWXE56Un5/v/JUzke8fiURkwYIFsmDBAmfVp3322Ue6d+8u4XBYiouLZc6cOWqg5Oqrr27yIz0jI0Mefvhhueiii2TLli2ybNkyOeOMM2TcuHEybtw46dGjhwQCASkvL5dVq1bJkiVLYi6BPnjwYBk8eLCsX79eVq9eLRdeeKEcfvjhakbPwQcf3GE/UjMyMmT//fd3lhbe9UO6pYSKvXr1cv4/zB/fHTW4k5GRIY899pjceuutMnPmTIlEIvLKK6/Ia6+9JqNGjZLRo0dL9+7dxefzSWlpqaxatUoWLlyofkCYIXIiO//K/8c//lEuvfRSqaurk3nz5smJJ54oRx11lAwZMkTq6upk7ty5KjfU0UcfLeeee26b/z/Gjx8vhx12mMyZM0fq6urkZz/7mRx11FEyYsQICQaDsmzZMvnss88kGAzKz3/+c/nnP//Z5vfykkR9f5Pdz372M/noo48kFArJl19+KT/60Y/k6KOPlv79+0t1dbV8/fXXzvV6xRVXyOOPPx5zf8cdd5z86Ec/kvfee09CoZDcfvvt8vLLL8vBBx8subm5smHDBvn444+lqqpKpk6dKosXL3ZmsDUnkf1nZWWlTJs2TZ599lkZNGiQjBkzRgYOHCi5ublSWVkpa9eudb4rIjtDRs4444w2nlntvPPOk+eee06uuuoqmTRpkhxwwAGSkZEhq1evllmzZjlLy/fs2VN++9vfJuQ9W5Kfny933nmnXHvttRIKhWTmzJlywgknOJ9/ZWWlfPbZZ7J69WopLCyUo48+Wl5//XURkd2a7Nn04x//WGbOnClfffWVNDQ0yDXXXCMHHnigHHjggZKRkSGrVq2SWbNmSWNjo1x44YXOkvbJavXq1c5M2V3s6/1Xv/pVk9ddddVVCUkMDiA1MbgDeMQrr7wS13a9evWSU089VS655JKoYSa73HPPPXL55Zc7g0ZfffWVEzayy8iRI+XBBx+Uxx57rMX3njp1qvz3v/+Vr7/+WmpqalRSZ5GdA07mFPZEvX9aWpr4/X4Jh8NSX18v8+bNi/pXyKysLLn22muj5ljp16+fvPzyy3LnnXc6eQEWLVqkfuTbevfuHTUh9M033yzXXXedBINBWbhwYZPZGnfffXeHzkA46KCDnMGdXeJZLWPixImyfv36JvvqKHl5efLXv/5V/vvf/8oTTzwh27Ztk1AoJIsXL465asfw4cPl6quvliOPPLJJ27hx4+Rf//qX3HjjjbJlyxaprq5uNlzA5/PJmWeeKb/+9a/b/UPpnnvukZ///OeyatUqCQaD8uGHH6pBy/T0dLnxxhvl2GOPTZnBnUR+f5PZmDFj5I477pDf/e53EgwGpaysrEkS4fT0dLnuuuvkhz/8YYuDOyJueMau2W1Lly5tkq/lsMMOkzvvvNMJ8YgV/pSo/tMcuNu4cWPMnGtjxoyRBx98MO4QsJYcddRR0r9/f/nzn/8c9VocOHCg/P3vf5c+ffok5D3jccQRR8gf//hHuf3226Wurk5KS0vl1VdfVdt0795d/vKXv6icXdHCF80/BonsTGDfHn6/Xx5++GH51a9+5bz/119/LV9//bXa7sQTT5Trrrsu6Qd3ysrKWvyDWHPtP/7xj3fXIQFIAQzuAB6Vk5Mj+fn50qVLFxk8eLCMHDlSxo8fL5MnT46ZyNjUtWtXee655+TVV1+V9957T1avXi319fVOyMPUqVPllFNOifsv5Onp6fLEE0/IK6+8Ih999JF8//33UllZGXUKdqLev2/fvvLxxx/LnDlz5JtvvpEVK1bIli1bpLKyUnw+n3Tp0kWGDh0qkydPltNOO63FJU4LCwvloYcekhUrVsg777wjX3/9tWzevFkqKyslPT1dunbtKoMHD5YxY8bIYYcdJhMnToz6YHzEEUfIiy++KP/5z39k4cKFsm3bNqmvr2/yYN1R7ATI9ipa0Rx44IHqh+SgQYM6fKlYn88nZ599tpx22mkye/Zs+eKLL2TRokVSUlIi5eXl4vf7paCgQIYMGSJjx46VY445psVQjLFjx8rbb78tb775psycOVNWrlwpZWVlkp2dLb1795ZJkybJ6aefLiNHjkzI/0PPnj3lxRdflJdeekk++OADWbt2rTQ2NkqvXr3koIMOknPPPVdGjhyZ0HC8PV2iv7/J7LTTTpPRo0fLc889J/PmzZMdO3ZIdna29OrVSw4++GA5/fTTZb/99ov7+snIyJD7779fTjrpJHnttdecpOmFhYUyfPhwOemkk+SEE04Qv9/vhAGZudWak4j+8/bbb5dTTjlFvvrqK1m0aJGsW7dOSkpKpL6+XrKzs6VPnz4yatQoOe644+Soo45K+OyU8847TyZMmCAvv/yyzJs3T4qKiiQjI0OGDBkixx13nJx77rkJy/HTGscff7yMHz9e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the above plot, the columns of $W$, extracted by the NMF, are plotted separately in grid images. This is done for $d=\\{4, 16, 64, 144\\}$, respectively. The columns of $W$ are the basis vectors of the new subspace that the images are projected onto. Each vector contains some feature of the original images, so that specific linear combinations of these basis vectors should yield a representative reconstruction of the original images. The specific linear combinations are given by the weights that make up the elements of $H$. \n\nThe contents of the different columns in $W$ differ, however each of them capture some underlying feature, e.g. hair, glasses, hats, cigarettes etc. Some of the grid images show clear resemblance of specific features, however others show weaker distinction between distinct physical features, that, from a human standpoint, are harder to interpret as single features. One explanation for this is that, since the pictures are represented as numbers in numerical matrices, and not by actual physical objects, the computer does not distinguish between real life objects and features that produce a precise matrix reconstruction. \n\nThe consequence of altering the rank of the factorized matrices is that it changes the precision of the reconstructions, so that a higher rank reconstruction is more true to the original matrix, than a lower ranked one. In a higher ranked NMF, the number of basis vectors, meaning the number of storage units that hold information about characteristics of the original matrix, is greater than in a lower ranked one. In a sense, this means that the \"information density\", meaning the distinctiveness of the characteristic that the basis vector represents, of each basis vector is decreased, hence allowing each basis vector to store smaller, less distinct features, with higher precision. For the reconstruction of the Cryptopunk dataset, increasing the rank of the NMF, hence, means also increasing the number of basis vectors that are able to represent such special features. This is exactly what is evident in the above plots for varying rank ($d=\\{4, 16, 64, 144\\}$). The lower ranked NMF ($d = \\{4,16\\}$) predominantly shows grid images with whole faces that consist of more than one feature, however, the higher ranked NMF ($d = \\{64, 144\\}$) shows grid images with single features. The reconstructions will be further examined in the following sections.","metadata":{"tags":[],"cell_id":"791dd0da101145fdbd51dd12730bae8e","deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":169},"deepnote_cell_type":"markdown"}},{"cell_type":"code","source":"def ex2d():\n    for W, H, d in zip(WList, HList, dList):\n        \n        \"\"\" Reconstructing RGB channels \"\"\"\n        reconstruction = W @ H\n        facesWithOpacity = np.zeros(faces.shape)\n        facesWithOpacity[:,:,:3,:] = reconstruction.reshape(faces[:,:,:3,:].shape)\n        \n        \"\"\" Adding opacity channel \"\"\"\n        facesWithOpacity[:,:,3,:] = opacityMatrix\n\n        plotimgs(facesWithOpacity, d, 8, filename=f\"Reconstruction_images{d}.png\")\n\n        \"\"\" Saving the d=64 reconstruction for later tasks \"\"\"\n        if d == 64:\n            saveFaces = facesWithOpacity\n\n    return saveFaces\n\nfacesWithOpacity = ex2d()","metadata":{"tags":[],"cell_id":"8c0d99d993c941d0a9422b151d63fd49","source_hash":"26f7cbeb","execution_start":1649447486465,"execution_millis":13589,"deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":175},"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"code"},"outputs":[{"data":{"text/plain":"<Figure size 1152x1152 with 64 Axes>","image/png":"iVBORw0KGgoAAAANSUhEUgAABHYAAAS9CAYAAAAiHt73AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAAEAAElEQVR4nOzdd5jU5fX//9f2XliW3gQRRaWDgNixxt419pbExMSGJRpb1Fg+auwmsSs27B1FEUGadFZEKdJByrK9zszO7w9+zBc8Z2BXFtjB5+O6vC45HGbeO3PP/b7f977nnLiCgoKwAAAAAAAAEHPid/YBAAAAAAAA4NdhYwcAAAAAACBGsbEDAAAAAAAQo9jYAQAAAAAAiFFs7AAAAAAAAMQoNnYAAAAAAABiFBs7AACgyVmxYoV69OihHj166KKLLtrZh7NTvPfee5HX4Mknn9zZhwOgnpi/AOxoiTv7AIBd2VFHHaWVK1eaeFxcnNLS0pSZmanMzEzttttu2muvvdSzZ08NHDhQiYk756P58ssvq6ysTJL05z//eaccQ1Pyww8/aPTo0ZKkAQMGaMCAATvlOKKNI0lKSEhQRkaGWrZsqe7du2vo0KE6+OCDd9oYQnQrVqzQ+++/L0nac889NXTo0J18RDvWl19+qR9//FGSdOKJJ6pdu3Y7+YiApuXHH3/UWWedpWAwGImNHDmSzwpizkMPPaTnn38+8uf+/ftv9mcAjY+VP7AThMNhVVZWqrKyUmvWrNFPP/0U2UDIz8/XSSedpEsuuUSZmZk79LiGDx8e2UBgY2fDxs5TTz0V+fPO2tjZklAopNLSUpWWlmrBggX68MMP1a1bN913333q2rXrzj48bGLlypWR8XTCCSf85jZ2Ro8erQ8++EDShs8SF6vA/xMMBnXLLbdstqkDxKKCggK99NJLO/swgN8cNnaAHeSMM85Qhw4dIn+ura1VWVmZ1q1bpzlz5mjx4sUKh8Nat26dnnnmGX388ce66667tN9+++3Eo0ZT88txFAwGVVhYqClTpkTuhpg3b54uvfRSvf7662rduvXOOlQAQD0988wzmjt3rpKSkhQIBHb24QC/Sm1trW655RaFQiHGMrCDsbED7CBHH330Fu/4WLVqlV5//XUNHz5ctbW1WrVqlf785z/r6aefVp8+fXbgkaIp29I4+vjjj/WPf/wjstnz+OOP66677trBRwg0jnbt2qmgoGBnH8ZOddJJJ+mkk07a2YeB7WzevHn63//+J0m67LLLqKeEmPXkk09q4cKFSklJ0XnnnadnnnlmZx8S8JtB8WSgiWjTpo2uvvpqDR8+XC1btpQk1dTU6G9/+5uKi4t37sEhJhx77LE655xzIn/+4osv+G0ZADRhG7+CFQgE1LVrV1166aU7+5CAX2XOnDl64YUXJEl/+tOf1KlTp517QMBvDHfsAE1M9+7d9fDDD+uCCy5QIBBQcXGxXnjhBV111VVufmVlpcaOHavJkydr7ty5Wr58uSoqKpSamqr8/Hz17NlTxx57rPbff/+oz9mjR496xdq2bavPPvus0Z9/U0uWLNHbb7+tqVOnasmSJaqsrFRCQoKys7PVvn179enTR4MHD1a/fv2UlJS0xceaMGGCPv/8c02fPl3r1q1TTU2NcnNztffee2vo0KE67rjj3CLDTz755Ga1dSTpqaeeMjFJuvPOO5vUb9SHDh2qF198UZJUUVGhZcuWqUuXLlv8N7/2dfIEg0GNHDlSY8eO1Xfffaf169erpqZG2dnZ2m233dS3b18dfvjh2meffbb4OGPHjtWnn36qWbNmad26dZKkvLw89erVS0cffbQOPfTQLf779957T7fccosk6fLLL9ef//xnlZeX6+2339bIkSO1bNkyVVVVqUWLFho0aJAuuOACde7ceas/39y5c/XOO+9o5syZWrFihSorK5WUlKScnBx17NhRAwYM0ODBg9WjRw8lJCSYY9nogw8+iNSb2dTGY91o08LZG+9emTBhgj744APNnj1b69atU1VV1Wbj8KKLLtLUqVMl1a/w6sbPuvf5/qVwOKwxY8Zo9OjRmjlzpgoLC1VVVaWMjAx17NhRvXr10mGHHbbZXWWbHs9GF198sfv4mx7vihUrdPTRR0uqX+HNwsJCvfnmmxo/fryWLl2q0tLSyLwxZMgQnXHGGcrPz9/iY3iv9/Tp0zVixAjNnDlTa9euVVpamrp27arf/e53OuWUU7ZroXJvHP/SzTffHBlLzz33nAYMGKCFCxfq9ddf16RJk7R69WqlpaWpc+fOOuuss3TkkUcqPv7//V6vurpaH3/8sT744IPI69ayZUsdfPDBuvTSS7f6mtXW1mrChAmaNGmS5syZE3mMpKQk5eXlad9999URRxyhI444YrPn3ZKqqiq98cYbGjVqlBYvXqxAIKCWLVtq4MCBOvPMM9WtWzdNmTIlMo5OOOEE3X333Vt8zMrKSr333nsaN26cFixYoKKiIiUlJalFixbq37+/Tj311K3OS5K0Zs0avf3225o0aZIWLVqksrIyxcfHKzMzU23btlWvXr20//77q3///kpPT9/q4z333HP6/vvvFR8fr3/+859bPa/9Wt68MG3aNI0YMSIyz6anp0fG9sknnxyZwzybnic3zj/r1q3Tm2++qS+//FIrV65UMBhUq1atdMABB+iiiy6K/NJqaxYuXKhXX31VEydO1Jo1a5Senq727dvrqKOO0mmnnaaMjAx33O8ooVBI77//vj766CMtWLBAlZWVys/PV+/evXXGGWeob9++O+xYmopAIKB//OMfCoVC2muvvXThhRfqo48+2tmHBfymsLEDNEE9evTQ8ccfr3feeUeS9Nprr+nPf/6zkpOTN8ubP3++fv/736u6uto8Rnl5ucrLy7V48WJ98MEHGjJkiO6//35lZ2c32nE29vO//PLLeuihh0zxyGAwqLVr12rt2rWaMWOGnnvuOT3++OM6+OCD3cdZvXq1brzxRnMxKW1YlK9Zs0ZjxozR888/r0ceeUS77bZbw37wLdj0YlTa8R1N8vLyNvtzaWlp1NzGfp2mTZumf/zjH1q+fLn5u/Xr12v9+vWaPn26nnnmGb3wwgvq16+fySssLNR1112nKVOmmL9bsWKFVqxYoU8++UR9+/bVgw8+uNWLzo1+/PFHXX311Vq2bJl5zLffflsffPCB7rvvPh1xxBHuvw+Hw3rooYf04osvKhwOb/Z3oVBI1dXVWr16taZMmaInn3xS77zzjvbYY496HVt9BQIB3Xbbbfrwww8b9XHra8GCBbrxxhsjtZw2VVJSooKCAhUUFGj48OH617/+peOPP36HHdu7776r++67TxUVFZvFN4672bNn64UXXtB1112n008/vV6PGe09r62t1bRp0zRt2jR9+umneuKJJ+p1Ab+jvP322/rXv/6l2traSKyqqkrr16/XtGnT9NVXX+mee+5RfHy8Fi1apL/+9a9asmTJZo+xfPlyvfLKK/r000/17LPPRi3EXlJSomOOOSbSTXFTwWAw8pn97LPPtM8+++jhhx/eat2vn376SX/+85+1YsWKzeJLlizRkiVL9O677+qGG27Y6ob1pr744gvdeeedWr9+/WbxmpoalZeXa9GiRXrrrbd02mmn6e9//3vUzZWRI0fqtttuU2Vlpfm7jWPtu+++0yuvvKK///3v+v3vf7/F41qwYIH+85//SJLOOecc9xcq28u///1vPffcc5vFampqNGXKFE2ZMkVvvfWWHn/88XrPsZMnT9b1119vXuPFixdr8eLFeu+99/TEE09sddPjlVde0QMPPLDZOqCmpkZFRUUqKCjQm2++qUcffbSeP2XjKyws1F//+lfzNdFNz08XX3xxveeZXcVTTz2lBQsWKDExUXfccQedOYGdgE8d0ESdddZZkY2dyspKzZ49W/37998sp7KyUtXV1YqLi1P37t211157qWXLlkpNTVVZWZl++OEHTZ48WcFgUOPHj9c111yj//3vf+a3ptdee60k6emnn45sBGyMbeqXXboa6/kl6auvvtL9998f+fNee+2lvn37RhaVRUVFWrhwoWbOnOkuqjdatmyZLrzwQq1Zs0aSlJ2drSFDhmi33XZTUlKSVq5cqbFjx0a6kZ1//vl644031KZNm8hj7L///kpPT9ecOXM0cuRISdLgwYPdu4723XffqMeyMxQWFm7257S0NDevMV6nTY0aNUrXX399ZDGempqqQYMGaY899lB6erpKSko0b948TZ8+XdXV1aqrqzOPUVJSovPPP19Lly6VtKGV+/7776+9995b8fHx+v777zV+/HgFg0FNnz5d5513nl5//XXl5ORs8TVZvXq1/vSnP2ndunXq2rWrBg8erLy8PK1evVpffvml1q5dq0AgoJtuukl77bXXZsWpN3r11Vcjt5hLUp8+fdSjRw81a9ZMwWBQRUVFmj9/vmbNmrXZBbW0YYxce+21WrZsmUaMGCFJ2meffTbbANyod+/eUX+Oe++9Vx9++KFSUlJ04IEHqmvXroqLi9P8+fPNpm9jmzFjhi6//PLIxkliYqL69++vvffeW1lZWSovL9eCBQs0bdo0lZeXKxQKRf7tmWeeqYMPPlgjR47UnDlzJNki4Btt7b30vPrqq7rnnnsif27durUOOeQQtWzZUuvWrdPXX3+tFStWqKqqSv/85z9VXV2t8847b6uP+/jjj+uFF15QWlpa5PWWpFmzZmn8+PGSpKlTp+r+++/X7bff3uDj3h7Gjh2rF198UfHx8TrwwAO1zz77KCEhQbNnz9a4ceMkSZ988ol23313nXLKKbrsssu0evVqde7cWQcccIDy8vK0atUqjRw5UqWlpVq/fr2GDRumN998093sCAQCkU2drl27qnv37mrTpo3S09NVWVmp+fPna+LEiaqurtacOXP0pz/9Sa+99lrUeennn3/WJZdcErlLLyUlRQcddJD22GMPBYNBzZo1S99++63uvvtuXXjhhfV6TUaMGKG77rorsjnXtWtX9e/fXy1btlQgENDcuXP1zTffKBgM6s0331RJSYkefPBB8zjff/+9brzxxsjY3m233bTffvupVatWio+PV2lpqRYtWqTp06dvcUN9o1AoFPkKVrt27fTXv/61Xj9PY3j11Vf10ksvRebYjXcqzZkzRxMmTFAoFNKcOXN02WWX6ZVXXtnqxuWPP/6of/3rX6qqqlLPnj3Vr18/ZWVlacWKFfr8889VVlam8vJyXXPNNXr//fejfs7ffvtt3XvvvZE/t2nTRocccohatGgR+SwvWbJEf/3rX9WtW7fGe0HqqaqqSpdddpnmz58vSYqPj9fgwYO17777Kj4+Xt99950mTJigZ5999jfV3ez777+P3FF5/vnna++9997JRwT8NrGxAzRRe+21l7KysiKL5mnTppmNnaysLF155ZU6+eST1bx5c/dxli1bpmuvvVZz587V5MmT9fHHH5vfpG9cIL/22muRBWl9Fs2N9fySNrtovvvuu3XCCSe4jxcIBDRmzBh3gyEQCOjaa6+NbFZccMEFuuKKK5SammryHnroIQ0fPlxFRUW66aabNvuaR+/evdW7d2+99957kY2d3r171/tCYmcaNWpU5P9TUlLcu2wa63Xa6KefftLNN98cWcgeeuihuvXWW93f9FZWVurjjz9Wbm6u+bu77747sqmTn5+vxx9/3Hw14ocfftBf/vIXrVmzRsuXL9cdd9yhhx56aIuvyTvvvKPExETddtttOu200zb7u6uuukp/+tOfNHPmTFVXV+u5557TbbfdZh5j4/hMTEzUk08+qcGDB7vPVVlZqc8//3yzO9O6du2qrl27asqUKZGNnd13373B42nEiBHq3r27HnnkkagbbNtDYWGhrrnmmsimTu/evfWvf/3L3ZgJBAL64osvNnvvN25gzZ8/P7Kxs7Vi8vU1b948PfDAA5E/n3322bruuus224QYNmxYZBxL0kMPPaT+/fure/fuW3zs//3vf+rVq5ceeugh8xWSzz//XMOGDVM4HNa7776ryy+/XK1atdrmn2dbvfDCC2rZsqUef/xx8/N98sknuuGGGyRJL774ombOnKk1a9Zo2LBhOv/88xUXFxfJ/cMf/qDzzjtPq1at0sKFC/XFF1/omGOOMc+XlJSkSy+9VKeffrratm3rHlNhYaFuuukmTZgwQQsXLtSLL76oP/3pT27u3XffHdnU6dSpk5588kl17Nhxs5yJEyfqqquu2uycEc2sWbN0zz33KBwOKy8vT3feeacOOuggk7ds2TJdeeWVmj9/vj7//HO9++67OvnkkzfLGT58eGRT5y9/+Yv++Mc/bvaabRQKhTR58mSlpKRs8dief/55fffdd5Kk22+/Pepm1/bw8ssvq1mzZnr88cfVs2fPzf6uoKBAf/nLX1RUVKQFCxbo0Ucf1Y033rjFxxs+fLjS09P12GOP6ZBDDtns76644gpddNFFWrx4ceTrkl4doVWrVm32y53TTz9dN95442ab1sOGDdMDDzygV1991dx9uSM88cQTkU2d7OxsPfHEE2YzftasWfrLX/7S6O2+N/2aaGNorLuJA4GAbrnlFgWDQXXq1Mn9uiiAHYPiyUATFRcXt9lXOVatWmVyunTpoksvvTTqpookdejQQY8//njkov2tt95qtGNszOf/4YcfJG24CI62qSNtuJA44ogj3N/Wffjhh5o7d64k6dxzz9WwYcPMZsXGx7jhhht02GGHSdrwW/fp06dHfc5Y8eGHH+q1116L/Pmoo45yLy4a+3V67LHHVFVVJUk64IAD9PDDD0e9fT89PV2nn366+ZrSTz/9FNlEi4+P12OPPebWu9hrr7302GOPRWo/jBo1SvPmzXOfa1NXXnml2dSRpIyMDN1xxx2RP3/55Zcmp7i4WD///LMkaciQIVE3dTb+fCeddNJ2ucjPycnRU089tUM3daQN9Ss2XmzvueeeeuaZZ9xNHWnDmDnmmGN2WL2LZ555JlIg/JBDDtFNN91k7izZOI6HDh0qacNXhDZ2INqSVq1a6cknn3Trghx55JE66qijJEl1dXUaPXr0tv4ojSIhIUGPPfaYu2n1u9/9ToMGDZK04Sua48aN0wUXXKALLrjAbFC0atVqsztIvvjiC/f5cnJydOWVV0bd1JGk5s2b69///nfkdYx2Dpg3b57GjBkjacN79vjjj5tNHWnD3ZO33367+UqkZ+NXezduyHqbOtKG89RTTz0VuTPF6+Szcc7MysrSZZdd5m7qSP/vTkPvq6Yb/fTTT5H6NCeffHLkfdlRwuGwHnzwQbOpI234Kvimm6UjRowwX6/y3HnnnWZTR9qwSb9xQ1GKPpaGDx8euRt3v/320y233GLuRExKStLf//53DRkypF7vf2MqKSnR66+/Hvnzfffd595h2atXL/3f//3fDj++neW///2v5s2bp7i4ON12221b3dAEsP1wxw7QhG16u3JJScmvfpyWLVuqX79+Gj9+vAoKClRbW7vdv7rR0Off+NWcmpqaX/08Gzc1UlNT6/Vbo4suuihyQTZmzJhGKXi4vVs0b/p1FkmR1ubffvvtZhscnTt31tVXX+0+RmO+TmvXro1shiQkJOgf//hHvQukburDDz+MLISPPPLILX7Fbe+999bRRx+tjz/+WNKGQsTDhg2Lmp+Xl7dZt7Bf6tKli7p27RopqPrzzz9vVgdk068VefWkdpQzzjhji5uo20MgENDbb78d+fNNN93UZBbulZWVm92hFm28b/r3G8fqV199FSmuHM0FF1ywxb8/4ogjIpuRGzemd7ZDDz10i1+DOPjggzVp0iRJGy6SL7nkki3mbrStP196eroOPvhgvfnmm1q9erWWL1+u9u3bb5azaaHV4447bos1vY455hj95z//0U8//RQ158cff4xsRB955JFbLYzcqlUrHXPMMXr77be1dOlSLVy4ULvvvnvk7zeeowKBgOrq6rZYWHhLNn4Fq7a2Vvn5+Vucu7aXwYMHb3Hzdb/99tOgQYM0adIkBQIBffrpp1ucQ/fcc08deeSRUf9+//33V0ZGhioqKjR//nyFQiHz+m2czyXpz3/+c9SNM2nDHVMbvw65o3z++eeR9Unfvn11wAEHRM0dPHiwBg4cqMmTJzfa81922WUqLy9vtMf7NV97/aUffvhBzz77rCTptNNO26EFrAFYbOwATdim32vf2gk9FApp4cKF+umnn1RaWqqqqqrNfmNUVFQkacOidPny5Q0qPFkf2/r83bp10+zZs7Vs2TI99NBDuvzyyxt0a3pxcXGkqGvPnj2VlZW11X+z5557Rv5/4y3xTd3Gr/JEk5CQoMMPP1w33nije9dMY79O3377beR97t+//6++tXvGjBmR/49WwHhTRx11VORCYNN/6xk4cOBWO8106tRJCxYskLShCOqmGzt5eXnKz8/XunXr9O2332r48OE688wzt1v3mmii3W2wPc2ZMyfyFawOHTo0qW4v3333XeTrf127dt3qnNapUyd1795dc+fOVSgU0uzZs7d4cbalv9v4eBvV546GHWFr3Qc33UzZe++93a9EbpSdna2cnByVlJRE7tjaknA4rMWLF2vBggUqLi5WZWXlZueATYuqL1682GzszJo1K/L/W+t6tzFnSxs7GzewpA132tXHXnvtFfn/7777brONnT333FM//fSTqqurdeutt+rGG2/8VRfHL774ombPni1pQ0ezxmxoUF8b717bksMPPzzyGs6aNWuLGztb+6zEx8erY8eOmjt3rmpra1VeXr7Za7ds2bJIfbicnJytzjM9evRQixYttHbt2q3+HI1l5syZkf+v7+vXmBs73h2nO9PGLljBYFAtW7bUNddcs7MPCfjNY2MHaMI27fDyy8LFG5WVlenpp5/W+++/X++LC6+Dya/VWM9/8cUXR1q6P//88xoxYkTkdvYePXqoe/fuW7yQnjdvXuQi4ttvv21wd5GNG0+xrn///ho2bFjUr0I19uu0cOHCyP9vS0eXjbV1JG219skvc37Z0eeX6vPVpYyMjMj//7I4d1xcnC6++GLdf//9CofDuu+++/Tf//5XQ4YMUd++fdWzZ09169btV92p1BD1acfe2DZ9f5taofBN3/dNL8i3ZOPGzsZ/v6UL0i19vUja8pjZWbY21jf9ZUF9PhcbC59v/Kqlp6amRi+99JLefPNN9yvDHu8csOkcUJ+OclvL2fQOxptvvlk333xzvY5to1/Odeeff75GjRqlYDCojz76SKNGjdJ+++2n/v37q2fPntp3333dr7RuatGiRXryySclbbjwP/zwwxt0TI1l0836aDb9uvPixYu3mLu1z4q0+dirrKzcbGNn0/d+Y1H4renatesO3djZ9DWoz3xTn9c4lj3zzDORXxLdcsstUdeoAHYcNnaAJmzTzhrebwZXrFihSy65xLSF3Zpfdu35tRrz+YcOHao77rhDDzzwgMrKylRRUaFRo0ZFvmqRlpamIUOG6JRTTtGBBx5o/n1xcfGv+hk22tKFS1Py3HPPRW53DofDKiws1IIFC/TSSy9p3Lhxmjx5ss477zw999xzbh2Uxn6dNv2K4C9brTfEpmN9S3cRbNSsWbPI/5eVlSkcDke9GGjoV4e82gjnnXeeKisr9fTTT6umpkbFxcX6+OOPI3cNZWVl6ZBDDtEZZ5yxxc5W26I+d1c1tk3Hy47+GtjWNHTM/DJva52LtjZuNh1vXpe3naEhx1yfr+NuzI9WL6SkpER/+MMf9P333zfgKP2v3Db0/dxaTmPPdfvuu68efvhh3X777Vq3bp1qamo0bty4SLex5ORkDRgwQCeddJKOPPJIs9FbV1enW265RTU1NcrKymrwRlNjaujru7XPSkPGkmQ/L9v6Wd4RtrYe+6UdfXw70o8//hipU3bMMce4tZUA7Hhs7ABNVF1d3Wa/cfR+I3bTTTdFNlXatm2rs846S3379lW7du2UmZmplJSUyGLq5ptv1gcffNCox9jYz3/KKafo8MMP18iRI/XNN99o5syZkd+aVlVV6YsvvtAXX3yhIUOG6KGHHtrsN4Cb1kHZY489tliA2ROLv22Ki4tTfn6+8vPzNWjQIN1zzz169dVX9fPPP2vYsGEaPny4ucvpt/g6NZY//vGPOvXUU/Xxxx9r0qRJmjlzZuQrkmVlZfrwww/14Ycf6sQTT9Ttt9+uxMTGPcVu7zuCgIa65557Ips6eXl5OvPMM7Xffvupffv2ys3N3ewc8MQTT+g///nPDju2Tee6k046abOvVdWHt0F78MEH69NPP9WoUaM0duxYTZ8+PdJdsLa2VuPHj9f48eP14osv6tFHH1WLFi0i//a9996LfN3suuuui3pXJeB56623GrXGzmmnnfarz+f/+te/FAwGlZubu9WOaQB2HDZ2gCbqhx9+2Owk/stW599//32kMGS7du00YsSILX5XvzG/frU9nz87O1tnnHGGzjjjDIXDYS1atEhTpkzRqFGjIt9XHz9+vO644w7dd999kX+36W/QmjdvHhOtyRvbsGHDNGXKFM2fP1/ff/+9XnzxRdNWtrFfp00fb1vqjGRnZ0duqy8uLt7q3Smbfk0iKyurXrfuN4b8/PxIJ6G6ujr9+OOP+vbbb/XZZ59Fima///77atmypf72t7/tkGP6pU1fi611ZtnanWqb/tZ5Yw2MpmLT+aa+xeU3vYtjZ9Q22ZUUFRXp008/lbThM/jaa69t8Ss5W7sozcrKioyx4uLirV50bu2OnE3npoEDB+q4447bYn59paam6vjjj9fxxx8vaUPtoClTpmj06NEaN26cQqGQvvvuO1177bWbtbze2FlPkm699Vbdeuut9Xq+o48+OvL/l19+eaO0k67P3Uw78rOy6Xxf3zuttvWOrIZq6HzT2Mf39NNPN2q78yOOOOJXb+xsHMvFxcWbFVnfkqlTp272de3GarcO4P/h139AE/XGG29E/j8zM9PUL9lYfFHa8NvIrS28NhaGbSw74vnj4uLUpUsXnXnmmXrmmWf0wAMPRC5aR44cudniatPCqfVpf70rSkpK2qzDyrPPPms2Wxr7deratWvk/7elG9imbY3r04Fn05xNi9juSPHx8erevbsuuOACvfrqq7r22msjfzdixIid9vWcX9ay2JKt1UTZ9C6HplZgfNP3fWPdnK3ZNG9LXZewdQUFBZExfvjhh2+1zsr8+fO3+Pebvp9by61Pzo46J7Rv314nn3yyHnvsMT3//PORryXNmDGjyXRL+6X6vB6b5mzvz8qm7/2CBQvq1Sq8sdc0W7Ppa7CxtsyW1CcHABoTd+wATVBBQYE+/PDDyJ/PPvts85Wahnzf+4cfftCyZcu2+rybfnXEa0e6vZ9/a4466ig98cQTWrRokerq6rRkyRL17NlTktS6dWt17txZixYt0vr16zVp0iQNGjRom57vl69HLNh///3Vt29fTZ8+XeXl5Xr22Wd13XXXRf6+sV+n/fbbT/Hx8aqrq9PUqVO1cuXKehXS/KU+ffpo2rRpkqRRo0ZttTPW559/vtm/bQrOP/98Pfnkk6qqqlJJSYnWr1+/2dctNh1P23PTZ9NaOEuWLNmsCOovTZgwYYuPte+++yozM1Pl5eVatmyZpk+f/qs7Y206hzXG52nfffdVYmKigsGgFixYoEWLFm2xwPSyZcsiF9oJCQnbVOwbDTsHrFu3bqvd63r16hW5C/Srr77aamesMWPGbPHvBw8erMcff1zShvnib3/7W6N/PfKX+vTpowEDBkRacS9evDhSaHfPPfes91dfN/3a8hFHHBHpENlYBXm//PJLnXHGGVvN2ahXr16N8rzRdOjQQc2bN1dhYaFKSko0ffp09evXL2p+QUHBDi2cLG14DTa+L19++aXOO++8LeZ/8cUXjfr8n332WaM+3rY44ogj6tVwYtmyZZHPffPmzTfrTrfpLyAANA42doAm5ocfftBVV12lQCAgaUOR2AsuuMDkbfoViS0Vrqyrq9MDDzxQr+fe9LbckpKSLRbD3R7P31C/LBT6+9//Xnfffbck6b777tMrr7xS78WDV3x309vD6/tVj6bgT3/6k/7whz9I2nDnyIUXXrhZrYfGfJ3y8/M1dOhQjRo1SqFQSHfeeaeeeOKJBteDOf744/Xss88qHA7r888/14UXXqi9997bzf3xxx8jXwGRpBNPPLFBz7W9hEKhzX7uX3bI+eXna3vZtGPYF198EXWTrKysTC+++OIWHysxMVGnnnpqJO+ee+7R8OHDG1yQWmr8nz89PV1HHHFEZCw88sgjevjhh6Pm//vf/47cCXDYYYfxVaxtVN9zgLThtd9a0f5jjz1Wzz//vCTp448/1sUXXxz1TpGRI0du1rHNs7FT1XfffacVK1bo6aef1uWXX77Ff7PRloqxN8Smn5OhQ4fWq022tPnGzrXXXtvoX1mZMGGCpk6dar7ivdHUqVM1ceJESRs2ZDf9Otj28rvf/U4vv/yyJOmpp57S008/HfU9eOKJJ7b78fzSUUcdpfvvv181NTWaNm2aJkyYoP3339/NnTx5cqO2Om9qNr0zeEvee++9yMZO586dI+sOANsHX8UCmohVq1bp4Ycf1jnnnBMpxpiSkqJHH33U/W3opr81//DDD/X111+bnNLSUl1//fWaPHlyvRapmy6iv/322y3mNubzr1y5Uueff75GjhwZ9asj4XBYr7zyihYtWiRpw4bXprfaS9Kpp54a+e3oggULdOGFF27xlvPq6mqNGjVKF154oXthsunrMW3atHrdZbFixQr16NEj8l9DO4Y1hsGDB0cKf1ZXV+uZZ57Z7O8b+3W64oorIr9R/uabb3T11Vdr3bp17mNVVlZqxIgR5msUXbp0iVw8hEIh/fWvf3W/XvPjjz/qL3/5i4LBoKQNvzmsT2vkbTF16lRdfvnlGjt2bGTD9ZeCwaAeffRRVVRUSNrwm/Vf1i/o2LFj5C64goKC7daJ7dBDD408z8iRIzf7zftGa9eu1RVXXLFZ3Y9oLrroosidRz/88IMuu+yyqHfg1dbW6tNPP9WUKVPM3236efL+/te49NJLI3cCffnll7rvvvvMexQIBPR///d/kQ57iYmJkY1P/Ho9e/aM3AHz7bffbvb14Y1qamp077336oMPPtjqOWjPPffUQQcdJGnDOPrrX/+6WRvsjSZNmqTbbrutXue066+/PnKMTz75pP7v//5vi7V+Vq1apWeeeUZ//OMfzd+dcsopevvtt7e4KTlq1ChNmjRJ0oZxtr3vdJE2XDxvPN8cddRR9fo3cXFxuvbaa92vV86ZM2ezr5WefvrpO6Qj3rnnnhs5j0yePFl33XWX+1m+9957NX78+Hq9/415Ps7JydnsLqcbbrghUgx7UwUFBbruuut2WN03ANiIO3aAHWTkyJGaM2dO5M+BQEBlZWUqLCzUd999p0WLFm32vfK2bdvqrrvuito6uWvXrjrkkEM0ZswYhUIhXXHFFRo4cKD23ntvZWRkaOnSpRozZoxKS0vVtWtXde7cOXJhE81BBx2kTz75RJJ0++23a+rUqerYsWNkYZyZmRm5lbwxnz8cDmvGjBmaMWOGUlNT1aNHD+2xxx7Ky8tTXV2d1q1bp/Hjx2+2KLviiivM19OSkpL06KOP6sILL9TKlSs1d+5cnXrqqerZs6d69uyp5s2bKxAIqLi4WPPnz9d33323xYvrTp06qVOnTlqyZIkWLFigCy64QAcccMBmd/IMGjTIbDA1BZdffnnk4uStt97SRRddpNatW0tq/NepS5cu+uc//6m///3vCgaDGj16tCZMmKBBgwZpjz32UHp6ukpKSjRv3jxNmzZNNTU1eu6558zj3HzzzZozZ46WLl2qNWvW6Oyzz9aQIUO09957Ky4uTnPnztU333wT2dRp3769brvttu3w6m0uHA7rm2++0TfffKOsrCz16NFDu+++u5o1a6ba2lqtWbNGY8eOjWxmxcXFuYWTU1JStN9++2nixIkqLi7WOeeco6FDhyo3NzdyEbDxAmRbtGrVSqeccorefPNN1dXV6aqrrtIBBxwQ+driwoULNXbsWFVVVekPf/hDpG1tNM2bN9cDDzygyy+/XFVVVZoxY4ZOOOEEDRgwQHvvvXfkq1oLFy7U1KlTVV5erjvvvFMDBgzY7HEOOOCAyNf2RowYoaKiIu2zzz6b3dl04oknKiMjo94/a7du3TRs2DDdc889kqThw4dr9OjROvjgg9WiRQsVFhZqzJgxm80d11xzTWRjE7/exkL3r776qiTprrvu0vvvv6/evXsrNzdXK1eu1Ndff61169YpPz9fhxxyiN56660tPuYtt9yiM888U+vXr9fixYt1yimn6OCDD9Yee+yhYDComTNnRn7pcOGFF0bu8Il2Ed2nTx/deuutuuOOOxQKhfTSSy/pnXfe0cCBA9WlSxdlZGSooqJCq1ev1vfffx+p27Jp7bCN5s+fr9tvv1133XWX9t13X+25555q3ry54uPjVVhYqClTpmxW9+X888/f4l2vO9N5552nl156Seeee66GDBmiffbZR9KGO6+++eabyFclO3furCuvvHKHHFPbtm01bNgw3XnnnZI23G06btw4HXroocrPz9/ss9yxY0d169at0b/utDVXXHGFJk6cqAULFqi4uFjnn3++9t9//8icPWfOHI0fP16hUEgXXHDBVu+IBIDGxMYOsIOMGDGiXnktWrTQSSedpEsuuWSrFzh33XWX/vjHP0Y2jLzbf7t3766HHnpITz311Faf+6ijjtKbb76padOmqaKiwvwGtm3btpvVCGis509ISIhc8FVXV2vKlClRf6OfkpKiv/3tb1HrA7Rp00ZvvPGGbr/99sidCrNnz96s2PMvtWzZMurXMq6//npdeeWVkYuKmTNnbvb3d955Z5Pc2Nl/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reconstruction to a matrix from its constituating NMF-factors has several effects on the resulting matrix. Above are the reconstructions of the original images, given by the NMF-method, for rank $d = \\{4, 16, 64, 144 \\}$, and the reconstruction plots are vastly different.\n\n$\\textbf{d=4}$: The reconstruction of the grid images from the rank $4$ NMF seem to grasp contours and the most dominant facial features, however the reconstructions are oddly homogenous. A peculiar observation is that the outline of the characters seem to be preserved, and not expanded nor shrinked, even for $d=4$ - which is surprising because other facial features seem so dissociated. What is the most elegant about this observation is that from a basis of 4 different features ($W$'s), the product produces so many distinct outlines (!). By simply looking at the outline of the initial features for the $d=4$ it seems \"impossible\" that a linear combination of only these features can produce all the reconstructions, because the outlines of the initial features seemed to be so clear cut. However by assessing the initial features with a digital colourmeasurer, very dim pixels become apparent, meaning that feature basises span a wider subspace than what the human eye can distinct. This can of course also be examined by assessing the matrices directly, however we thought that this, from a human point of view, was a fascinating and illustrational point to make about NMF. \n\n$\\textbf{d=16}:$ In the reconstruction of the grid images from the rank $16$ NMF, more details, such as more distinctive coloured features and sharper contours are apparent. The grid images still look grainy, however they are starting to resemble the original dataset. \n\n$\\textbf{d=64}:$ The reconstructions are recognizable and quite precise, however, there is some deviation from the original images. The skin colour on the faces vary with different shades. The colours look more diluted, and especially the stronger colours are not as bright and clear in the reconstructions. Overall, the original image look cleaner and sharper. Some features that were shared by multiple images appear differently in separate images in the reconstruction, meaning the adding of multiple features might have disturbed the appearance of each of them individually. Some features, however, seems to be extracted and reconstructed with high precision, such as the 3D-glasses.\n\nIt is of interest to give a quantitive measure of the compression of the dataset, and we do this by calculating the percentwise reduction in dataset size. The original matrix contains a total of $24 \\cdot 24 \\cdot 3 \\cdot 500 = 864000$ elements. The compressed $WH$ approximation contains a total of $24 \\cdot 24 \\cdot 3 \\cdot 64 + 64 \\cdot 500 = 142592$ elements. This corresponds to a compression of 83,5% of the original dataset, i.e. now storing the data in a dataset 16,5% the size of the original one. 6 times the number of images can be stored in the compressed $WH$ form, however, one must take into consideration the loss of data.\n\nIt is as expected that $d=64$ is not sufficient to yield a perfect reconstrution of the original images. The image matrix was found to have a rank of $373$, meaning significantly more basis vectors than 64 is required to extract all the information of the original images. However, the reconstructions are recognizable, and for certain objectives, such a compression is of very good use. What degree of precision is tolerable depends on what the data are to be used for. In the case of image compression, one would in most cases seek for a more precise reconstruction than the one showed in the plots above.\n\n$\\textbf{d=144}:$ The $d=144$ reconstruction is similar to the $d=64$ reconstruction in that the characters in a greater detail are starting to resemble the original dataset, however colours are slightly more crisp and popping, and the skin of the characters are slightly smoother for the $d=144$ reconstruction. The reconstruction still does not exactly equal the original image set, however, from a human standpoint, the characters are now distinct and unique, meaning that the characters from the reconstruction can unambigously be mapped onto the original dataset in a one to one mapping between the associated images.  \n\nAs discussed in earlier sections, a weakness of NMF is the enforcement of non-negativity. In the case of image processing, even though the orignal matrices are non-negative, they could, and most likely do, produce negative eigenvalues and eigenvectors. This means that linear combinations of some key features does not exclusively add together, but also subtract and cancel out. In practice, this could mean that if some basis vector contains the eyes, and another contains a hairstyle, and these two overlap for some pixels, we could have another basis vector with negative elements which ensures that in the overlapping of the hair and eyes, the eyes are hidden behind the hair. Because the NMF is exclusively an additive method, meaning the matrix is reconstructed by positive linear combinations of non-negative basis vectors, some features can overlap and disturb the appearance of one another. This is why in some cases, a perfect reconstruction is impossible with NMF, no matter how large $d$ is chosen.","metadata":{"tags":[],"cell_id":"56b16818c25447daa905f59160623513","deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":181},"deepnote_cell_type":"markdown"}},{"cell_type":"code","source":"def ex2e():\n    maxIterations = 1000 \n    kList = np.arange(0, maxIterations, 1)\n    dList = [16, 32, 64, 144]\n\n    plt.figure(figsize=(20, 5))\n    for d in dList:\n        norm = NMFImages(faces, d, maxIterations)[3]\n        plt.plot(kList, norm, label = f'd = {d}') \n    plt.legend()\n    plt.title(f'Norm as function of number of iterations in NMF', fontsize = 16)\n    plt.xlabel('Number of iterations, k', fontsize = 14)\n    plt.ylabel(r'$||A - W_k H_k||_F$', fontsize = 14)\n    plt.semilogy()\n    plt.grid()\n    plt.show()\nex2e()","metadata":{"tags":[],"cell_id":"cef548e8cc884cdf81df1d386847e2eb","source_hash":"1c90953a","execution_start":1649447500059,"execution_millis":235572,"deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":187},"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"code"},"outputs":[{"data":{"text/plain":"<Figure size 1440x360 with 1 Axes>","image/png":"iVBORw0KGgoAAAANSUhEUgAABJkAAAFTCAYAAACagd1eAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAAB9FElEQVR4nO3dd3gc1dnG4d+7VV2yLffeAdvYgLGpxvReQ+gfmJJACgFCCAGSQBJIQqiBAKGXQCAJCZ1QjekdbAjFFPdeZMtWL3u+P2ZXXq1W0qquJD/3lb125syZM++sdq3o4cysOecQERERERERERFpC1+6CxARERERERERke5PIZOIiIiIiIiIiLSZQiYREREREREREWkzhUwiIiIiIiIiItJmCplERERERERERKTNFDKJiIiIiIiIiEibKWQSEZG0M7NZZubMbKOZ9UrYFohuuyJN5XUJZraNmc02s03R1+OoNNUxxcyuMLPeSbZ16Z+TmV1qZkvMrMbM5qa7nlSZ2RwzeyPddTTHzAaY2ZNmVhR9L5zfSL+Z0e0z49rON7NjOqnUZDUVRN/XOybZNsfM5qShrCaZ2SIzu6+dx3Nm9tsk2640M5fQNifa/61Gxrs3un1ZI8dJfHT597iIiDQvkO4CRERE4uQDFwO/SHchXdD1wCjgOGAjMD9NdUwBLgceBIoStu0KLEvcoSsws2nAVcA1wOPA5rQW1DP9GtgLmAWsBBY10u8jvPfK53Ft5wNvAP/psOqaVoD3vl6GV1+8H3Z6Nak5GtjUAeOeb2Y3OefWpdB3M7CrmY1xzn0TazSzLOBYGv+cPQ9ckdDWEeciIiKdTCGTiIh0JS8A55rZDc651R1xADMLO+cqO2LsDrYt8Jpz7rl0F9IY59w76a6hCdtGn//qnFuQ1kq6oHb6XGwLzHPOPdZUJ+fcJqDD3yvt9Vl3zn3efK/O55z7uAOGfQ2YDlwCXJhC/0+A/sAp1A+NYrPSnscLFBOt6+L/XoiISCvpcjkREelKrow+/7K5jmY2zcxeMrMSMys1s5ejs1Xi+9xnZsvMbFcze8vMyoE/mdmI6OUZ55jZH8xslZltNrMHzSzLzMaY2fPRsb8xs9NSqKevmd1uZl+ZWZmZLTWzv5vZ4IR+48zsMTNbY2YV0cu3/mVmSf/DT+zSImAE8H+xS0vizm9Rkn3qXd4Td3nSEWb2FzNbF308aGYFCfsGzOxiM/s8Wt9aM3suerneLODeaNev4y5zGRHdt8HlcmZ2kJm9bWblZlZsZo+b2fgk9b5hZvuZ2UfR1+9/ZnZ0c697dP8m3wvR1+K+6Oq3yepMGG9R9LU5wcy+iI75gZntkaTuOY3sf1/ceuxy0N3M7J/R99pqM7sk7jX6OHqc981sp0bqOjL6ulSa2ZdmdlySPpPNu2RtQ/Q1f9PM9kzok/Rz0cTrYWZ2gZnNN7MqM1sZfR/lRbePiL4nZwJ7Jr4vkoxX73K56Ht4OHBy3L7xr1+bzin6c5wdfS+XRF/r0+L2HQEsjK7eGVfDrOj2Bj9nMxtv3ud4Y7Smd8zsoIQ+V0THGWtmz0SPvdjMfm1mvrh+OWZ2s3n/FlSa92/DS2a2TWM/k9jr1sj7bBcze8i8S2tXmNlNZpbR1FhxlgK3AT+0hH+7mvA3vJAp3ql4s9JKUxxDRER6CIVMIiLSlawE/gJ838yGN9bJzLYHXgV64V2acyqQB7xqZpMTuucDjwAPAwcDf4/bdgkwCDgN71Kf44G/Ao8Bz+BdjvIJcK+ZTWim9t5ARXTMg4CLgLHAmwl/4D0DDAZ+AById2lgJY3/To5dWrQWeDa6nGxmQCr+DDjgJOA3wHeibfEewbus7FngKOB7eJc1DYzWHgsCvxtXy8pkB4v+0f0MUIL32v4AmAi8keQP2NHRWq7HmwWxEviXmY1p6oRSfC/8EPhDdPmYaM13NTUusCfeTI5fRWv3A09bQijXQvcDn+K9rx4Hfm9mV+Ndwnd19DjZwONmFkrYdwxwE3Bd9By+AR4xs71jHcy7n9BbeO/F7+H9fNcDLyUJrpr6XCS6Cu/n8iJwOF54Mwt4JhqWrMR7TT8BPqaZ90USRwOr2DLrZVfgd+14TqOAR4GT8d7TTwF3mdk50e0r2TLz5g9xNTyTrFgzG4R3ad9k4MdsuYT1GTM7OMkujwGzo8d+HO+zFx9c3xAd4zfA/sDZwFy8S/ha42/At3jndBvwI7x/l1L1e6AG772f6vFGmdluUPf67As80MQ+Zl6gHf+wFtQoIiJdlXNODz300EMPPdL6wPuD1eH9Id0b7w+2e6LbAtFtV8T1fzTapyCuLQ/vHkH/iWu7L7rvkQnHGxFtn53Q/p9o+ylxbb3w/uC6vIXn5AeGRsc7OtpWGF0/ohWv0TLgvoS2+4BFSfrOAebErc+MHvf+hH5/wQvGLLq+T7TfT1L5WSXZlvhz+gD4GgjEtY0EqoHrE+qtBsbGtfUDaoFLm3ldUn0vnBWtb0QKr/UiYAPQK65tanT/kxp7nRP2vy9uPfaa/TquLQCsiZ73yLj2I6J990o4jgN2SXh/fQm8Htf2MvAFEEro9wXweHOfi0Zei954IWjie++UxPcyXvDS4PVIMmbs/Tgz4TV7MEnfdj0nvDA3ANyJd2lf4r8JZ6XweboW79+EMQk1zQc+imu7Ijrm6QnjfQq8ELf+P+I+D6k+mnif/Sah39PAVymO92B0+XdAFTA6un4l4JK8Lm9El1/DuxQV4OfAkuhrfR+wLMlxXJLHfi19DfTQQw899Oh6D81kEhGRLsU5V4Q3W+NUS7isKs4M4Gnn3Ma4/TYBT+LdeDheNd4fWcn8N2H9y+jz83HjbsALA4Y2V7uZ/cDM5plZCd4foUuim2LnsR5YAPzRzL5nZmObG7OdJc7M+BQI491TBeAAvD/27mzrgcwsG9gR+IdzribW7pxbCLxJw5/T1865r+P6rcF73Yc1c6iWvBda4u3ozz7m0+hzc/U0pe79Fn1NvsH7439hXJ/YezDx/bbUxd3DxjlXC/wLmGZmPjPLxDvffwGR2OwQwICX8F6neE19LuLtAoTwbvQe7xG893hbXuMmtdc5RS9Xe9jMlkf7VOOFjo39+9KcGcA7Lu5G19Gfx8PAlNhlhHESP3f/o/776H1glnnffjjVzPytrKux431Ky9+31+LdtPs3KfZ/ADjOzMJ4swkfcs5Fmuj/X2DnhMe7LaxRRES6IIVMIiLSFd2ANxOlwVdpR/Um+aU4q/BmHsVbG/0DMJkNCetVTbQ3eU8TMzsXuBXvj99jgGl4f6AT29c55/Auh/kA77Kcr8xsgZn9oKmx21Hit8HFboocO7c+QJFzrrwdjtULLwxo7OfUu5naYvU1dy+ZlrwXWqJePW7LDaRTvbdNMsneV429BxOPk+xG+KvxAqC+eK+DH+8Sp+qEx4+BXvH3AaLpz0W82M+p3mscDcnW0/Dn2J7afE5mloN3md9kvEtT98QLNO7BC1hbW1dj7zmj4fsu2ecu/ud7LnA7cAZe4LTGzG4w7xvaWiPZ8Vp0rs65YrzLIk9M4VJh8ILATLzLjifQ9KVy4P0780HCQ9/4KCLSA+jb5UREpMtxzpWY2R/wZjRdk6RLETAgSfsAGv7R7tq5vMacALzsnKv7RiYzG5nYyXnfbHZq9P4jsXu63Gpmi5xziTOrmlOBFzIk6oMXALTUOqC3mWW2Q9C0Ae+1b+znlCxUao2WvBfaWwXepXmJOiJ46d9IWxXe/boygQhwC438gZ8wsyTVz0Xs5zQA+CzWGJ1R1If2+zkms5G2n9OueDcV39M590as0Rq50X6KmnrPOVr4vnPOleDdM+mS6L3ojgX+iPezvbgNdbbVzcD5eJfKfdZUR+dcsZk9gRfkfeCc+6LjyxMRka5IM5lERKSruhVYzpYbTcd7FTjEzHJjDdHlw/HuE5IOWXgzLOKd3lhn55kL/DTaNLEVx1wM9DezvrEGMxtN6y8DegFvJsZZTfSJzejJbGog51wp8CHw3fjLf6J/RO9G+/2c0vleWAyMi79Jt5nNAHIb36XVhppZbGYc0df0u8B7zrlI9PV+HS+4/CjJLJEPWnncd/DCjhMS2o/H+4+Vc1o5bqJKEt5T7XROsdlAdZ9NM+sFHJnk+CTW0IhXgV0s7tvzoj+P44GPo5drtopzbrFz7jq8S9xa829Cu3HOleH9+3sU3uyv5vwF76bqjX5ToYiI9HyaySQiIl2Sc67SzH4L3JFk8++Aw4CXo9/O5fD+i38WjV9i19GeAy42s0uB9/Buon1sfIfoN6H9GfgH3v14/Hg3663B+/aplvoX3mvxoJldj3dj8UvwZiS1mHPuFTP7N3C9mQ2N1hTEuwfNM865OXjfNAfwIzO7H++P90+cc1VJhvwV3v1hnjazW4EcvHu8FOPNUmsP6XwvPAJ8H7gn+lXyI/FCw+IOONZq4B9mdjnezKUfAOOizzE/xbsB8/NmdjfeJV2FePfG8jvnftHSgzrniszsOrxZNqV43zq4LV748AaNfANbK3wO7Glmh+FddrbOObeItp/TW8Am4Jboa5cN/BLvM5If12813uy/E8zsE6AUWOicSzYj8Aa8z+2L0TE34X2D4Tjg0BaeN2b2Nt49xD7F+ybGvfCCtftbOlYHuBP4Gd792poUnSn2RnP9RESkZ9NMJhER6cruxft2snqcc5/gfUPVJrw/xP5G9I8z59y8ziwwzm/x7qtyAd5Xlm8PHJjQZxXezcB/ivdH5cPAIOAw59yHLT1g9MbDxwKD8b4a/efRsb9q1Rl4TsD7VqyjojXeg3ePlZXRY86Lbj8c7w/K96PnkKy+5/D+6C4A/gn8Fe9bwfZwzq1oQ43xx0jbe8E59wpwDjAdbwbH6XjfuraxAw73Dd69e36G9y2IY4ETozXE6vkIb8bJeuAmvJlpfwYm4QU1rXUZ3vvqYLwba/8C7/K1Q5u5uXNLXIL37Wz/xHtPXQFtPyfn3FrgaLxA91G8e6HdRcKNzKPncRbe/ZReitZweCNjrgD2wLuE7LbouL3xXo/nUj7jLV4DjgMewgvtjgUucM79uRVjtatoeHxFuusQEZHuI/aVxSIiIiIiIiIiIq2mmUwiIiIiIiIiItJmCplERERERERERKTNFDKJiIiIiIiIiEibKWQSEREREREREZE2U8gkIiIiIiIiIiJtFkh3AR2psLDQjRgxIt1ltFlpaSnZ2dnpLkOkW9DnRSQ1+qyIpEafFZHU6LMikpqe8ln58MMP1znn+ia29+iQacSIEXzwwQfpLqPN5syZw8yZM9Ndhki3oM+LSGr0WRFJjT4rIqnRZ0UkNT3ls2Jmi5O163I5ERERERERERFpM4VMIiIiIiIiIiLSZgqZRERERERERESkzXr0PZlEREREREREROJVV1ezbNkyKioqOv3Y+fn5fPHFF51+3NbKyMhgyJAhBIPBlPorZBIRERERERGRrcayZcvIzc1lxIgRmFmnHnvz5s3k5uZ26jFbyznH+vXrWbZsGSNHjkxpH10uJyIiIiIiIiJbjYqKCvr06dPpAVN3Y2b06dOnRTO+FDKJiIiIiIiIyFZFAVNqWvo6KWQSEREREREREUmTK664gmuvvbbN45xxxhn069ePiRMnNth28803s8022zBhwgR+/vOft/lYjVHIJCIiIiIiIiLSzc2aNYvnnnuuQfsrr7zCE088wbx58/jss8/42c9+1mE1KGTq4tZtKuPLz96jpqY23aWIiIiIiIiISDu46qqrGDduHHvssQfz589vlzFnzJhB7969G7Tfdttt/OIXvyAcDgPQr1+/djleMgqZurg37/gJ2zx4Ly8/eXe6SxERERERERGRNvrwww955JFHmDt3Ls8++yzvv/9+0n4PPfQQU6ZMafA49thjW3S8r776itdff53p06ez1157NXq89hDosJGlXWy/z4lU3PUmHzx1Jxzz/XSXIyIiIiIiItJj/Oapz/h8xaZ2HXO7QXlcfviERre//vrrHH300WRlZQFwxBFHJO138sknc/LJJ7e5npqaGoqKinjnnXd4//33Oe6441iwYEGH3PxcIVMXN3LHfXl2iJ8Rn5dw4x/PJzx6f6bsMJ1po/rg9+lu+CIiIiIiIiI90UMPPcQ111zToH3MmDE8+uijKY8zZMgQjjnmGMyMadOm4fP5WLduHX379m3PcgGFTN1C2YxdGPn3NznwvudZ3ec51o0w/jTqQAYd+GNO2W20wiYRERERERGRVmhqxlFHmTFjBrNmzeKSSy6hpqaGp556irPPPrtBv/aayXTUUUfxyiuvsPfee/PVV19RVVVFYWFhm8dNRvdk6gYKZ5yC769/ZOmxO1Gem8GYD2G/p5+j/8Mn84N7XqWksibdJYqIiIiIiIhICnbccUeOP/54Jk+ezMEHH8zOO+/cLuOeeOKJ7LrrrsyfP58hQ4Zw993evZ3POOMMFixYwMSJEznhhBO4//77O+RSOdBMpm5j/MwjGT/zSABen30/Vb++mkFzijnKfsV5/uu447SdNaNJREREREREpBu47LLLuOyyy9p1zIcffjhpeygU4sEHH2zXYzVGM5m6oT33OY2Ce25lY47R54M19P7ynzzw9qJ0lyUiIiIiIiIiWzGFTN3UTuNmsuDsA8nb6OP4Vc9w04tfUFRale6yRERERERERGQrpZCpG/vOKb9j4QAf1V9H2KXybc1mEhEREREREZG0UcjUjeWGcll34A4UFPk4pfoN/v7uEqprI+kuS0RERERERES2QgqZurkpJ/yYiEFkxRLKNm/g5S9Wp7skEREREREREdkKKWTq5iaNmM7SgX5qVgU4IvNTnvl0VbpLEhEREREREZGtkEKmbs7MKJ04ij6rfRyT/T9mf7GaiuradJclIiIiIiIiIim44ooruPbaa9s0RkVFBdOmTWPy5MlMmDCByy+/vG7bySefzPjx45k4cSJnnHEG1dXVbS25UQqZeoA+u+9FsBb8Kz6hrKqaN75el+6SRERERERERKSThMNhZs+ezbx585g7dy7PPfcc77zzDuCFTF9++SWffvop5eXl3HXXXR1Wh0KmHmDi3t8BYPX6CNMzlvDf/+mSOREREREREZGu6qqrrmLcuHHssccezJ8/v83jmRk5OTkAVFdXU11djZkBcMghh2BmmBnTpk1j2bJlbT5eYxQy9QCF/UawId9P5cYgpxV+w4ufr6KqRt8yJyIiIiIiItLVfPjhhzzyyCPMnTuXZ599lvfffz9pv4ceeogpU6Y0eBx77LFJ+9fW1jJlyhT69evH/vvvz/Tp0+ttr66u5m9/+xsHHXRQu59TTKDDRpZOVTqiH9nLV7KT+4hNFfvx9oL17DWub7rLEhEREREREem6/vsLWPVp+445YBIc/MdGN7/++uscffTRZGVlAXDEEUck7XfyySdz8sknp3xYv9/P3Llz2bhxI0cffTT/+9//mDhxYt32H/7wh8yYMYM999wz5TFbSjOZeojw+PEMWA9FGz5nULiCZz5Zke6SRERERERERKSVWjqTKaagoIC9996b5557rq7tN7/5DWvXruX666/v0Jo1k6mHGDhlV2r+OYf5ZWHOGbWIa/+Xw5VHTSIUUI4oIiIiIiIiklQTM446yowZM5g1axaXXHIJNTU1PPXUU5x99tkN+rVkJtPatWsJBoMUFBRQXl7Oiy++yMUXXwzAXXfdxfPPP8/LL7+Mz9exGYESiB5i6I7edLc1JdnsH/qETRU1vP712jRXJSIiIiIiIiLxdtxxR44//ngmT57MwQcfzM4779zmMVeuXMnee+/N9ttvz84778z+++/PYYcdBsA555zD6tWr2XXXXZkyZQq//e1v23y8xmgmUw8RHjacqrCf6o1BBqx9i4KME3lq3gr23bZ/uksTERERERERkTiXXXYZl112WbuNt/322/Pxxx8n3VZTU9Nux2mOZjL1EObzUTG8H71XV7OxfB1njNnMi5+vpqK6Nt2liYiIiIiIiMhWQCFTD5K5zbYMXwNzwxkclTGX0qpaXv5iTbrLEhEREREREZGtgEKmHmTgDruRXQmfZgxj6MoXGJyfwQNvL0p3WSIiIiIiIiKyFVDI1IPkbDsBgFUbDFv/FedPrubdhUV8tqI4zZWJiIiIiIiISE+nkKkHCY8bhzMILd/M2kCAw/3vkRn0c++bi9JdmoiIiIiIiIj0cAqZehBfVhYMHsDwNY53hk4m46snOHbHwTw5dwXrSirTXZ6IiIiIiIiI9GAKmXqY3O0mMXKt8U5BX1j/Dd/fpoyq2gj3vrkw3aWJiIiIiIiISIIrrriCa6+9ts3jbNy4kWOPPZZtttmGbbfdlrfffrve9uuuuw4zY926dW0+VmMUMvUwGePH029DhI82rcL5Agxd8iRHTB7EPW8sYs2minSXJyIiIiIiIiId4LzzzuOggw7iyy+/ZN68eWy77bZ125YuXcoLL7zAsGHDOrQGhUw9TMb48ZiDjKXrWTh2H5j3MD/dZzjVtRFumv11ussTERERERER2epdddVVjBs3jj322IP58+e3ebzi4mJee+01zjzzTABCoRAFBQV12y+44AL+9Kc/YWZtPlZTFDL1MOFttgFg+FrH24O3hbL1jFj3KidOG8Yj7y1l4brSNFcoIiIiIiIisvX68MMPeeSRR5g7dy7PPvss77//ftJ+Dz30EFOmTGnwOPbYYxv0XbhwIX379uX0009nhx124KyzzqK01Pv7/4knnmDw4MFMnjy5Q88LINDhR5BOFRw0CF92NhOKfLxbvYGT84fCh/dz7tGP8O+PlvG7pz/n7tOmdnh6KSIiIiIiItLVXf3e1XxZ9GW7jrlN7224eNrFjW5//fXXOfroo8nKygLgiCOOSNrv5JNP5uSTT07pmDU1NXz00UfcfPPNTJ8+nfPOO48//vGPXHLJJfz+97/nhRdeaPmJtIJmMvUw5vMRHjeOcRsy+GD1h9RMOQkWvEK/mlVcsN84Zn+5huc/W53uMkVERERERESkCS2ZyTRkyBCGDBnC9OnTATj22GP56KOP+Pbbb1m4cCGTJ09mxIgRLFu2jB133JFVq1Z1SM2aydQDhbcZT+GTX7C5qprPh+/M9uaDD+7l9H0u5z8fL+eKJz9jj7GF5IT14xcREREREZGtV1MzjjrKjBkzmDVrFpdccgk1NTU89dRTnH322Q36tWQm04ABAxg6dCjz589n/PjxvPzyy2y33XZMmjSJNWvW1PUbMWIEH3zwAYWFhe12PvE0k6kHyhg/Hl9pBYWb4N2SRbDNYfDhvQRqyrjq6Ims3lzBDS9+le4yRURERERERLY6O+64I8cffzyTJ0/m4IMPZuedd26XcW+++WZOPvlktt9+e+bOncull17aLuO2hKay9EDhceMB2K10EO+ufJfv7fpj+OJJmPcwO077HidOG8a9by7k6B0GM3FwfpqrFREREREREdm6XHbZZVx22WXtOuaUKVP44IMPmuyzaNGidj1mIs1k6oEyxo8Dn49pxX34eM3HVAzcHgbvBO/cCpFaLj5wG3pnh7no0U+oqomku1wRERERERER6QEUMvVAvuxswmPHMmJpFVWRKj5eOxd2/REULYD5/yU/K8gfjpnEFys38eeXddmciIiIiIiIiLSdQqYeKnP77cn4ailB/Ly78l3Y9kgoGAZv3ADOsf92/Tlu6hBum/MtHy7ekO5yRURERERERKSbU8jUQ2VOmUxk82ZmuLFeyOQPwO7nwfIPYOGrAPzqsO0YVJDJTx7+mI1lVWmuWERERERERES6M4VMPVTm5MkA7Fncn8+LPmdT1SaYcgrkDIDXrgUgNyPIX07akTWbK7jwn/OIRFw6SxYRERERERGRbkwhUw8VGjUKX04OY5c7Ii7C+yvfh2AG7PZjWPQ6LH0PgClDC7jskG15+cs13Pbqt2muWkRERERERES6q24TMpnZUWZ2p5n9w8wOSHc9XZ35fGRuP4mcr1eQGcjk7ZVvext2Oh0ye8Hr19X1PW23ERwxeRDXPD+fpz9ZkaaKRURERERERLY+V1xxBddee22bxznjjDPo168fEydOTLr9uuuuw8xYt25dvfb333+fQCDAo48+2uYa0hoymdk9ZrbGzP6X0H6Qmc03s2/M7BcAzrnHnXPfA84Bjk9Hvd1NxvbbU/nV1+zWayfeWvGW1xjOgV1+CF89B6s+BcDM+NOx2zN1eC9++s95fLCoKI1Vi4iIiIiIiEhLzZo1i+eeey7ptqVLl/LCCy8wbNiweu21tbVcfPHFHHBA+8zlSfdMpvuAg+IbzMwP3AIcDGwHnGhm28V1+WV0uzQjc/JkqK1l77JhLN28lKWblnobpn0PQrn1ZjNlBP3ccepUBhdkMuve9/WNcyIiIiIiIiId5KqrrmLcuHHssccezJ8/v13GnDFjBr1790667YILLuBPf/oTZlav/eabb+Y73/kO/fr1a5ca0hoyOedeAxKnzUwDvnHOLXDOVQGPAEea52rgv865jzq71u4odvPv7Vb4AXhzxZvRDb1g5zPhs8dh3dd1/Xtnh/j796ZTmBPitHve433NaBIRERERERFpVx9++CGPPPIIc+fO5dlnn+X9999P2u+hhx5iypQpDR7HHntsi473xBNPMHjwYCZHM4KY5cuX89hjj/GDH/yg1eeSKNBuI7WfwcDSuPVlwHTgXGA/IN/Mxjjn/ppsZzP7PvB9gP79+zNnzpyOrbYTlJSUtPo8+gwcSOWcd+l9TG+e/ORJBqwaAEDQ7cAuviBrHr2Y+dv8pN4+501yXP1eLSfe8TZnTAyz26Cu+DYRSa4tnxeRrYk+KyKp0WdFJDX6rEh3kp+fz+bNmwHYeN31VH31VbuOHxo3joILf5p0W21tLS+++CKHHHIItbW1mBkHHXQQlZWVdTXFHHHEERxxxBFJx0nsG1NSUkIkEqnbXlZWxu9+9zsef/xxNm/ejHOOkpISwuEwP/7xj/n1r39NaWkp1dXVlJeXJx23oqIi5c93t0kPnHM3ATel0O8O4A6AqVOnupkzZ3ZwZR1vzpw5tPY8Vr32GsWPP8G+ww/j2aXPs/uM3Qn6gt7GmrcY+MHdDDzhRiiof13mzD2rOOfBD7njkyIoGMzPDhhPKJDuqytFmteWz4vI1kSfFZHU6LMikhp9VqQ7+eKLL8jNzQWgNBQk4ve36/jBULBu/ESbN28mIyODcDhc1ycUCtVbj3nooYe45pprGowxZsyYRm/SnZOTg8/nqxtr0aJFLFmyhD322APwZi/NmDGD9957j7lz53LmmWcCsG7dOl588UVyc3M56qij6o2ZkZHBDjvskNK5d8WQaTkwNG59SLRNWiFr2jQ2/P1h9iobyr+qS5m3Zh5TB0z1Nu7+E/jgHnjzJji0/p3se2WH+NuZ0/nt059xx2sLeOPrddxw/BTGD0j+QRERERERERHpbgZcemmnH3PGjBnMmjWLSy65hJqaGp566inOPvvsBv1OPvlkTj755DYda9KkSaxZs6ZufcSIEXzwwQcUFhaycOHCuvZZs2Zx2GGHNQiYWqorTk15HxhrZiPNLAScADyZ5pq6rayddwZgzMIK/Obn9eWvb9mYPwQmnwAfPQCbVzfYNxTwceVRk7jz1Kms2lTBoTe9zu+e/pzi8urOKl9ERERERESkR9lxxx05/vjjmTx5MgcffDA7R/9ub6sTTzyRXXfdlfnz5zNkyBDuvvvudhm3JdI6k8nMHgZmAoVmtgy43Dl3t5n9GHge8AP3OOc+S2OZ3VqgTx9CY0ZT++EnTP3uVGYvmc0FO12wpcMeF8Dch+Dtv8ABv0s6xv7b9Wen4XtxzfPzuefNhfzrg6XM2n0kp+82gl7ZoU46ExEREREREZGe4bLLLuOyyy5r1zEffvjhZvssWrQoaft9993XLjWk+9vlTnTODXTOBZ1zQ5xzd0fbn3XOjXPOjXbOXZXOGnuC7GnTKP/wQ/YbtDeLNi1iwcYFWzb2GQ0TjvEumytr/NvkemeH+MMxk3jqx3uw6+g+3PTy1+x+9Wx+89RnfLU6+Q3HRERERERERGTr0RUvl5N2ljVtGpGyMvYsGQTAS0teqt9hzwuhqgTeua3ZsSYOzuf2/5vK8+fPYP/t+vPgO4s54IbXOPrWN3nwncWs2VzREacgIiIiIiIiIl2cQqatQOy+TOF5X7N94fa8vOTl+h36bwfbHeVdMrdpZUpjjh+Qy59P2IF3LtmXXx66LZsravjl4/9j+u9f5ju3vcUdr33LgrUlOOfa+WxEREREREREpCtSyLQVCPTpQ3jbbSl94w32Hb4vn6//nJUlCWHSfldApAZmX9misfvkhDlrz1G8eMEMnjt/T87fdxzlVbX8/tkv2ee6V9n9j7O58J/z+M9Hy1ixsbz9TkpERERERESklTQhIjUtfZ3SeuNv6Tw5e+zO+nvvY58+l3ADN/Dykpc5ZbtTtnToPRKmfR/evgWmnw0Dt2/R+GbGNgPy2GZAHuftN5alRWW8+tVa3vp2HbO/XM2/P1oGQP+8MFOGFjBlaC+mDC1g+yH5ZIf1NhQREREREZHOkZGRwfr16+nTpw9mlu5yuiznHOvXrycjIyPlffTX/VYie489WX/nXfT5fAXb9t6WZxY8Uz9kApjxM5j7d/jvz2HWs+Br/US3ob2zOGWX4Zyyy3AiEccXqzbx3sIi5i7dyNylG3n+s9V1fYf1zmL8gFzG989l/IBcthmQy4jCbIJ+TbQTERERERGR9jVkyBCWLVvG2rVrO/3YFRUVLQpt0i0jI4MhQ4ak3F8h01Yia4cp+LKyKHnjDQ479jCu+eAaFmxcwKiCUVs6ZfaCA34HT/wIProfpp7eLsf2+YwJg/KZMCi/rq2otIp5Szfy6fJi5q/azPzVm5n95RpqI95UvKDfGNorixGF2Yzok83IwiyG98lmZGE2gwoy8fuUNouIiIiIiEjLBYNBRo4cmZZjz5kzhx122CEtx+4MPTJkMrPDgcPHjBmT7lK6DAuFyJo+ndLX3+Dgi37I9R9ez1MLnuK8Hc+r33HKyTDvEXjxchh/MOQO6JB6emeH2Hubfuy9Tb+6torqWhasLWX+6k18tbqERetKWbS+jLe/XU95dW1dv5Dfx9DemYwszGZ4n2xG9MmKPmczqCCDgGZAiYiIiIiIiHS6HhkyOeeeAp6aOnXq99JdS1eSvecelLzyCvlrStlt0G489e1TnLvDufgsLpQxg8P/DLfuCk9fACf83WvrBBlBP9sNymO7QXn12p1zrNlcycJ1pXXBk/dcyhvfrKOiOlLXN+AzhvbOYnifLEb0yfaeo7OhhvTK1CV4IiIiIiIiIh2kR4ZMklzOHnuwGih57XWO2PMILnrtIt5f9T7TB06v37HPaNj31/DCZfDhvTD1jLTUG2Nm9M/LoH9eBruM6lNvWyyAWrSulMXry1i0fsvzB4s2UFJZU9fX7zMGF2TWC6BigdSw3llkhfRxEBEREREREWkt/VW9FQkNG0Zo5EhK5sxh5km3kBvM5d9f/7thyASwyw/h25fhuUth+O7Qd3znF5yC+ABqepIAan1pFYvXl7JoXZn3vN57fmLucjZV1NTr3zc3zLDeWQzvncWwPlkMLshkQH4GA/Iy6J+fQW44oG8eEBEREREREWmEQqatTM4+e1P0wN8Illdz5JgjeeTLR1gzdQ39svrV7+jzwVG3wW27wb9mwZkvQjgnLTW3lplRmBOmMCfMTsN7N9i+sayKJUVlLF5fFn0uZUlRGe8sWM9jc5fjXP3+WSG/FzjlZTAwP4O+eWEKs8P0yQnRJydMn+wQhTlhemeHCAV0WZ6IiIiIiIhsXRQybWVy99mHorvvofSNNzhx9xN56IuH+NdX/+JHU36UpPMA+M7d8OAx8Pg58N0HvPCphyjIClGQFWL7IQUNtlVU17JmUyUri8tZtamC1ZsqWFVcyapN5awqruDdhUWs3VxJVW2k4cBAXkaAwhwvgOqVFSI3I0heZsB7zgiQlxEkNyNAXqb3nBMOkBUKkBnykxn0K6QSERERERGRbkch01Ymc8oU/L16sfnl2Qw7+GD2HLIn/5r/L7436XuE/KGGO4zeGw64Ep6/FF6/Fvb6eecXnQYZQT/D+niXzTXGOcfmyhrWl1SxvqSSdSVVrC+trFtfX1rF+hJvttTmiho2lVezubKm0fHiBXxGZtDvhU7R4Ckz5CerbjlAZtBHVihAOOAjHPQTDvjIaOWzz6fLAEVERERERKRtFDJtZczvJ2fmTDa//DKuupqTtjmJc146h+cXPc/how9PvtMuP4SVn8ArV0H/CbDNoZ1bdBdlZuRlBMnLCDKyMDulfWojjpLKGjZXVG8Jnipq2FxZTXlVhPLqWsqraiirqo0ue89lVbVURJ83lFbXbSurqqGyJkJlTfIZVakK+X3RsMpHOOAnHPSR0chzyO8jGIg++42A30fQ7yPkN4J+H4G4ZW/don29/YI+856j+8f6BaP9AgntfgVgIiIiIiIi3YJCpq1Qzj57U/zYY5R9+BG7Tt+V0fmjued/93DoqEPxWZLLtMzg8Bth3Vfw6Jlw2pMwdFqn190T+H1GfmaQ/Mxgu44biTiqaiNUVkeorKmlopnnypoIFdVNP1fGrZeW1lBR7e1fXRt7uHrLHcVn1AusAj7D7zMCPm/dWzb8Pi+cKt1czi1fvlWvT1P7BHwW18dX1zfor7/u9Wm4XjdWdIyGx7C6sKyx9YDPh88HfvPWdYN5ERERERHpjhQybYVydt8dC4fZ/NJLZO8ynbO2P4tLXr+EV5a8wr7D902+UzATTvon3HMAPPRdOOM56Ldt5xYujfL5jAyfn4ygH2jfACsVzjlqItHQqcYLvGoiW5arayPU1G5ZTrZeF1rVRKiJhmbVNdG26Fi1EW9bTa13vGTrkXIvxKmpdZTV1FAbiW3zxopf9/aNNFiPdFxmlhKfeYGkLxo6+c0Lsfxm+GLrvi2PWH+/z4c/GlYl7xe3Hl32+rFl3yb7JRsvum+s5kb6eQ/vvVq3bIZFn2NtZlvOx+L61evro15/f/x2X+Njp3JsERERERFpPYVMWyFfVhY5M/Zk8/PP0//SSzhoxEHcNvc2bv/kdvYZtk/jf2jl9IX/ewzuPgD+dgyc+QIUDO3c4qVLMrO6S9xIcmuvzjRnzhxmztylTWNEIo5a13gQVVvrqI5EA6vaWPuWwKtuvTY+0NrSPz4g88IvRyR6vLqHc14dcbXURuL7QW0kQq2jmX6OqprIlvFc3L4RR8SR/LgJ9cTGS3cA19GaDbjqAiovYGt8e/1tfl/DIK3x8Kz+cXxx2y263d/k9vhxtgRsiTUuXlzFR9VfYWyp2fAmr1rdev12X/T3g5nVa4v1IdreYLzYOHH7NTledBmsQVuj49W1JdYde923jFe/RiP2a6+uLa7dl7Bf3Xhx+9V/Her3rbccPQZ1x2h8PGPL+yX+5yIiIiLSlSlk2krlHnQQm198ifKPPiJr6lS+t/33+NWbv+K1Za+x19C9Gt+x1wg45T9w7yFw/+HepXMFwzqtbpHO4PMZPoygP92VdD3OxYdReGFU7ZZQqrGwzEHdducg4rzAyluPLke2tDXYHtmyT6x/bd2+W7Y3Nnazx65XQ/xx4vtuqa020tT2LWPHgrnE4yTWXRtxVNUmOXaD80p4jSKNj10bSVZT9HjRZb79Ot1vKWmhxNCqsbAtFszRIGyrH+L5jMbDsVTGqxeOxQd60Tasru4tbXEnE78e169+W/1+ycYn6X4JfeLbmtiWeNyiogruXfBeo+eRWF/9fo2ff1OvU+rn2PxrGB9OJpSV/LVJOlaS80gcLOmxG55HUz9j6rU1cezEPk2cY/PHbv44JBm/yfdXw92aPMfEOpvqk1h/0/2s2T7JJK01heN9s7iaRW8ubH6sVM4phRoaH6v5827tWMl2Tj5WG+pv5fsimcQ62nLeqbyOqf+3kOY7pjJWKodL9T/QpDZW2/sUZKX5v8h3AoVMW6ncmTOxcJhN/32OrKlTOXTUodw+73Zu/vhm9hi8B35fE39dD5gIp/wbHvoO3HMQnPoEFI7tvOJFJG3MovejSnch0mberL+ZuLjwyQHOgcNrq7fMlkCLhPZYgOW8DQlt1B2j0fHqtdUfz0VnzzUYL37cWN3R9ojbUkdsnEjc9lj9kUjieAnLbHltaNCWZLxGzjFx3EbHizvfLT+X+uMRCxNJfu7xr0nsNSPuHOu/jl7x3uvQxHjxP5e4863/s9qyX0xsKXlb/fXEfjTo5+qtN7stth4rOEm/ZMdOrA+grNrhL6+u19jwPOK2ucRtbTjHRuqLX0n1PBqcf8NSmvlZJTnHJMehhecR/x5N7N/Wc0w+VlPn0fj5S4q++DzdFYh0abuN7sP3e/ifzvo7YSvly84mZ6+92PSCd8lc0B/kJzv+hJ+/9nOeWfgMR4w+oukBhu4Ms56Bvx3tBU3/9xgM3L5zihcRkXYTm7XiS+m/4YlsfbxAdvd0lyFdSF3Q1dIgLUnA1fRxkrTRsDF5v8Q+SfZL8ZiJHRur4c0332T33XeP65ds/ObrSPW8U2lqz9fQ6+cS1pN0Srpf6+po7WuY/JhtOe9k/drvtWhu7NaOk6rOrCk7HGDZ5x+kUFX31SNDJjM7HDh8zJgx6S6lS8s7+CA2v/ACZR98SPb0aRw44kDu/+x+bv74Zg4YfgAZgYymBxgwCU7/LzxwpHf53HfuhPEHd07xIiIiIiJpUHeZYtJsfusN7HNCRq/snn8pkEhbLevhE/6SfF999+ece8o59/38/Px0l9Kl5ey1F5aZyabn/guAz3xcOPVCVpWu4sEvHkxtkMKxcOaL0Gc0PHwivH6d5hWLiIiIiIiIbIV6ZMgkqfFlZZEzcy82v/AirqYGgJ0H7MzeQ/fmjk/uYFXpqtQGyh8MZzwHE78DL/8WHj0dKoo7sHIRERERERER6WoUMm3l8g46mNr16yn7YMt1oRdPuxjnHFe/d3XqAwUz4Tt3wX5XwOdPwm17wOK3279gEREREREREemSFDJt5XJm7IllZbHpmWfq2gbnDObsyWfz0pKXeG3Za6kPZgZ7XABnPO8t33cIvPw7qK7ogMpFREREREREpCtRyLSV82Vmkrf//mz673NEKraEQadtdxoj80fyh3f/QEVNC0OioTvDOW/A9ifA69fCX3eHhS0Iq0RERERERESk21HIJOQffTSRkhI2v/RyXVvQH+Sy6ZexrGQZd356Z8sHzciDo2+DU/4NkRq4/3D4z/eheFk7Vi4iIiIiIiIiXYVCJiFr2s4EBw2i+LHH6rVPHzidw0Ydxj2f3sP8ovmtG3zMfvDDd2DPC+Gzx+DmneClK6B8Y5vrFhEREREREZGuQyGTYD4f+UcdRelbb1G9qv43yl2888Xkh/P55Zu/pDpS3boDBDNh31/DuR/CdkfBGzfCnyfDK7+H0vVtrl9ERERERERE0q9VIZOZ/a69C5H0yj/qSHCO4iefqtdekFHAr3f9NV8Wfcldn97VtoMUDINjboezX4URe8CrV8ONE+G/v9BldCIiIiIiIiLdXGtnMh0aWzCz+9qnFEmn0LBhZE7dieLHHsM5V2/bPsP24ZCRh3DHvDtaf9lcvIGT4YSH4IfvwnZHwnt3wI3bwz9OgW9nQyTS9mOIiIiIiIiISKdqj8vltm+HMaQLKDj6aKoWLqRi3rwG2y6Zdgl54TwufeNSKmsr2+eA/baBo/8K582FXX8Ii96Evx0NN+8Ab9yg2U0iIiIiIiIi3UhrQ6a+ZnaUmY1s12okrXIPPAjLzGTjfx5rsK0go4Df7f47vtrwFTd+eGP7HrhgGBxwJVz4JRxzF+QN9m4OfsMEuOdgeO9OKF3XvscUERERERERkXbV2pDpeuBw4BFglJm9aWZ3mdmFZnZI+5Unncmfk03ewQdT/PTT1JaUNNg+Y8gMTtrmJB784kFeX/Z6+xcQCMP234XTn4VzP4K9fwnlRfDsz+Dacd4sp/fuhI1L2v/YIiIiIiIiItImrQqZnHM3OOfOdM5Nd84VAKcATwAh4KR2rE86Wa8TT8SVlVH8xBNJt/906k8Z22ssv3zzl6wr78DZRX1Gw14XwQ/fgR+8BXucDxsWeYHTjZPgll3gxV/DNy9BZcNATEREREREREQ6V3vckwnn3ELn3FPOuT84505pjzHbwswON7M7iouL011Kt5M5aSIZEyey4eGHG9wAHCDsD/OnPf9EaXUpv3zzl0RcB9+k2wz6T4B9fw0/+Rh+/CEc+HvI6Qdv3woPfgf+OAzu3NcLnb56AcqKOrYmEREREREREWmgXUKmriYaeH0/Pz8/3aV0S71OPJGqb76l/IMPkm4f02sMF029iDeXv8lDXzzUucUVjoFdfwSnPQm/WAz/9xjscQH4Al7o9Pfvwp9Gwp8nw79mwZs3waI3oHJz59YpIiIiIiIispUJNNfBzBYCDae0NO9G59xNrdhP0izvkINZffXVbHj4YbJ23jlpn+PGH8ebK97k+g+uZ1LhJKb0m9K5RQKEsmH0Pt4DoKoMlr0PKz6CFR/Dsg/hs9hNzA16DYe+22x59NsGCsdDKKvzaxcRERERERHpYZoNmYBZrRx7USv3kzTzZWZScPTRFP397/Rfu5ZA374N+pgZV+5xJSc8fQI/nfNT/nn4PynMLExDtXFCWTBqL+8RU7rOC5xWfAxrvoC1X8I3L0OkOtrBIG8Q9BoJvUdEn0dCr+hyVu80nIiIiIiIiIhI99NsyOSce7UzCpGupeCE4ym6/342PvoohT/4QdI+eaE8bph5A6c8ewoXzrmQuw68i6Av2MmVNiO7EMbu7z1iaquhaCGs/QLWfAlFC2DDQvj6RShZXX//UK4XQuUNgrzByZcze3n3jhIRERERERHZiqUyk0m2QuGRI8nefXeK/v53ep95Jr5QKGm/8b3Hc/lul3PJ65dw/QfXc/G0izu50lbwB6HvOO+x3ZH1t1WVet9iV7TQC56Kl8Om5bBpBXw7G0pWQeLNzv0hyO7rBVrZ/eKW+8Y9Cr2blWf1gUC4005VREREREREpLMoZJJG9TnzDJaccSabnnySgmOPbbTfYaMO47N1n/HgFw8yMn8kx40/rhOrbGehbO/b7PpPSL69ttqb7bRphRc+FS/31kvXQela77HmC++5tjL5GIFMb/ZTZgFkFHjPmb22LCdrC+VAONerT7OmREREREREpAvSjb+lUVm77kp4u21Zf/c95B9zDOZr/MsIL5x6IYs2LeL37/6eIblD2G3Qbp1YaSfyByF/iPdoinPeN9qVrq0fQJWtg/KN3qMi+rxxCayc5y1XlzZTgEXDphwI58Qt52551G3LiwunsiCYDcFML6gKZm1Z9nexSxxFRERERESkW9KNv6VRZkafM89kxYU/o+SVV8jdd99G+wZ8Aa6ZcQ2nPncqF865kAcPeZDRBaM7sdouxgwy8rxHnxa8DjVVUFEM5Ru2hFAVG73AqnIzVJVAZUl0OdpWWeIFWLE+lZvB1aZ+TF/QC51CWfWfg1nRQCqzkeVoUBXI8B7BDG+WViAcbQ/XX1eYJSIiIiIi0qPpxt/SpLwDD2Tt9Tew/q67mwyZAHJCOdyyzy2c9OxJ/PClH/LAwQ/QP7t/J1XaQwRCkNPXe7SWc1BTEQ2jNnnBVFWZN0uqqgyqyxtZLvXW6/qWQMmahu2J96RKlfnjwqiMhHAqtpwknIqt+4Pesj/kPQJhr80f9l43fwj8YXI3fQ2r+3rtyfbxBXTJoYiIiIiISAdo0z2ZzOws59xd7VWMdD0WCND79NNZfeWVlH30EVk77thk/4E5A7ll31s44/kz+P6L3+e+g+6jV0avTqpWAC9ACWZ6j7aEVck4B7VV3g3Sq8ugugJqyqGm0guiaiq8R3XFluXE9epo/3r7VXoztkpWJxmnvEXB1k4AHzXVw+JCp1DjYVQswErs5w95z75A9DkYffbHLSdui18PxLUnrsf18wUa9m3iklUREREREZF0a+uNvw8zswXOudkAZpYF3OOcO6HtpUlXUXDM0az7y19Yf/sdZN3+12b7b9dnO27e52Z+8NIP+OFLP+SuA+8iO5jdCZVKhzOLziwKA70777i11V64VVMZXY4+11QmLFfx6dwPmbTdeO/Sw9rK6H5V3nNC32bHrCyJ2xY3TqQaamuiz9W07rZ1rWC+poMrXyAadvm9mWN164HovvHr/i1969YDXpBVbz3ZeC0cP7ZsPm/ZfN5x6q3Htsc9Guzj996DDfZpbszYfprBJiIiIiLSkdoaMp0KPGtmK4AI8HfgljZXJV2KLyuL3rNOY+2Nf6Z83jwyJ09udp+dB+zMdXtdx3mvnMe5s8/lL/v8haxgVidUKz2SPxqshJoPK9cv88N2Mzu+pniRWi9sioVOkZq49bgwqm69poltycZIZcxqr45IjTfzK1LTcL2mMrpeG91WG7deA5FIM+s1nfu6tjtrx+AqMQiL6xMLtGLtWFx7fFtCO3Hbk/ZNNmZiXxrZ39fgWMMWL4LXP0qhVpLun9LxY7Wn9Ez947do3xb2rfccOx4tPF6y80tljGbOT2GoiIiIdGOtCpnM7AZgLjAPOAt4CPABpzvn5rZXcdJ19Drl/yi6737W3nQzw+5O7QrJvYbuxe/3+D2XvHEJP3z5h9yy7y2a0SQ9U2zGDhnprqTjRSJxoVNjoVaSEMtFvHXnEtYjceuR6HokSZ9II/s0tz1hvJTHTKXOxmqIPuPi2l1Cm9vS1mRfV7+twRjR5yaPFdcnziiAhZ367pEWSSXUaiqsa499WxL40YrjJQZ06QgYk7xeCc9jl6+AsmcaOT9aeLwUfl7JXpukywnHr1umkfZk9TY2dqrLKRynTbXQSHuqr0Wqx0/1OG05fhOvVyrHqTdO4nip9km23sh+rejji80Qb0uNCtpFur3WzmR6BdgeOBTYFhgMvA0caGaDnXPPtFN90kX4c7Lp872zWHPNtZR9+CFZO+2U0n6HjDoEn/n4xeu/4JwXz+HW/W4lN5TbwdWKSIfx+QCfvi2wO4oFW9Hw6dVX57DXnns2EXLRsC1pyNVcX9fIM41vb3bfxsaIpLBP/DMtPF6yWluzT6SR+pt7Tjw/Wni8FvwMUvpZNHX85n4WcftGIiker71+9rToeP2qq6HIn7BvS99rDpGebgbA6+09aiphVbK2FvRpcr/4Pm0ZpyNqbFBYG4PJNtZYLx9sr2C0vWpsRLJ9km5r6/a45QETITCz6bq6uZRCJjPLdc5tjq07554EnozbngFMxAue9gMUMvVAvU46ifX33sfam25m+P33pbzfQSMPIuALcNGrF3H2i2dz2363kR/O77hCRUSkoboZHwB+nC/ofbujiDTpzTlzmDlzZtsHak0oGdsvcdm5+uN6Cy1YbmLspMvUb2/VMZurBVpeV2uOSUJ7K47Z7PFpQV2pvv5Jfh5J25rr00iN7dBnwYIFjBo1spHjN1Vza861vc6DFPuko8Z6xXWxGhvZJ201NlJT0s9kwnGa29bW7YnbKjZBDj1aqjOZNprZ18CHcY+PYsGTc64C+CD6kB7Kl5lJ4ffOYvUf/kjpO++Svcv0lPfdb/h+3LD3Dfx0zk/53gvf49b9bqUws7ADqxURERHpQuoFvSI9z5LaOYzac2a6yxDp+ubMSXcFHSrV78M+EXgCGAD8CpgNbDCzL83sITP7qZnN6KgipesoOOEEAv36sfbGG3HJkuMmzBw6k5v2uYlFmxZxyrOnsHjT4g6qUkREREREREQ6W0ohk3Pun865i51z++J9b7kBv8YLnvoBl+Ldp6lLMLPDzeyO4uLidJfS4/jCYQrP/THlc+ey+YUXW7z/HoP34O4D7qasuoz/e/b/+HTtpx1QpYiIiIiIiIh0tlRnMtVxW6avPB0NnvZ3zhUCI9u3tNZzzj3lnPt+fn5+ukvpkQqOOYbw2LGsue46XFVVi/ef1HcSfzvkb2QHsznzhTN5demrHVCliIiIiIiIiHSmFodMjXHOLWmvsaRrM7+ffj+/iOolS9jwyCOtGmN43nD+dsjfGJk/kp+88hPu/+z+Fl9+JyIiIiIiIiJdR7uFTLJ1yd5jD7J32411t9xKbSsvSyzMLOTeA+9l32H7cu0H13LpG5dSUVPRzpWKiIiIiIiISGdIKWQyswfN7Hwz293MsqLNmnayFTMz+v38Imo3bWLdbX9t9ThZwSyu2+s6zt3hXJ5Z8Ayn/vdUVpasbMdKRURERERERKQzpDqTaSDejb5fB2LTVq4yswvNbKaZ5XVIddKlZWyzDfnfOYaihx6icsHCVo9jZnx/++9z0z43sWTzEk545gTeWP5GO1YqIiIiIiIiIh0t1W+X29c51xsYA5wE/AnIAC4BZgMbzOyrDqtSuqx+55+PLxxm9VVXtfmeSjOHzuTvh/6d3hm9+cFLP+Ca96+hqrblNxYXERERERERkc7XonsyOecWOOf+5Zz7hXPugOi3yo0Cjgce7ZAKpUsLFBbS9yfnUvrmm5S8/HKbxxuVP4qHD32YE8afwAOfP8Apz57CwuLWz5ISERERERERkc7Rpht/m9lZzrlFzrlHnXOXtldR0r30OvFEwmPHsPoPfyRS0fYbd2cEMrhsl8u4ae+bWFm6kuOfPp4HP3+Q2khtO1QrIiIiIiIiIh2hrd8ud5iZ7RNbMbMsM2vdd9pLt2XBIP0v+yXVy5ez/q67223cvYftzaOHP8pO/Xfi6vev5tTnTuWbDd+02/giIiIiIiIi0n7aGjKdCvzWzLYxs3HAa8DzbS9LupvsXaaTe/BBrL/jDqoWLWq3cftn9+fWfW/lD3v+gSWblvDdp7/LbXNv072aRERERERERLqYVoVMZnaDmZ2Gdz+ms4CHgH8AZznn7m3H+qQb6X/JJVg4zMrLr2jzTcDjmRmHjTqMJ456ggOGH8Ct827l6CeO5rVlr7XbMURERERERESkbVo7k+kVYChwKfAvYCSwAjjQzA5tp9qkmwn260e/n/2Msnffpfg/j7X7+L0zenP1jKu5ff/b8fv8/OjlH/Gjl3/Ekk1L2v1YIiIiIiIiItIyKYVMZlYYv+6ce9I5d6Vz7jjn3CRgEHA5sBbYr/3LlO6i4LvHkjl1J1b/6U/UrF/fIcfYbdBu/Pvwf/OzqT/jw9UfctQTR/Hnj/5MaXVphxxPRERERERERJqX6kymJWZ2m5mNSbbROVfhnPvAOXePc+6CdqxPuhnz+Rj4m9/gyspY/fs/dNhxgv4gp004jaeOeoqDRhzEXZ/excH/PpgHP39Q92sSERERERERSYNUQ6YzgZ2AL83scTPbvQNrkm4uPHo0fc45m03PPMOmF17o0GP1zerL7/f8PQ8f+jDje4/n6vev5rDHDuPxbx6nNlLboccWERERERERkS1SCpmccw8756YB+0SbXjWzt83sO2ZmHVeedFeF3/8+GRMmsOryKzrssrl4EwsncucBd3LH/nfQO6M3v3rzV3znye/w3MLnFDaJiIiIiIiIdIIW3fjbOfeac+4oYFvgI+B+4Gsz+5GZZXZAfdJNWTDIoD/+gUhpKSsvv7xdv22uKbsO2pWHD32Y62dej8Nx0WsXcdQTR/HY149RHanulBpEREREREREtkat+nY559zXzrkf4X3D3P3AbwF9xZfUEx47lr7nnUfJSy9T/MQTnXZcM2P/4fvz2JGPcf3M68kMZPLrt37Nof85lIe/fJiKmopOq0VERERERERkaxFIpZOZ3QIUAPlJnnM6pjTpCXrPOo3Ns2ez+sqryJo6ldCQIZ12bJ/52H/4/uw3bD9eX/46d35yJ79/9/fcNvc2jht/HCdscwKFmYXNDyQiIiIiIiIizUp1JtMPgKOBb4HbgcuA/wNmAmOB/kBGB9Qn3Zz5/Qy6+mowY/lPL8RVd/4la2bGjCEzeODgB7j3wHuZ0m8Kd3xyBwc8egC/fOOXzC+a3+k1iYiIiIiIiPQ0qYZMU4HHgbOBo4A1zrk5zrmPnHPfOufWOue6zPfGm9nhZnZHcXFxuksRIDRkMAN/91sqPvmEtX/+c9rqMDOmDpjKTfvcxFNHP8V3xn6HFxa/wLFPHctZL5zF7CWzqYnUpK0+ERERERERke4s1W+X+8g5dxLerKXFwPNm9rqZHd6h1bWSc+4p59z38/Pz012KROUddBAFxx/P+rvupuT1N9JdDsPzhnPZLpfx4rEvcv6O57OweCHnvXIeB/77QG6bexurSlelu0QRERERERGRbqWl3y631Dn3U2AY8CRwi5l9YWZnmlmoQyqUHqP/Jb8gPHYsKy6+mOpVXSPEyQ/nc+akM3nuO89x48wbGVswllvn3cqB/z6Qn8z+CXOWztG30omIiIiIiIikoLXfLlcMXAvsBDwE/AlY1H5lSU/ky8hg8I034CoqWPaT84hUdZkrLAn6guw7fF/+uv9fefaYZzl9wunMWzuPc2efyz7/3Icr37mSuWvm4pxLd6kiIiIiIiIiXVKq3y73DN43ycU/Yt8qZx1TmvRE4dGjGfjHP7D8J+ex+ne/Y+DvfpfukhoYmjuU83c6nx/t8CPeWv4WTy94mse/eZx/zP8HQ3KGcPDIg9l76N5MKJyAz1qV04qIiIiIiIj0OCmFTMAa4CtgA7Ax7nljQptIs/IOOICKs89m/e23kzFxEr2OPy7dJSUV9AXZa+he7DV0L0qqSnh5ycs8veBp7vnfPdz56Z30y+zHzKEz2XvY3kwbMI2QX1eMioiIiIiIyNYrpZDJOXd6RxciW5e+PzmXis8+Y9WVV5IxfhyZU6aku6Qm5YRyOHLMkRw55kiKK4t5bdlrvLL0FZ5a8BT//OqfZAYy2bH/juw6cFd2GbgLY3uN1SwnERERERER2aqkOpNJpF2Z38/ga69h4XePY9lPzmPEv/5JsH//dJeVkvxwPoePPpzDRx9OZW0l7658lzeWv8E7K9/h2g+uBaB3Rm+mD5zOtAHT2KHfDozMH6nQSURERERERHo0hUySNv6CAob85S8sPukklp7zA0Y8+Dd82dnpLqtFwv4wM4bMYMaQGQCsKl3Fuyvf5Z2V7/DOynf478L/ApAXymNy38ns0G8HpvSbwsTCiWQGMtNZuoiIiIiIiEi7UsgkaZUxfhyDb7yBpef8gOUX/owht/wF8/vTXVarDcgeUHdZnXOOxZsW8/Gaj5m3dh4fr/mY15e/DkDAAozrPY7t+mzHtr23ZUKfCYztNVb3dRIREREREZFuSyGTpF3Onnsy4JeXseo3v2X1H69mwGWXprukdmFmjMgfwYj8ERw99mgAiiuLmbd2HnPXzOWTtZ/w/KLnefSrRwEI+AKMLRhbFzyN6TWGMQVjyA/np/M0RERERERERFLS6pDJzGYA7znnKtqxHtlK9TrxRKoWL6HovvsIDR1K71P/L90ldYj8cH69y+uccywrWcbn6z/n8/Wf88X6L3hpyUv8++t/1+3TL7MfowtGM6bXGMYWjGV0wWhGF4wmO9i9Li0UERERERGRnq0tM5leAbYFvmqnWmQr1++in1G1bCmr//AHAv36knfQQekuqcOZGUNzhzI0dygHjjgQ8IKnVaWr+Hrj13y78Vu+2fgNX2/4mn/O/yeVtZV1+/bL7MewvGEMzxvuPed6z0Nzh5IRyEjXKYmIiIiIiMhWqi0hk7VbFSJEv3HummtYctb3WH7Rz/Hl5JKzx+7pLqvTmRkDcwYyMGdg3YwngNpILctLlteFT4s3LWbJpiW8svQViiqKtuyPMSB7AMPyhjEkZwiDcgYxKGcQg3MGMyh7EH2z+uqb7kRERERERKTd6Z5M0qX4MjMZetutLD71NJadey7D7r6brB13SHdZXYLf52dY3jCG5Q1j32H71tu2qWoTSzYtqQueFm9OHkABBH1BBmYP3BI8xYVQ/bP60zezL0F/sDNPTURERERERHoAhUzS5fjz8hh2150sOvlklp5zDsP/9gAZ48enu6wuLS+Ux8TCiUwsnNhgW3lNOStLVrKidAUrSlawvGQ5K0q85TlL57C+Yn29/obRO6M3/bL60T+rP/2y+tU9Yuv9s/uTE8zBTBMaRURERERExKOQSbqkQGEhw++5h0UnncySM89i+AMPEB41Mt1ldUuZgUxGFYxiVMGopNvLa8pZWbqSFSUrWF26mjVla1hd5j2vKF3B3LVz2Vi5Mem4sdCpb1ZfCjMKKcwspE9mn3rr+eF8hVEiIiIiIiJbAYVM0mUFBw9m2D13s/jU01h82qkMv/9+wqOSByXSepmBTEblj2JUfuOvbWVtJWvK1tR7rC5bXRdKzV0zl3Xl6+rdmDwm4AvQJ6MPhZmFjT76ZHrbMwOZHXmqIiIiIiIi0oEUMkmXFh49muH338fiWaez+NTTGH7/fYRHj053WVudsD9c9y14jXHOUVpdyrrydd6jYh3rytbVW19dtprP1n9GUUURERdpMEZOMIfCzEJ6Z/Smd0ZvemX0oldGr/rrYW+9IKOAoE/3jhIREREREekqFDJJlxceM4bhD9zP4tNO84Km++4lPHZsusuSBGZGTiiHnFAOI/JHNNm3NlLLhsoNrC9fz7rydawtX8u68nV16+vK17GweCEfrfmIjZUbkwZSALmhXC98Cm8JozZt2MTSz5fSK6MXBeEC8kP5FIQLyAvnkRvK1TfriYiIiIiIdJC2hExXAevaqxCRpoRHjWL4/dGg6bRZDLv7LjK23TbdZUkr+X3+ukvlxtP0Td1rI7VsqtrEhooNrK9Yz4aKDWyo2EBRZVHd8oaKDSwrWcYnaz9hQ8UGXnz/xaRj+cxHXiivLnSKhVD5Ye9REC6oW65bD+WTHczWfaVERERERESa0eqQyTn3q/YsRKQ5XtD0AEvOOIPF/3cqQ265hezp09JdlnQwv89fd9ncKJq/J9fsV2az0247UVRRRHFlsfeoKmZjxUaKq4rr2jZWbmRt2Vq+2fANxVXFlFaXNjpmwAJbQqlYCBVqJJSKPueF8sgMZCqcEhERERGRrYYul5NuJTxqJCMe/jtLzvoeS886i0HXXkvegQekuyzpQnzmqwt9WqK6trpBCFUvpIpbX1myki8qv2BT1SbKa8obHTPkCzUIofJCeWQHs8kKZpEVyCI7mF23nh3MJjtQfz0rkIXf52/ryyIiIiIiItLhFDJJtxMcOJARDz3I0nN+wPLzz6f28l/T64QT0l2WdHNBf7DuEr6WqKytbBhKxdYTQqvFmxazqWoTZdVllNWUNXqvqUSZgcxGA6m65fhtCUFV3bZAlmZXiYiIiIhIh1HIJN2Sv6CAYffew/LzL2DVFb+hevly+l5wAebTTZ2lc4X9Yfpl9aNfVr8W7eeco7ymnLKaMkqrS+seZdXR9Zq45fhtNd7y2rK1LKpe5LXXlDU5oyqez3xkBbKSzpxqLKCq1z9uPSuQRdgf1kwrEREREREB2iFkMrMRwA7AFOfc5W2uSCRFvsxMhvzlZlb97krW33kXlQsWMvhPV+PLzk53aSLNMrO6YKels6eSqY3U1gVWsZlSjQVU9cKraJi1oWRDvf0qaytTPnbQFyQjkEGmP5NwIExGIIMMf0aD53AgnLQ9I+BtC/vChP1hQv5QvefE5YAvoNlYIiIiIiJdUMohk5kFgO2IBkrR5+2BfMCAlUCXCJnM7HDg8DFjxqS7FOlgFgwy4DdXEB4zhtV//COLTj6FobfeQnDQoHSXJtKp/D4/uaFcckO57TJedaTaC50SAqv4sKqipsJ71CY811RQWVtJeU05RdVFSfvUutpW12YYIX8oaQhV77mR0Kq5fcP+MEFfkKA/SMgXarAc8nvPCrtEREREROpLKWQys4/wAqYQsAL4DPgQ2AM4DnjBObe5o4psKefcU8BTU6dO/V66a5GOZ2b0PvX/CI0cwfILfsrC7x7HkD/fSNbUqekuTaTbCvqCrbqBeqqqI9X1wqjKmkoqI5VU1VZRWes9xy9X1lbWW26srSriLW+q3NRov+pIdbudR9AXrBc8xZ6D/mDDbb5Q0vZk+yXbFvKHCPgC9caJLce3BXyBumef6RJiEREREek8qc5k2ha4FrjGOVccazSznwBfdKWASbZeOXvuyYh/PMLSH/6QxafNot+FF9L79FmaaSDSBQV9QYKhILm0z8yrloi4SIOwKj6gqqzxgqiq2irvOVJFdW011ZHoozbaFt+ntoqaSE2DtthzY2NWRaL71VZT42ra/Vx95msQPMWeqyuqufnJm+vWk/VJ9txsH3+QgCU8+wL1lpsaL+AL4Dc/fvPr328RERGRbibVkGlH4M/Ao2Z2oXPukw6sSaTVwqNHM/LRR1l56WWs+dOfKP/4Ywb+/ir8uZ3/h6yIdE0+83n3gwpkpLuUemojtdS4mgYhVXzA1SDAioZVNRFvvxq3JbCK7RcLv2LLsfWVq1dSkFNQt14TqaG8przeevxy4nNbLnlMVSycCvgC+H1+AuY9B31B/OavF0oFfUGvT3Q9ft/4/eP3SdaebP/YuMn2bzBetJamao61K0QTERGRnialkMk59wVwgJkdAzxmZq8Bv+zQykRayZ+by+Cb/kzRffez5tprqTj2WIbcdBMZ48enuzQRkUb5fX78+An7w51yvDlz5jBz5sxW7x9xkUZDqAZtccFXvRCrkbZYwFXrauuWG6xH+8XCudpIbV17bGZZY/vXulqqI9X19om4SPu9uCmKBVBNBVv1Qqv4kCq+b0LgFT9u/HixGWLJlmOXV8aHZc32jYVo5sfn89Udt7F9Y9t1GaeIiEjP1aJvl3PO/cfMngV+AXwC+IBgRxQm0hZmRp/TZ5G5/SSWn38Bi447nv6XXkrBcd/VfzkWEWkHPvPV3US9J4i4SF1gFR9eJQ254vukGIzFnuvCLddw/1SPWVlTSZkr2zJe7BiJ48XV0hkzz1oiPnBqLJxKDLPqBVvN7NtcgOYzX73l2HYzq9fmMx/fbP6GDV9vqNevuX2StafSJ1l7Y8fT/58REZGuqEUhE4BzrgK4wszuA24AXjaza4GbnXOl7VyfSJtk7bQTIx/7Dyt+/nNWXX45Ja++ysArf0egd+90lyYiIl2Iz3z4/D6CPfS/nTnnvCDN1XqPSG1dCBVrjy3HArBG+0bDsPjlZP2TLcf6NjhOsn0aOU5s3+raaspdefP1JlmudbUtm732Vsf9bFrLsBYHVvH7mBk+os+xtiTb65bNV9c/1i+xPXGc5rYnO2a9fRs5flPjNNU3tt7UedaNk9A/2bb4Y9b1j71GTfVvbD1+/7jjA/XqbnQ9uj9Gg3FERDpLi0OmGOfcIuBoMzsAuBH4KdCvfcoSaT+BwkKG3nUXRQ88wNrrb2DBEUcy6Korydlrr3SXJiIi0iliQYMff7pL6TKcc9S4Gpxz1LrauudYGBVxESIuwptvvcn0XabXa4v1id8nvj2VPqnsm+o+ie3J+gB16845IsQtuwgRki/H960bN7o9ti3pGC6CwzV5zKa2x7bFt0vrtTnsioVX8YFeQhBXXlbODY/fkFowliQIa1GNjQR8iTUC9faJPQP1xkmlX712o0Fbg+cm+jU4Xlx7/Hk21S9pXcnOK9X6W3Neyepq5HVM/PklO1aq9cZ+1qnWEGtLNn5MvfOLW48tJ/tZRBsbPf7WqtUhU4xz7gUzmwz8pB3qEekQ5vPRZ9YssnfdjRUXXcTSs8+h4Lvfpd/PL9JNwUVERLZCZkbQmp+51ivQi0E5gzqhImlOu4RZuEbHqdse1ye2HB961W2PC9vqtif2b2w9fv+44wH1am50PVkdTdXdwjoS+yfWkWys1TWrKSworFdjhAg4trzWsfUkx2hs3KQ1Jnntm3rtYv28/7l6bXXPzfSLvQcT94nvqzBUEiWGVtMGTOOk0ElprqpjtTlkAnDOVQPXtcdYIh0pY/w4Rvzrn6y96SaK7r2PktdeY8AVl5O7997pLk1EREREmqAZeV1bW79QoidpLoyK3w4kD7uShV9Jxq7XlhCU1Qvn4mtI6J+shvi+sXEa9EuhhkZDveZemybqTfU1jK8rsU9jP6sG7SQZp7HXzGts9LUFGJI7BJa3z/usq2o2ZDKzhRD3aqfuRufcTa3YT6RD+cJh+l90EXkHHcTKSy9j2Q9+SN5hh9H/sksJ9OqV7vJERERERKQbi7/MSyTRnOVz0l1Ch0plJtOsVo69qJX7iXSKzEmTGPnvR1l3x52su/12St98k/6XXkLeYYdt1dfQioiIiIiIiLRGsyGTc+7VzihEJB0sFKLvj39E7gH7s/KXv2LFRT9n478eZcDlvyY8enS6yxMRERERERHpNnzpLkCkK8gYN44RD/+dAVdcTsWXX7LgqKNZc931RMrK0l2aiIiIiIiISLegezKJRJnfT68TTiB3//1Zc+11rL/zToqfeZr+F/+C3AP21yV0IiIiIiIiIk3QPZlEEgT69GHQH35PwbHfYdVvfsvy884jc6ed6H/xz8ncfvt0lyciIiIiIiLSJemeTCKNyNppJ0b+599s/M9/WHvTzSw67njyDjmEvj/9KaEhg9NdnoiIiIiIiEiXonsyiTTBAgF6HXcco597jj4/OIfNs2ez4JBDWHPttdRu3pzu8kRERERERES6DIVMIinw52TT77zzGP3cf8k7+GDW330P3+63P+vvuotIeXm6yxMRERERERFJO4VMIi0QHDCAQVf/kZH/fpSMyduz5trr+OaAAyh68CEiVVXpLk9EREREREQkbRQyibRCxnbbMeyOOxj+0IOER4xk9ZVX8u1BB7Hx0UdxNTXpLk9ERERERESk0ylkEmmDrJ12YtgD9zP07rsI9Clk5S9/xYJDD6P4qadxtbXpLk9ERERERESk0yhkEmkjMyNn990Z8c9/MOSWv2DhMCsuuogFhx7Gxscf18wmERERERER2SooZBJpJ2ZG7r77MvLxxxj85z9jGRms/MUlfHvwId5ldLpnk4iIiIiIiPRgCplE2pn5fOQdeAAjH/sPQ269BX9+Pit/+Su+OeggNjz8sG4QLiIiIiIiIj2SQiaRDmJm5O6zDyP+9U+G3nkHwX79WfWb3/Ltvvux7o47qS0uTneJIiIiIiIiIu1GIZNIBzMzcvbck+EP/51h995DeOxY1l5/PV/vvQ+rrryKqqVL012iiIiIiIiISJsF0l2AyNbCzMjedVeyd92Vii+/pOje+9jwyCNs+Pvfyd1/f/qcPovMKVPSXaaIiIiIiIhIq2gmk0gaZGyzDYOu/iNjXn6JPmeeQenbb7PohBNZdOJJFD/9jG4SLiIiIiIiIt2OQiaRNAr270+/Cy9k7Cuz6X/ppdSsX8+Kn/2Mr/fehzU33kj1ypXpLlFEREREREQkJQqZRLoAX3Y2vU/9P0Y/91+G3nkHmZMmsf72O/hm3/1Ydu65lL79Ns65dJcpIiIiIiIi0ijdk0mkCzGfj5w99yRnzz2pWracjf94hI3/epTNL75EaORICo49lvwjjyBQWJjuUkVERERERETq0UwmkS4qNGQw/S68kDGvzmHQ1X/EX1DAmmuu4euZe7P0xz9m8+xXcDU16S5TREREREREBOihM5nM7HDg8DFjxqS7FJE284XD5B95JPlHHknlggVs/Pe/KX7iSUpeehl/30IKjjqK/KOPITxqZLpLFRERERERka1Yj5zJ5Jx7yjn3/fz8/HSXItKuwqNG0f+iixj7ymyG3PIXMidtz/p77mXBIYew6ORT2PCPf1JbXJzuMkVERERERGQr1CNDJpGezoJBcvfdl6G33sKYV2bT72cXUrthA6suv5yv9tiTpT/+MZuee55IZWW6SxUREREREZGtRI+8XE5kaxLs148+Z51F7zPPpOLzz9n05FMUP/sMJS+9jC8nh9wDDiD/8MPImjYN8/vTXa6IiIiIiIj0UAqZRHoIMyNzwgQyJ0yg388vouzddyl+8ik2P/88xf/5D4F+/cg98EDyDjyAzB12UOAkIiIiIiIi7Uohk0gPZH4/2bvtRvZuuxG54nJKXnmF4qefYeM//sGGv/0Nf99Ccvfbj7wDDyRr6lQsoH8KREREREREpG30l6VID+fLyCDv4IPJO/hgaktKKXl1DptfeJHix59g48OP4O/Vi9z99iX3gAPJnj4NC4XSXbKIiIiIiIh0QwqZRLYi/pxs8g89lPxDDyVSXk7J66+z+fkX2PTsf9n4r0fx5eSQvcce5O49k+wZMwj06pXukkVERERERKSbUMgkspXyZWaSd8AB5B1wAJHKSkrffIuSV16hZM4cNj/3HPh8ZO6wA7l7zyRn770JjRqFmaW7bBEREREREemiFDKJCL5wmNx99iZ3n71xkQgVn31OySuvsHnOK6y59jrWXHsdwWHDvMBp5kyydtpJl9WJiIiIiIhIPQqZRKQe8/nInDSRzEkT6fuTc6letcqb3fTKK2x4+BGK7n8AX1YWWdOnk7377mTvvhuhESM0y0lERERERGQrp5BJRJoUHDCAXiecQK8TTiBSVkbp229T8sYbdZfXAQQHDaoLnLJ32QV/QUF6ixYREREREZFOp5BJRFLmy8oid999yd13XwCqliyh9K23KH3zTTb9979s/Ne/wIyMCRPImjaNrJ2nkrXTTvjz8tJcuYiIiIiIiHQ0hUwi0mqhYcMIDRtGrxNOwNXUUP7Jp5S++Sal777Dhr/9jaJ77gGfj4xttiFr553JmrazFzppppOIiIiIiEiPo5BJRNqFBQJk7bgDWTvuQN9zf0ykooLyeZ9Q9t57lL3/Phsefpii++8HM8Ljx5M1dSqZO0wha8oUAoMG6Z5OIiIiIiIi3ZxCJhHpEL6MDLKnTyN7+jQAIpWVVHzyCaXvv0/Z+++z8dFH2fDggwAE+vYlc4cdyJwyhcwpU8iYsB2+cDid5YuIiIiIiEgLKWQSkU7hC4e9S+Z23hkAV11NxVdfUf7xXMrneo/NL7wAgAWDhLfblqwpO5A5ZTIZkyYRHDxYs51ERERERES6MIVMIpIWFgySOWECmRMmwCknA1Czdi3l8+ZRPncuZXPnsuGRR7xL7AB/fj4ZE7YjY8JEMiZMIGPiBAVPIiIiIiIiXYhCJhHpMgJ9+5K7337k7rcfEJ3tNP8rKj77jIr//Y+Kzz5j/X33QXU1EAueJkRDJy98wrk0noGIiIiIiMjWSyGTiHRZFgySOXECmRMnwPHHARCpqqIyFjx99j/KP/uM9ffeCzU1APTNymTxdhMIb7MNGduMJzx+G8Jjx+DLyEjnqYiIiIiIiPR4CplEpFvxhUJkTppI5qSJwPGAd1Pxyq+84GnB7Nlkb9rMxv/8B1dW5u3k9xMaMYKMbbYhvM1473n8eAJ9++pyOxERERERkXaikElEuj1fOEzmpElkTprE5gED2GnmTFwkQvXSpVR8OZ+KL7+g8sv5lH38EZueeaZuP3/v3ltmO40bR3jMaMKjR+PLykrj2YiIiIiIiHRPCplEpEcyn4/Q8OGEhg8n78AD6tpri4upmD+fyi/nUzH/Syq/nM+Ghx7CVVXV9QkOHkx4zBjCY8cQGjOG8JixhEePwpeZmY5TERERERER6RYUMonIVsWfn0/2tGlkT5tW1+ZqaqhaspTKb76m8ptvqPrmGyq//oaSt96qu8k4ZgSHDPHCp2gAFR4zhtCoUbrfk4iIiIiICAqZRESwQIDwqJGER42EA7bMevLCpyVUfv1NvQCq5PXX6240DhAYNJDwiJGERo4kNGok4ZHecqB/f8znS8cpiYiIiIiIdDqFTCIijfDCp1GER42CuEvuXHU1VYsXU/nNN1QuWEDVwkVULVhA8WOPEYndbBywzExCI0YQHjmCUCyEGjmS0IgR+HOy03FKIiIiIiIiHUYhk4hIC1kwWHfZXDznHDVr1lK1cCFVixZStXAhlQsXUv7p/9j03PMQidT1DfTrFw2dRhAaOozQ8GEEhw4jNHSIbjwuIiIiIiLdkkImEZF2YmYE+/cj2L8f2btMr7ctUlVF9eLFVC5c6M18WuiFUJv/+xy1xcX1+gb69iU4fJgXPg0bSnDYMELRhz8/vzNPSUREREREJGUKmUREOoEvFCI8dizhsWMbbKstLqZqyVKqly6haskSqpYspWrJYkrffJPix9bUHyc/3wuchg6tC6KCgwd7j/79sGCws05JRERERESkHoVMIiJp5s/PJ3NSPpmTJjbYFikvp2rpUqrjwqfqJUsp/+QTNj33XL1L8PD5CAzoT3DQIEKDBxOIPgcHDSI4eDCBgQPxhUKdeGYiIiIiIrI1UcgkItKF+TIzyRg3joxx4xpsc1VVVK9cSfXy5VSvWEHV8uXURJ9L33+fmlWr64dQZt6leNHQKThoEMFBAwn0H0Bw4AACAwbgLyjAzDrxDEVEREREpKdQyCQi0k1ZKERo+HBCw4cn3e6qq6levaYuhIp/Lv/kEzY9/zzU1NQfMyODYP/+BAYOjD4PIDjAC6CC0TZffr6CKBERERERaUAhk4hID2XBIKEhgwkNGZx0u6utpWbdempWr6J65aq65+pVK6lZtZrS996jZs0aqK2tP25mZjR46k9wwMC65+DAAd6sqP79FESJiIiIiGyFFDKJiGylzO+v+za8zO23T9rHC6LWUbNyJdWrVlG9ahU1K1dRvXo1NStXUvrWW9SsXVv/sjy8WVaBvn3rP/r1bdDm790b8/k643RFRERERKSDKWQSEZFGeUFUf4L9+5PZSB9XU0PN2rXebKhVK6les4aatWu9x5q1VC5YQOm77xLZtKnhzn4/gcLChoFUfCjVpw/+Pn3whcMdeq4iIiIiItI2CplERKRNLBDw7tc0cCCwQ6P9IhUV3qyoNWvjQqgtgVT1ihWUz5tHbVFR0v19OTle4FRYSKB3b/yFfQj0KSTQpzf+Pn28sKp3b/yFhfiys3W5noiIiIhIJ1PIJCIincKXkUFoyBBCQ4Y02c9VV1Ozfv2WIGrdOmqLirz7R61fR+36IioXLKD2vfeoLS5OOoaFw3UzoLxgqg+B3n0IFG5piwVW/vx8XbInIiIiItIOFDKJiEiXYsEgwQHet9o1x1VXU1O0gdr166hZXxQNodZTs77Ia1u3nurVq6n47DNqiooa3MQcAL8ff+9eBHr1xt+7N/5eBd5yr17R9l7R5d74C3oR6FWAhUIdcOYiIiIiIt2bQiYREem2LBisu3l5c1wkQm1xsRdCxc2KqlkfXd6wkdqiIiq/+JLSDRuINDJLCrxL9+oCqYJoANWrF4He0UCqV3RbtN2Xm6vL90RERESkx1PIJCIiWwXz+Qj08mYmhceMaba/q6nxQqmiImo2bKC2aAO1GzdQU1TkBVIbNlBbVET12jVUzJ9PbVERrqoq+WCBAP6CAvwF+fjzC5pZjq4XFOhm5yIiIiLSrShkEhERScICgbp7N6US9TjncGVl1MQCqA1F1G7Y4F3OtyH62LiR2uJiqpcupeLTT6nduLHxYAqwzEz8+flbwqfYcnxbQcL2/HwsoF/vIiIiItL59P9CRURE2oGZYdnZhLKzYcjglPeLlJd7M6Y2bow+4paL6y9Xfv11XVvS+0tF+XJzG4ZT+Xn48vLw53nL4SVLKc3IxJ+fhz8vD19+vr6VT0RERETaRCGTiIhIGvkyM/FlZqZ0o/MY5xyRkhIvcNqQPJCKX65asoRIcTG1mzdDJAJAAbDk9tsTivHhz83Fl5+PPy8WPkWDqbzceiGVPy8PX25e3HIu5ve33wsjIiIiIt2OQiYREZFuxszw5+biz82FIUNS3s9FIkTKyogUF/Pu7NnsMHYctZuKiWzaRO2mzVuWizdRu2kTkU2bqF65ktpN3jrV1U2O74vW5MvNxZebgz8nN9qWgy8n2pabiy87Z8tyTnR7bq43k8rna+vLIyIiIiJpopBJRERkK2E+H/6cHPw5OdQMHUr2LtNT3tc5hysvp3bzZmqLY8GUF0hFNtcPpmpLSohs3kz1mtVEvv2WyObN1JaUQE1NMwUavuxsL5jKyUkIq7aEUluWtzz7srPrHhYK6bI/ERERkTRQyCQiIiLNMjMsKwtfVhbB/v1bvL9zDldRQe3mzUSiIVTt5hIiJZu9trrl6LYSr6127TqqFi7aElQ1M5sK8L7NLy508mVnNwiifDnZ9fvk5ODLarjdsrIUWImIiIikSCGTiIiIdDgzw6L3n6Jfv1aN4ZzDVVZ696OKD6tKS4mUlBIpjXuUlHjPZd56bfTSv/htOJdK4fiyspIGVf6chCArKxtfVia+rCzvXOPWfZnR9qwsLBhUcCUiIiI9Uo8MmczscODwMWPGpLsUERERaSdmhmVk4MvIIFBY2KaxYpf/RUpLvcv7SsviQqqSeoFVbSywivUpKaG6qIjK2PbS0tRmWMUEAnWhU91zVhaWFQ2m6triA6ssfJlZ+LLjAquEIMvCYYVXIiIiklY9MmRyzj0FPDV16tTvpbsWERER6XriL/8L9O3b5vEiVVVESktxZWVEysu9G6yXRZ/Ly4iUlXmhVrL26Hpt0Qaqly2v29+VleFaEl75fPgyM72wKjMaRmVkeGFURgaWmYEvIxNfZgaW0UhbVrS9ri2j3ji635WIiIg0pUeGTCIiIiKdyRcK4QuFoFevdh3XVVc3CK1cNJyKlJd7s6vKt4RWLj7Eqqjwgq2KCqo3FePKK+q1uYqKlhcUu+wxOqOsRQFWZgYWCuPLCHuzrsIZ+MIhLCMDC4fxhcPecijk7R8O69sGRUREuhmFTCIiIiJdlAWD+INB/Hl57T62i0S8e1zFBU+R8nJcRQWR8gpcRTmR8goiFeVbAqpkbdF9azdvombNmvrjVVS07FLCBBYM1g+hwmEsI4wv3ERbRhgLeYGVLxzCwhnR7V6wZeFYiBUXctULv3TZoYiISGspZBIRERHZCpnPt+Vm7O08Ayueq64mUlnpBU+VVbjKimi4VYmrrPC2VVTiqqKBV91ypdevMtpWWRntW1G3vWbz5obbo4+2sFDIC5tCIQqd49u8vC1tYW/WmoXCdX28tnDcfkEv1Ipr84VDcdvj+sTGCCX08fvb6ScgIiLSeRQyiYiIiEiHic3GIien047pIhFcVdWWMKvKC6ci8WFWNPCKhVle4FW1JcSqqsJVVrFy8WJ69e5NpKrS26eqyrskcePG6DG847iqqug+lVBb2/aTCAS8SwfjAq8GYVY0lEpsSxqCxcKt2HJiuBXXVrddQZeIiLSQQiYRERER6VHM58MyMiAjA39+28aaP2cOO86c2aJ9XE2NFzpVVuKqqr2QKxZ6xbfFwqm4oMpVxfWprKwXeNXvU+Xdoys6cytSXVUXgsX6tVkgsCXkqgug4gKsWOgVTrYeC7ZCScKthusNgq5QCIJBXbooItLNKGQSEREREWlHFghggQC+rKy01eCcw1VX14VQrjIaVsVCqEovqIqFXd6lhlX1g666YKv+et2sropKaoo34arjgrLYcSoqIBJp20mY1QVPvsQgKyOjfqgVu+9WdL3u3lx1gVdG/fArdk+uBuNHHwq4RERaRSGTiIiIiEgPY2ZYKAShEOTmpqUGV1OzJXSqTAizqqsSwq3EsKsy7n5dVfXu01UXdEVDri2hV8WWY7Xm2xPjxQdcoVDyUCtuFlcqoVbiZYsWDHlhViiYsBz0ZoAFAvqGRRHpdhQyiYiIiIhIu6ub0ZWd3enHTjqTq95y1ZYbz8dmaFVW1J+9FQu14gOvuJlc9QKuxBvPO9c+JxIIbAmdgsEtj/hgqrG2WGCVGGA16NPUepLxEmtRECYicRQyiYiIiIhIj5LOmVzOOYh9q2LipYkVFVuWq6u9e29Vxz2qqlq2HmurqiJSWtrsPu1yU/pE0SCsr8FXmVlbwqdYQJbsEQpuCdCCScKvxP1DDcdocv9Q8uPj9+sySJEOppBJRERERESknZgZhEL403ipYmNcbW3djemTBlFVzYRZja1XVbFs0SJ69+/XYD+qa+qWI2VlDcetrvZqit+npqZjXgCzeiEWDcKrUPKQK+nD206j20NbxkgSkiUeg/j9YiGZZolJN6SQSUREREREZCtgfj/m90M43O5jfzFnDgNb+E2MjXGRSDQMq8ZVV0FCCNXwkWx7Vb3Qqn5A1nTIVReKlZdH90+yT3wo1l6XRyby+5sOuhJmezUIvAJNhWRbgrJ6s70a2z9ZUBYfkgUCmiUmgEImERERERER6ULM59tyuSOdf0+vlnK1tckDqFgwVVMNLQ7J4kOw+JlhycavIVJegdu0uYkxaur27yj1wqpQCiFX4myxhCBryyWRoUbGaG62WRACycfWLLGOo5BJREREREREpJXqZohlZKS7lGbF7hnW3CWLDWZ81TTcp/44zQVlNfVml0UqyreMUdXY8as6fpZYM5dFUi/IShJ2pRyUeY9AYd+OOZ8uRCGTiIiIiIiIyFYgds8wC4XSXUpK6maJxUKouuCrqn7Y1dgllVXV9fdP2LfeJZWNXRJZUUmkpLSZSzZTmyWWtcsuMOu0Tnjl0kchk4iIiIiIiIh0OXWzxLoB51zT9w+rqcFCIRYuXpzuUjuUQiYRERERERERkTYws7obpzeph4dMutuViIiIiIiIiIi0mUImERERERERERFpM4VMIiIiIiIiIiLSZgqZRERERERERESkzRQyiYiIiIiIiIhImylkEhERERERERGRNlPIJCIiIiIiIiIibaaQSURERERERERE2kwhk4iIiIiIiIiItJlCJhERERERERERaTNzzqW7hg5jZmuBxemuox0UAuvSXYRIN6HPi0hq9FkRSY0+KyKp0WdFJDU95bMy3DnXN7GxR4dMPYWZfeCcm5ruOkS6A31eRFKjz4pIavRZEUmNPisiqenpnxVdLiciIiIiIiIiIm2mkElERERERERERNpMIVP3cEe6CxDpRvR5EUmNPisiqdFnRSQ1+qyIpKZHf1Z0TyYREREREREREWkzzWQSEREREREREZE2U8jUxZnZQWY238y+MbNfpLsekXQys6Fm9oqZfW5mn5nZedH23mb2opl9HX3uFW03M7sp+vn5xMx2TO8ZiHQuM/Ob2cdm9nR0faSZvRv9TPzDzELR9nB0/Zvo9hFpLVykE5lZgZk9amZfmtkXZrarfq+INGRmF0T//9f/zOxhM8vQ7xURj5ndY2ZrzOx/cW0t/l1iZqdF+39tZqel41zaSiFTF2ZmfuAW4GBgO+BEM9suvVWJpFUNcKFzbjtgF+BH0c/EL4CXnXNjgZej6+B9dsZGH98Hbuv8kkXS6jzgi7j1q4EbnHNjgA3AmdH2M4EN0fYbov1EthZ/Bp5zzm0DTMb7zOj3ikgcMxsM/ASY6pybCPiBE9DvFZGY+4CDEtpa9LvEzHoDlwPTgWnA5bFgqjtRyNS1TQO+cc4tcM5VAY8AR6a5JpG0cc6tdM59FF3ejPeHwGC8z8X90W73A0dFl48EHnCed4ACMxvYuVWLpIeZDQEOBe6KrhuwD/BotEviZyX2GXoU2DfaX6RHM7N8YAZwN4Bzrso5txH9XhFJJgBkmlkAyAJWot8rIgA4514DihKaW/q75EDgRedckXNuA/AiDYOrLk8hU9c2GFgat74s2iay1YtOu94BeBfo75xbGd20CugfXdZnSLZmNwI/ByLR9T7ARudcTXQ9/vNQ91mJbi+O9hfp6UYCa4F7o5eW3mVm2ej3ikg9zrnlwLXAErxwqRj4EP1eEWlKS3+X9IjfMQqZRKTbMbMc4N/A+c65TfHbnPeVmfraTNmqmdlhwBrn3IfprkWkiwsAOwK3Oed2AErZcjkDoN8rIgDRS3aOxAtmBwHZdMMZFiLpsjX9LlHI1LUtB4bGrQ+JtolstcwsiBcwPeSc+0+0eXXscoXo85pouz5DsrXaHTjCzBbhXWq9D959ZwqilzlA/c9D3Wcluj0fWN+ZBYukyTJgmXPu3ej6o3ihk36viNS3H7DQObfWOVcN/Afvd41+r4g0rqW/S3rE7xiFTF3b+8DY6Lc2hPBurvdkmmsSSZvotfx3A184566P2/QkEPv2hdOAJ+LaT41+g8MuQHHclFWRHss5d4lzbohzbgTe747ZzrmTgVeAY6PdEj8rsc/QsdH+W8V/bZOtm3NuFbDUzMZHm/YFPke/V0QSLQF2MbOs6P8fi31W9HtFpHEt/V3yPHCAmfWKzh48INrWrZg+612bmR2Cd18NP3CPc+6q9FYkkj5mtgfwOvApW+4zcynefZn+CQwDFgPHOeeKov8n6C9407nLgNOdcx90euEiaWRmM4GfOecOM7NReDObegMfA6c45yrNLAP4G959zoqAE5xzC9JUskinMrMpeDfIDwELgNPx/kOsfq+IxDGz3wDH433b78fAWXj3i9HvFdnqmdnDwEygEFiN9y1xj9PC3yVmdgbe3zcAVznn7u3E02gXCplERERERERERKTNdLmciIiIiIiIiIi0mUImERERERERERFpM4VMIiIiIiIiIiLSZgqZRERERERERESkzRQyiYiIiIiIiIhImylkEhERkR7BzO4zs6fTXUc8MzvSzL42sxozu6+RPnPM7C+dXFqzumJdZjbCzJyZTU13LSIiItKQQiYRERFps2jA48zsVwntM6PthemqLc3uBv4NDAfOa6TPMcAlsRUzW2RmP+uE2mLHm2VmJc3VJSIiItIchUwiIiLSXiqAi8ysb7oLaU9mFmzlfgVAH+B559xy51xxsn7OuSLn3OY2lNjY8UNt2b+j6hIREZGeSyGTiIiItJdXgEXArxrrkGxmU+IlUHF9DjazD82s3MxeN7MhZraXmc0zsxIze9rM+iQ5xi/NbHW0z71mlhm3zczs52b2bXTcT83slCS1nGhms82sHDi7kXPpZWb3m9mG6FgvmdmE2DkAG6JdZ0fHnNnIOHWXpZnZHLxZT9dE93Fx/XYzs1fNrMzMlpvZbWaWlzDObWZ2rZmtBd6Mtv/UzD4xs9LofndFA7BYnfcC2bHjmdkViXU1d77R7bOir/m+Zva/6PFeMbORcX2GmtkTZlYUPY8vzeyEZK9LKszMZ2a3mNlCMxvb2nFERESkfShkEhERkfYSAX4BnGNmo9thvN8A5wPTgV7AP4BfA98HZgITgCsS9tkLmAzsC3wHOAC4Om77lcCZwI+A7YA/ALeb2aEJ4/wBuDXa5/FG6rsvWtuRwDSgDHguGmq9Fa2PaB0Do23NOQZYBvw2us9AADObBLwAPBk9v2OAKcA9CfufAhiwJ3BqtC2C9zpOAE6K1npzdNtb0W1lcce7thXnGxPGu8TuDGBXoAD4a9z2W4EsYO9oPecDGxs5XpOiM8wewvuZ7+6c+7o144iIiEj7CaS7ABEREek5nHPPmtmbwFVAq2eoRP3KOfc6gJn9FS8Y2ck591G07X7g2IR9aoHTnXMlwP/M7GLgbjOL3Vvop8ABsXGBhWY2DS90eiZunJudc482Vlh01swRwF7Oudeibf8HLAFOds7dZWZrot2LnHOrUjlh51yRmdUCmxP2uQj4h3PuurgafgB8bGb9nHOxYy10zl2YMOaNcauLzOznwBNmdppzrsrMir1ujdfY3PkCd0W7BoAfOefmR/tcC9xjZuacc3iztP7tnJsXqzeV1yWJbOApvBBrhnOuqJXjiIiISDtSyCQiIiLt7WLgbTO7po3jfBK3vDr6/GlCW7/EfaIBU8zbQAgYjTfLJgNv9o2L6xPEu8wv3gfN1LYt3gyht2MNzrliM/sUb/ZTe9sJGGNmx8e1WfR5NBALmT5M3NHM9sGbXbQtkA/48V6TAcCKFI+f6vlWxgKmqBXRY/UCioA/A381s4OAl4HHnHMNak7Bg8BKYG/nXGkr9hcREZEOoMvlREREpF05597D+0a1PyXZHIk+W1xbYzfWro4fNjp2YltL/r9MrO/heJeaxR4T8C6ri9eW4MI136XFfHizhabEPSYDY4G5cf3q1W1mw/FmaH0BfBcvrDojurlNNwaPE3++NY1s8wE45+4GRuLdB2oc8FbsHlAt9AwwEdi9FfuKiIhIB1HIJCIiIh3hUrz7Ah2U0L42+jwwrm1KOx53kpllx63vAlQB3wKfA5XAcOfcNwmPxS08zhd4/z9q11hD9Cbck6LHaYsqvNlG8T4CJiSp+xvnXHkTY03FC5MucM697Zz7ChiUwvEStdv5OueWOefucM4dx5Z7bLXUXXj3c3rczPZvxf4iIiLSARQyiYiISLtzzn0D3AGcl7DpG2ApcIWZjTOzA4BftuOhA3j3AJoQDR/+CNzpnCt1zm3Gu6n1tWZ2hpmNMbMpZnaOmbUo6IjeZPoJvJuG7xm9MfeDwCbg7208h0XAnmY22LZ8C9/VwDQz+6uZ7RCt/TAzu72Zsb7G+/9755vZSDM7ES+cSTxehpntb2aFZpaVOEh7na+Z/dnMDjKzUWY2BS+EbFUo55y7A7gABU0iIiJdhkImERER6Si/JeHyqejlbicAo4B5eN8gd2k7HvNV4DPgFeAxYDbw87jtv8L7RrqfRfu9iPftb625AfXpwHt43/j2Ht63ph3UzMyiVPwaGIo3+2otgHPuE2AGMALvHOfhfQPe6uRDeKL7nYd3w/PPgbPwzj2+z1t43wD3cPR4Pye59jhfH94N3D/He+1XA6fFNprZHDObk+pgzrnbgQtR0CQiItIlmPdFHyIiIiIi6WVmi4G/Ouf+kO5aREREpOU0k0lERERE0s7MJuDdM+u6dNciIiIiraOZTCIiIiIiIiIi0maaySQiIiIiIiIiIm2mkElERERERERERNpMIZOIiIiIiIiIiLSZQiYREREREREREWkzhUwiIiIiIiIiItJmCplERERERERERKTNFDKJiIiIiIiIiEib/T8wG1ox/Yf/sAAAAABJRU5ErkJggg==\n"},"metadata":{"needs_background":"light","image/png":{"width":1177,"height":339}},"output_type":"display_data"}],"execution_count":null},{"cell_type":"markdown","source":"Above are plots showing how the norm changes as the number of iterations increases in the NMF algorithm, for $d=\\{16, 32, 64, 144\\}$. In the previous sections, NMF reconstructions for $d=16$, $d=64$ and $d=144$ have been examined. For $d=16$, the reconstructions were dissociated and blend, and few distinct features were reconstructed with high precision. For $d=64$, more features were learned and reconstructed to a higher degree of precision, however, the deviation from the original images were noticeable. For $d=144$, the reconstructions were sharper and more detailed features were more apparent. It is difficult to predict exactly which convergence value for the norm the different rank approximations will yield just by examining the plots, and it is also difficult to say something about how well the images are reconstructed for a given convergence value of the norm. One must take into consideration the size of the matrix that is reconstructed, and the scaling of the values in the matrix. The norm is proportional to the scaling, and in general more non-zero elements corresponds to a larger norm (not always). We have a $(24 \\cdot 24 \\cdot 3 \\times 500)$-matrix, where all elements hold a value between $0$ and $1$. \n\nThe norm converges to a value of around $85$ and $65$ for $d=16$ and $d=32$ respectively, while for $d=64$, it converges to around $40$. The algorithm requires more iterations before it converges for higher rank approximations, hence it is somewhat difficult to see whether the norm has indeed converged to a final value for $d=144$. However, the graph undoubtedly flats out close to $1000$ iterations, and it seems to converge to a value close to $10$.\n\nIt is as expected that the norm converges to a smaller value for higher rank approximations, however as discussed above, it is difficult to conclude anything from each convergence value individually. To really know anything about the precision, in the practical sense, not numerical, of the image reconstructions, one must examine the plots, not the value of the norm. Comparing different values of the norm for different rank approximations however, is useful, and tells us something about the cost/benefit-ratio of increasing rank, which will be further examined in the next section.","metadata":{"tags":[],"cell_id":"2d3f40e00da449a78fb0e5e30e2e7f73","deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":193},"deepnote_cell_type":"markdown"}},{"cell_type":"code","source":"def ex2f():\n    maxIterations = 1000 \n    dList = [16, 64, 128, 256, 373, 512, 1024]\n    normList = np.zeros(len(dList))\n    for i in range(len(dList)):\n        W, H, opacityMatrix, norm = NMFImages(faces, dList[i], maxIterations)\n        normList[i] = norm[-1]\n\n    plt.figure(figsize=(13, 6)) \n    plt.axes([0, 0, 2, 1])\n    plt.plot(dList, normList) \n    plt.title(f'A = Image Matrix with shape (24*24*3 x 500)', fontsize = 20)\n    plt.xlabel('Number of columns in W, d', fontsize = 18)\n    plt.ylabel(r'$||A - W H||_F$', fontsize = 18)\n    plt.axvline(x = 387, label = 'Elements in WH = elements in A', color = 'r', linestyle = '--')\n    plt.legend(fontsize = 18)\n    plt.semilogy()\n    plt.grid()\n    plt.show()\nex2f()","metadata":{"tags":[],"cell_id":"866b3085e37946489e9ce26f19fbbdf9","source_hash":"275cff0e","execution_start":1649447735671,"execution_millis":2165155,"deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":199},"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"code"},"outputs":[{"data":{"text/plain":"<Figure size 936x432 with 1 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is a plot showing the final value of the norm for varying values of $d$. The computations are done with the total number of iterations set to $1000$, for $d=\\{16, 64, 128, 256, 373, 512, 1024\\}$. $d=373$ is included since it is the rank of the image matrix, and it is of interest to examine whether the norm converges to a smaller value if $d$ is chosen larger than the rank, or if the $d$=rank indeed yields a best possible approximation. It is expected that, in general, larger $d$ corresponds to smaller norm, however at some point it is expected that the norm converges to the same value even if $d$ is increased, as there is a limit to how precise a reconstruction the NMF might yield (this limit could be a perfect reconstruction, but that is not the case here). One must also take into consideration the fact that for larger $d$, more iterations might be required before the norm converges. Hence, the algorithm might not converge within the set number of iterations for larger $d$, and the plot might not show a true representation of which $d$ yields the most precise approximation. \n\nIn the plot, the value of $d$ which corresponds to the number of elements in $W$ and $H$ equalling the number of elements in the orignal image matrix is marked with a vertical line. Increasing $d$ further than this  value is meaningless if the sole purpose is to reduce the size of the dataset. This value is found by solving the equation\n\n$$\n\\# \\text{elements in W and H} = \\# \\text{elements in original image matrix}\n$$\n$$\n\\Rightarrow d \\cdot 24 \\cdot 24 \\cdot 3 + 500 \\cdot d = 24 \\cdot 24 \\cdot 3 \\cdot 500,\n$$\n\nand is equal to $387$ (after rounding down). \n\nThe plot confirms that the higher the rank of the approximations, the more precise are the reconstructions. Even when $d$ is increased beyond the original matrix rank of $373$, the norm converges to a significantly smaller value. Examining the point at which the size of the reconstructed dataset equals the size of the original dataset, we see that the norm converges to a value of around 6 for this $d$. In other words, even by reconstructing the images to a dataset of equal size to the orignal one, the NMF is not capable of a perfect reconstruction. This all but confirms the limitations the non-negativity constraint imposes on the reconstructions. If the purpose is to obtain a compressed dataset, one must accept a norm of at least 6.\n\nThe graph decreases at a higher rate for smaller values of $d$, whiler for larger $d$ it flats out. This means that for smaller rank approximations, the cost/benefit ratio of further increasing $d$ is smaller, i.e. the improvement of the reconstruction is relatively greater compared to the increase in runtime and datasize for smaller $d$ than for larger $d$. Hence, for larger $d$, it is increasingly more important to carefully examine whether further increasing the rank is indeed beneficial. This is even more important when noise is added to the equation, which it will be throughout the rest of the project.","metadata":{"tags":[],"cell_id":"57b1a8aba6b04d4f95cf92e68a6b7a8a","deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":205},"deepnote_cell_type":"markdown"}},{"cell_type":"markdown","source":"## Task 3","metadata":{"tags":[],"cell_id":"afa8c13dfdf942b7a16dcdbf0fc19ae6","is_collapsed":false,"formattedRanges":[],"deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":211},"deepnote_cell_type":"text-cell-h2"}},{"cell_type":"markdown","source":"In the following section static noise is added to the images. The greatest consequence of adding the static noise is that previously equal features - the 3D glasses, the cigar, the single earring - now look different. This has the consequence that a better NMF, being an NMF with higher rank, will learn the noise. This means that a better reconstruction actually will shift a reconstruction away from its original state (without the noise). This phenomenom os called overfitting, and is crucial concept in this section. \n\nThe NMF used in this section can remove noise without knowledge of the original unpolluted dataset, so the method is unsupervised. However, because we have access to the original dataset, the norm of the difference between the denoised dataset and the original dataset will be calculated in order to analyse what NMF rank-values yield the best denoising. \n\nTo mimic the effects of random processes that occur in nature, we have applied a model called $\\textit{Additive Gaussian noise.}$ This model accurately reflects many systems and is a simple model to handle mathematically. We have applied the model in the following way:\n$$ \nA_{noisy} = A + \\sigma E \n$$    \nwhere $\\sigma$ is a positive scalar which represents the noise level and E is a matrix with the excact same shape as the original matrix A. It is called Gaussian noise because the components of the matrix $E$ are realizations of the standard normal distrubution. Furthermore we have made some assumptions to avoid certain difficulties. We only added noise on the colour channels that are non-zero for each respective pixel. We also clipped the values of each pixel to hold a value between 0 and 1, to make sure that the noisy images are plottable images.\n\nFor all plots and subtasks in task 3, we are using $\\sigma = 0.10$ and \n$N$(Number of images) $ = 500$.","metadata":{"tags":[],"cell_id":"7f64301132a04ca7875c9edf2e58d179","deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":217},"deepnote_cell_type":"markdown"}},{"cell_type":"code","source":"def add_noise(imgs_reshaped):\n    \"\"\"\n        Adds gaussian noise to images as described in text.\n        Note that imgs must be given as a (24*24*3, N) numpy array, i.e the reshaped images\n    Input:\n            imgs_reshaped: (1728,N) numpy array\n            sigma: scalar, noise level\n    Output:\n            noisy_faces: (1728,N) numpy array containing noisy images\n    \"\"\"\n    # Noise level\n    sigma = 0.10\n\n    # Array that will store the rgb channels of the noisy images\n    noisy_faces = np.copy(imgs_reshaped)\n\n    # Number of noisy values we need\n    nnzero = imgs_reshaped[np.nonzero(imgs_reshaped)].shape[0]\n\n    # Sample noisy values and add noise\n    noise = np.random.normal(0.0,1,nnzero)\n    noisy_faces[np.nonzero(imgs_reshaped)] += sigma*noise\n    \n    # Clip to lie between 0 and 1 so that we can still interpret them as images\n    noisy_faces = np.maximum(0.0,np.minimum(1.0, noisy_faces))      \n\n    return noisy_faces\n\n\"\"\" Global variables for task 3 \"\"\"\nopacityMatrix = faces[:,:, 3, :]         # Stores the opacity channel in 24 x 24 x N array\nimagesWithoutAlpha = faces[:,:,:3, :]    # Removes alpha from the images\nimagesWithoutAlphaReshaped = np.reshape(imagesWithoutAlpha, (np.prod(imagesWithoutAlpha.shape)//N, N))\nnoisyFaces = add_noise(imagesWithoutAlpha)\n\n\"\"\" Reconstructing noise images with opacity \"\"\"\n\nnoiseWithOpacity = np.zeros(faces.shape)\nnoiseWithOpacity[:,:,:3,:] = noisyFaces.reshape(imagesWithoutAlpha.shape)\nnoiseWithOpacity[:,:,3,:] = opacityMatrix\n\ndef ex3a():\n\n    plotimgs(noiseWithOpacity, d = None, nplot = 8, filename=\"Noisy_Images.png\")\n    noisyFacesReshaped = np.reshape(noisyFaces, (np.prod(noisyFaces.shape)//N, N))\n    \n    noiseResidual = np.linalg.norm(imagesWithoutAlphaReshaped - noisyFacesReshaped, ord = 'fro') # Calculate frobenius norm\n    print('||A - A_noisy||_F for 500 images = ',noiseResidual)\n    return noiseResidual\n    \nnoiseResidual = ex3a()","metadata":{"tags":[],"cell_id":"7eba019393af49638f755f552ca922c9","source_hash":"8250a108","execution_start":1649449900867,"execution_millis":3536,"deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":223},"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"code"},"outputs":[{"data":{"text/plain":"<Figure size 1152x1152 with 64 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- A_noisy||_F for 500 images =  41.711047061456455\n","output_type":"stream"}],"execution_count":null},{"cell_type":"markdown","source":"In the above plot we see a representation of the images containing noise. The noise is represented in the plot as random pixels in the faces which are given random amounts of noise, corresponding to random colours, polluting the skin colour and appearance of separate features in the faces.\n\nExamining the norm of the difference between the matrix containing the noisy images and the matrix containing the original images, $||A_{noisy} - A||_F $, equal to $41.7$, it is obvious that there is indeed a difference between the noisy images and the original images, also mathematically. Nevertheless, the norm is not neccessarily the best way to describe difference between images from a human standpoint. For example, two face images with a minor difference in the colour of the skin can have a major difference in norm, but two face images where the eyes are completley different can have a small difference in norm. The norm will not necessarily reflect what we humans consider similar, but it will reflect wether or not the values of the pixels are close or far off. This must be taken into consideration when computing and interpreting the value of the norm in denoising processes.","metadata":{"tags":[],"cell_id":"d68246ad9995447bbeb4b088e6bd4237","deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":229},"deepnote_cell_type":"markdown"}},{"cell_type":"code","source":"def ex3b():\n    d = 64\n    Wnoisy, Hnoisy, opacityMatrix, norm = NMFImages(noiseWithOpacity, d, maxIterations)\n    \n    WnoisyReshaped = np.reshape(Wnoisy,(24,24,3,d))\n\n    plotimgs(WnoisyReshaped, d, 8, filename=\"W_noisy_columns_images.png\")\n    plotimgs(W_reshaped, d, 8, filename=\"W_Columns_images.png\")\n\n    \"\"\" Reconstruction, \"denoised\" images \"\"\"\n    facesNoiseRGB = noisyFaces[:,:,:3,:] # Lagrer rgb verdiene til rekonstruering\n\n    reconstructionNoise = Wnoisy @ Hnoisy # (1728,500)\n    \n    denoiseWithOpacity = np.zeros(faces.shape)\n    denoiseWithOpacity[:,:,:3,:] = reconstructionNoise.reshape(facesNoiseRGB.shape)\n    denoiseWithOpacity[:,:,3,:] = opacityMatrix\n    \n    plotimgs(denoiseWithOpacity, d, 8, filename=\"Noisy_images_reconstructed.png\")\n    plotimgs(facesWithOpacity, d, 8, filename=\"Reconstruction_images.png\")\n    \n    noiseReconResidual = np.linalg.norm(imagesWithoutAlphaReshaped - reconstructionNoise, ord = 'fro') # Calculates frobenius norm\n    reconImages = facesWithOpacity[:,:,:3,:]\n    reconImages = np.reshape(reconImages, (np.prod(reconImages.shape)//N, N))\n\n    reconstructionResidual = np.linalg.norm(imagesWithoutAlphaReshaped - reconImages, ord = 'fro')\n\n    print('||A - A_noisyRecon ||_F for 500 images = ',noiseReconResidual)\n    print('||A - A_Recon ||_F for 500 images = ', reconstructionResidual)\n\nex3b()","metadata":{"tags":[],"cell_id":"5e837a2f1c8640548b7e87a3bf74fc0e","source_hash":"e7571a8e","owner_user_id":"6994fb84-46cf-483d-91ee-5452102ea79a","execution_start":1649449904414,"execution_millis":83948,"deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":235},"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"code"},"outputs":[{"data":{"text/plain":"<Figure size 1152x1152 with 64 Axes>","image/png":"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\n"},"metadata":{"image/png":{"width":1142,"height":1213}},"output_type":"display_data"},{"data":{"text/plain":"<Figure 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size 1152x1152 with 64 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- A_noisyRecon ||_F for 500 images =  42.699617815418755\n||A - A_Recon ||_F for 500 images =  38.876361390036934\n","output_type":"stream"}],"execution_count":null},{"cell_type":"markdown","source":"The above plots show the reconstructions of the noisy images and the columns of $W$ interpreted as images. \n\nThe reconstruction of the noisy images $WH_{\\text{noisy}}$ is less noisy than the original noisy images, i.e. noise is removed when the NMF is applied on the polluted dataset with $d=64$. With $d=64$, $W$ consists of 64 columns which results in the NMF not learning that many features. The effect of this is that some of the noise is being overlooked and not saved in $W$. For larger values of $d$, $W$ contains a higher number of columns and therefore would have more space to save data, both features and noise. So for higher values of $d$ the reconstruction of the noisy images would contain more noise. By comparing the reconstructed images $WH$ for the noisy dataset and the original, unpolluted images we notice they are almost identical, which confirms how applying the $NMF$  with $d=64$ removes almost all the noise. However, the norm of the difference from the original images for both reconstructions are quite similar, they only differ with a value of about $3.8$. This is likely a result of the fact that the Frobenius norm does not take into consideration what is \"similar\" from a human point of view.\n\nIn the plot that represents the columns in $W$ interpreted as images, we observe as in task 2 that each column in $W$ contains some key feature of the original image. By comparing the columns of $W$ from task 2 and $W_{\\text{noisy}}$ interpreted as images it looks like the noise has minimal effect on $W_{\\text{noisy}}$. For most of the images, it seems as $W_{\\text{noisy}}$ detects the same features as $W$, with the exception of a few images where $W_{\\text{noisy}}$ clearly detects noise instead of a feature. This all indicates that executing NMF for d = 64 stores more actual features of the images, rather than the noise that the images contain. As the noise is spread arbitrarily across the dataset, \"on top of\" the original images, it is as expected that the NMF does not recognize it as important features of the dataset, thus not storing it in the columns of $W$.\n\n","metadata":{"tags":[],"cell_id":"f787f3bf9f3646bd81329d2c9ca2dfb8","deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":241},"deepnote_cell_type":"markdown"}},{"cell_type":"code","source":"def ex3c():\n    dList = [64, 96, 112, 128, 256, 512, 1024]\n    normListNoise = np.zeros(len(dList))\n    normList = np.zeros(len(dList))\n\n    for i in range(len(dList)):\n        Wnoisy, Hnoisy, opacityMatrixNoisy, normNoisy = NMFImages(noiseWithOpacity, dList[i], maxIterations)\n        reconNoiseReshaped = np.reshape(Wnoisy @ Hnoisy, (np.prod((Wnoisy @ Hnoisy).shape)//N, N))\n        normListNoise[i] = np.linalg.norm(imagesWithoutAlphaReshaped - reconNoiseReshaped, 'fro') #Faces64 is images without noise\n        \n        W, H, opacityMatrix, norm = NMFImages(faces, dList[i], maxIterations)\n        normList[i] = norm[-1] # Siste elementet i norm listen som er feilen ved siste iterasjon\n    \n    minIdx = int(np.argwhere(normList == np.min(normList)))\n    minNormD = dList[minIdx]\n    print('\"Best fit\" value of d = ', minNormD)\n\n    minIdxNoise = int(np.argwhere(normListNoise == np.min(normListNoise)))\n    minNormDnoise = dList[minIdxNoise]\n    print(' \"Best fit\" value of d for noise reconstruction = ' , minNormDnoise)\n\n    plt.figure(figsize=(13, 6))\n    plt.axes([0, 0, 2, 1])\n    plt.plot(dList, normListNoise, label = r'$||A - W@H_{noise}||_F$') \n    plt.plot(dList, normList, label = r'$||A - W@H||_F$')\n    plt.axhline(y = noiseResidual, color='r', linestyle='--', label = r'$||A - A_{noisy}||_F$')\n\n    plt.legend(fontsize = 18)\n    plt.title(f'A = Image Matrix with shape([24*24*3] x 500)', fontsize = 20)\n    plt.xlabel('Number of columns in W, d', fontsize = 18)\n    plt.ylabel('Frobenius norm of the error', fontsize = 18)\n    plt.semilogy()\n    plt.grid()\n    plt.show()\nex3c()","metadata":{"tags":[],"cell_id":"46fe9b5a0fc14ecb9fee04e466cd7d37","source_hash":"1945a4eb","owner_user_id":"c2406dbd-950c-4bc1-b1b5-47d2744c1a77","execution_start":1649449988353,"execution_millis":4116973,"deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":247},"deepnote_to_be_reexecuted":false,"deepnote_cell_type":"code"},"outputs":[{"name":"stdout","text":"\"Best fit\" value of d =  1024\n \"Best fit\" value of d for noise reconstruction =  128\n","output_type":"stream"},{"data":{"text/plain":"<Figure size 936x432 with 1 Axes>","image/png":"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\n"},"metadata":{"needs_background":"light","image/png":{"width":1934,"height":506}},"output_type":"display_data"}],"execution_count":null},{"cell_type":"markdown","source":"Above is a plot showing the reconstruction error for the noisy images and the orginal images respectively, after conducting the NMF algorithm for ranks $d=\\{64, 96, 112, 128, 256, 512, 1024\\}$. \n\nIt appears from the plot that the reconstruction error for the noisy images as a function of $d$ yields a \"U\" -like shape, while the reconstruction error of the original images as a function of $d$ yields an \"L\" -like shape. The reconstruction error for the noisy images reaches a point of minimal value at approximately $d = 128$, which is the \"best fit\" and provides the lowest reconstruction error. In other words, this choice of $d$ provides the optimal balance between learning more of the features of the original images, while at the same time avoiding learning too much of the noise. This rank corresponds to a reconstructed dataset 33% the size of the original, meaning the NMF has reduced the size of the data considerably while at the same time removing noise from the dataset. \n\nAs the value of $d$ is smaller, i.e. less than $128$, we observe underfitting. Our algorithm may manage to not capture too much noise, but it is unable to capture the complexity of the data beacuse there simply is not enough columns in $W$ to do so. For larger values of $d$ ($d > 128$) we observe the phenomena called overfitting. Our algorithm learns more noise aswell as more features, instead of just fitting the features. $W$ will be able to store more data, and thus store more of the noise. The more noise the reconstructed images contain, the more they differ from the original images. This is reflected by the plot in that the reconstruction error increases slowly, but surely. As $d$ increases the reconstruction error will converge towards the dotted line, and eventually tangent it. This dotted line represents the difference between the original images and the same images containg (all) the added noise. After the reconstruction error has reached its minimum, this dotted line can be interpreted as a kind of upper limit for the error. For large values of $d$ the NMF algorithm will learn almost all the noise, but it cannot learn more noise than what is orignally added to the images. So as long as the algorithm learns essentially all the \"features\" of the images for larger values ​​of $d$, then this horizontal, dotted line can be interpreted as an upper limit on how large the value of the reconstruction error can ever be (disregard the smaller $d$). However, due to non-negative constraint, the NMF algorithm will not always be able to make perfect reconstructions of the images, no matter the value of $d$. Therefore it is not entirely correct to call it an upper limit, but in our situation this size sort of acts as an upper limit for the reconstruction error.\n\nAs discussed earlier we notice an \"L\"-like shape when the reconstruction error of the original, unpolluted images is plotted as a function of $d$. For small values of $d$ the graph decreases rapidly, and for large values of $d$ the graph flattens out. This a consequence of the fact that there exists a limit to how presice a NMF reconstruction can be. At some point the reconstruction error converges to the same value even if $d$ is increased further.","metadata":{"tags":[],"cell_id":"b5ef472ec8b64876b9bb41659071962c","deepnote_app_coordinates":{"h":5,"w":12,"x":0,"y":253},"deepnote_cell_type":"markdown"}},{"cell_type":"markdown","source":"### Conclusion\n\nData manipulation provide different ways of interpreting datasets. This project has examined the Lee and Seung's multiplicative update mehtod for non-negative matrix factorization, and the method has been applied on the Cryptopunk dataset. In a broad scheme of things our result can be devided into three comprehensive measures: $\\textbf{I)}$ the compression of datasets using NMF, $\\textbf{II)}$ the ability of the NMF-method to extract underlying features in a dataset, and $\\textbf{III)}$ the ability of the NMF-method to remove noise and irregularities from a dataset.\n\nThe consistent/general trend of the NMF-method for decomposing the Cryptopunk dataset is that higher rank approximations yield reconstructions that are more representative of the original dataset, with respect to the Frobenius norm. However, perfect reconstructions were not obtained, even when the resulting dataset was larger than the original - which is likely a result of the limitations of the method due to the non-negativity requirement. We observed the methods ability to extract underlying features of the dataset, and for increasing rank, higher detailed features decompositions were learned, yielding more representative reconstructions. However, as a result of the method being purely mathematical, it does not care whether the features are interpretable from a physical point of view. This can be a disadvantage if the ambition of the NMF is to extract the constituating features, however, this may not always be the case. \n\nFor the polluted dataset containing noise, we found that NMF can be a tool for removing noise and irregularities. When denoising the images, the different rank approximations yield varying quaility reconstructions. For lower rank approximations, the method learns too few features, hence producing a bad reconstruction, i.e. underfitting, however, for higher rank approximations, learning more features means learning more noise, resulting in a bad reconstruction, i.e. overfitting. By comparing the reconstructions of the polluted dataset with the original, unpolluted, dataset, using the Frobenius norm, a minima - a rank that minimises underfitting and overfitting - can be determined. The rank of the reconstruction that produces this minima is the rank of the NMF that produces the best possible reconstruction for the NMF compared with an unpolluted image, however, in order to find this minima, knowledge of the unpolluted dataset is necessary, meaning that optimal results really can only be obtained by a supervised implementation, which can be a constraint for the method. 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