From 88f7dfb3ee3b09646f9f3bd3f5835fc949a2e4f2 Mon Sep 17 00:00:00 2001 From: muatik Date: Wed, 19 Apr 2017 23:47:11 +0300 Subject: [PATCH] adds singular value decomposition (SVD) notebook --- ALS.ipynb | 51 +- SingularValueDecomposition.ipynb | 1321 ++++++++++++++++++++++++++++++ 2 files changed, 1357 insertions(+), 15 deletions(-) create mode 100644 SingularValueDecomposition.ipynb diff --git a/ALS.ipynb b/ALS.ipynb index a77a7a0..4a3710b 100644 --- a/ALS.ipynb +++ b/ALS.ipynb @@ -2,7 +2,10 @@ "cells": [ { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "deletable": true, + "editable": true + }, "source": [ "### Aternating Least Squares" ] @@ -11,7 +14,9 @@ "cell_type": "code", "execution_count": 109, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [ @@ -25,7 +30,9 @@ "cell_type": "code", "execution_count": 110, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -57,7 +64,9 @@ "cell_type": "code", "execution_count": 111, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -93,7 +102,9 @@ "cell_type": "code", "execution_count": 112, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -117,7 +128,9 @@ "cell_type": "code", "execution_count": 113, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -143,7 +156,9 @@ "cell_type": "code", "execution_count": 114, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -195,7 +210,9 @@ "cell_type": "code", "execution_count": 118, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -258,7 +275,9 @@ "cell_type": "code", "execution_count": 106, "metadata": { - "collapsed": false + "collapsed": false, + "deletable": true, + "editable": true }, "outputs": [ { @@ -287,7 +306,9 @@ "cell_type": "code", "execution_count": null, "metadata": { - "collapsed": true + "collapsed": true, + "deletable": true, + "editable": true }, "outputs": [], "source": [] @@ -295,21 +316,21 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 2", + "display_name": "Python 3", "language": "python", - "name": "python2" + "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", - "version": 2 + "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", - "pygments_lexer": "ipython2", - "version": "2.7.10" + "pygments_lexer": "ipython3", + "version": "3.6.0" } }, "nbformat": 4, diff --git a/SingularValueDecomposition.ipynb b/SingularValueDecomposition.ipynb new file mode 100644 index 0000000..4e3e8d7 --- /dev/null +++ b/SingularValueDecomposition.ipynb @@ -0,0 +1,1321 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "from scipy.ndimage import imread\n", + "from matplotlib import pylab as plt" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "SVD is one of the matrix factorization tecniques. It factors a matrix into three parts with which we can reconstruct the initial matrix. However, reconstructing original matrix is not mostly the primary aim. Rather, we factorize matrices in order to achive following goals:\n", + "\n", + "1. to find principal components\n", + "2. to reduce matrix size removing redundant dimentions\n", + "3. to find latent dimentions\n", + "4. visualization\n", + "\n", + "In a simple terms, factorization can be defined as breaking something into its building blocks, in other terms, its factors. Using SVD, we can decompose a matrix into three separate matrices as follows:\n", + "\n", + "\n", + "\n", + "$$ A_{m x n} = U_{m x r} * \\Sigma_{r x r} * (V_{n x r})^{T} $$\n", + "\n", + "\n", + "\n", + "where \n", + "- U is the left singular vectors\n", + "- $\\Sigma$ is the singular values sorted descending order along its diagonal, and full of zeroes elsewhere\n", + "- V is the right singular vectors\n", + "- m is the number of rows, \n", + "- n is the number of columns(dimentions), \n", + "- and r is the rank." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true, + "deletable": true, + "editable": true + }, + "source": [ + "### Example" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "A = np.mat([\n", + " [4, 5, 4, 1, 1],\n", + " [5, 3, 5, 0, 0],\n", + " [0, 1, 0, 1, 1],\n", + " [0, 0, 0, 0, 1],\n", + " [1, 0, 0, 4, 5],\n", + " [0, 1, 0, 5, 4],\n", + "])" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "((6, 6), (5,), (5, 5))" + ] + }, + "execution_count": 40, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "U, S, V = np.linalg.svd(A)\n", + "U.shape, S.shape, V.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Left singular vectors" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "matrix([[ -6.60247087e-01, 2.26069179e-01, 5.21245353e-01,\n", + " 3.35555261e-01, 1.93472437e-01, -3.02061047e-01],\n", + " [ -6.08454501e-01, 3.95790275e-01, -5.15698492e-01,\n", + " -3.33151798e-01, -1.94432412e-01, 2.41648837e-01],\n", + " [ -1.01663330e-01, -1.23192712e-01, 3.35077540e-01,\n", + " 1.99266003e-01, -3.65560118e-02, 9.06183140e-01],\n", + " [ -2.85198477e-02, -7.22088959e-02, -1.20759911e-01,\n", + " 5.43202407e-01, -8.18365531e-01, -1.20824419e-01],\n", + " [ -3.04237047e-01, -6.17102951e-01, -4.95882375e-01,\n", + " 3.67195456e-01, 3.81958028e-01, 3.45227677e-16],\n", + " [ -3.00246415e-01, -6.25328844e-01, 2.99331094e-01,\n", + " -5.53899132e-01, -3.28350475e-01, -1.20824419e-01]])" + ] + }, + "execution_count": 44, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "U" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Singular values" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 11.09790031, 8.77186865, 2.12737197, 1.1338945 , 0.28195919])" + ] + }, + "execution_count": 48, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "S" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 11.09790031, 0. , 0. , 0. , 0. ],\n", + " [ 0. , 8.77186865, 0. , 0. , 0. ],\n", + " [ 0. , 0. , 2.12737197, 0. , 0. ],\n", + " [ 0. , 0. , 0. , 1.1338945 , 0. ],\n", + " [ 0. , 0. , 0. , 0. ,\n", + " 0.28195919]])" + ] + }, + "execution_count": 49, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.diag(S)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As you can see, the singular values are sorted descendingly." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Right singular values" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "matrix([[-0.53951628, -0.49815808, -0.51210235, -0.313581 , -0.31651043],\n", + " [ 0.25834007, 0.1788895 , 0.32869029, -0.62611284, -0.63340695],\n", + " [-0.46507778, 0.79607137, -0.23198155, 0.17366444, -0.25690125],\n", + " [ 0.03850227, 0.28546552, -0.28533338, -0.67545312, 0.61593422],\n", + " [ 0.65146207, 0.06794765, -0.70319506, 0.15249073, -0.23074568]])" + ] + }, + "execution_count": 55, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "V" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Reconstructing the original matrix" + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "matrix([[ 4.00000000e+00, 5.00000000e+00, 4.00000000e+00,\n", + " 1.00000000e+00, 1.00000000e+00],\n", + " [ 5.00000000e+00, 3.00000000e+00, 5.00000000e+00,\n", + " -3.67959505e-16, -1.56125113e-15],\n", + " [ -9.90609674e-16, 1.00000000e+00, -2.61737894e-16,\n", + " 1.00000000e+00, 1.00000000e+00],\n", + " [ -1.26146165e-15, -1.19057085e-16, 9.22639348e-16,\n", + " 2.17346585e-16, 1.00000000e+00],\n", + " [ 1.00000000e+00, 9.59868501e-16, -2.12447460e-15,\n", + " 4.00000000e+00, 5.00000000e+00],\n", + " [ -3.52644538e-16, 1.00000000e+00, -3.34752709e-15,\n", + " 5.00000000e+00, 4.00000000e+00]])" + ] + }, + "execution_count": 71, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def reconstruct(U, S, V, rank):\n", + " return U[:,0:rank] * np.diag(S[:rank]) * V[:rank]\n", + "\n", + "r = len(S) \n", + "reconstruct(U, S, V, r)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We use all the dimentions to get back to the original matrix. As a result, we obtain the matrix which is almost identical. Let's calculate the difference between the two matrices." + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1.147077259824516e-28" + ] + }, + "execution_count": 72, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def calcError(A, B):\n", + " return np.sum(np.power(A - B, 2))\n", + "\n", + "calcError(A, reconstruct(U, S, V, r))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Expectedly, the error is infinitesimal." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "However, most of the time this is not our intention. Instead of using all the dimentions(rank), we only use some of them, which have more variance, in other words, which provides more information. Let's see what we will get when using only the first three most significant dimentions." + ] + }, + { + "cell_type": "code", + "execution_count": 74, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "matrix([[ 3.94981237e+00, 4.88767823e+00, 4.14692509e+00,\n", + " 1.24868071e+00, 7.78234206e-01],\n", + " [ 5.05025903e+00, 3.11156219e+00, 4.85366219e+00,\n", + " -2.46798640e-01, 2.20024748e-01],\n", + " [ -1.98464008e-03, 9.36200386e-01, 5.72220686e-02,\n", + " 1.15418812e+00, 8.58453376e-01],\n", + " [ 1.26607196e-01, -1.60149356e-01, 1.34873673e-02,\n", + " 4.51221266e-01, 5.67381466e-01],\n", + " [ 9.13808927e-01, -1.26174412e-01, 1.94533364e-01,\n", + " 4.26480954e+00, 4.76839959e+00],\n", + " [ 8.44951491e-02, 1.18558107e+00, -2.44310195e-01,\n", + " 4.58989058e+00, 4.36548284e+00]])" + ] + }, + "execution_count": 74, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "reconstruct(U, S, V, 3)" + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1.3652177156806771" + ] + }, + "execution_count": 76, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "calcError(A, reconstruct(U, S, V, 3))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Again, the reconstructed matrix is very similar to the original one. And the total error is still small. \n", + "\n", + "Now we can ask the question that which rank should we pick? There is trade-off that when you use more rank, you get closer to the original matrix and have less error, however you need to keep more data. On the other hand, if you use less rank, you will have much error but save space and remove the redundant dimentions and noise." + ] + }, + { + "cell_type": "code", + "execution_count": 79, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "matrix([[ 4.46552909, 4.00492841, 4.40416543, 1.05610721, 1.06310757],\n", + " [ 4.54003034, 3.98491818, 4.59915928, -0.05627442, -0.06181712],\n", + " [ 0.32953887, 0.3687332 , 0.22258654, 1.0303941 , 1.04158147],\n", + " [ 0.00712813, 0.04436238, -0.04610898, 0.49583588, 0.50138321],\n", + " [ 0.42318617, 0.71362219, -0.05019007, 4.44801272, 4.49738771],\n", + " [ 0.38065136, 0.67865191, -0.09658699, 4.47930305, 4.52907462]])" + ] + }, + "execution_count": 79, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "reconstruct(U, S, V, 2)" + ] + }, + { + "cell_type": "code", + "execution_count": 80, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "5.8909291953120331" + ] + }, + "execution_count": 80, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "calcError(A, reconstruct(U, S, V, 2))" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "A = np.mat([\n", + " [4, 5, 4, 0, 4, 0, 0, 1, 0, 1, 2, 1],\n", + " [5, 3, 5, 5, 0, 1, 0, 0, 2, 0, 0, 2],\n", + " [0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0],\n", + " [0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1],\n", + " [1, 0, 1, 0, 1, 5, 0, 0, 4, 5, 4, 0],\n", + " [0, 1, 1, 0, 0, 4, 3, 5, 5, 3, 4, 0],\n", + "])" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": true, + "deletable": true, + "editable": true + }, + "outputs": [], + "source": [ + "def reconstruct(U, S, V, rank):\n", + " return U[:,0:rank] * np.diag(S[:rank]) * V[:rank]" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "with rank 1, coverage: 0.3755, error: 164.0043\n", + "with rank 2, coverage: 0.6465, error: 57.1376\n", + "with rank 3, coverage: 0.7875, error: 28.2300\n", + "with rank 4, coverage: 0.9121, error: 5.6685\n", + "with rank 5, coverage: 0.9601, error: 2.3134\n" + ] + } + ], + "source": [ + "for rank in range(1, len(S)):\n", + " rA = reconstruct(U, S, V, rank)\n", + " error = calcError(A, rA)\n", + " coverage = S[:rank].sum() / S.sum()\n", + " print(\"with rank {}, coverage: {:.4f}, error: {:.4f}\".format(rank, coverage, error))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "As it can be seen above, more rank is used, less error occur. From another perspective, we get closer to the original data by increasing rank number.\n", + "\n", + "On the other hand, after a certain rank, using more rank will not contribute as much as " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": true, + "editable": true + }, + "source": [ + "Let's compare a reconstructed column to the original one by just naked eyes. Even it is reconstructed using only 4 dimention, we almost, with some error, get the original data." + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Original:\n", + " [[2]\n", + " [0]\n", + " [1]\n", + " [0]\n", + " [4]\n", + " [4]]\n", + "Reconstructed:\n", + " [[ 2.02371534]\n", + " [ 0.03754208]\n", + " [ 0.23000887]\n", + " [ 0.12832794]\n", + " [ 3.95717428]\n", + " [ 4.068986 ]]\n" + ] + } + ], + "source": [ + "print(\"Original:\\n\", A[:,10])\n", + "print(\"Reconstructed:\\n\", reconstruct(U, S, V, 4)[:,10])" + ] + }, + { + "cell_type": "code", + "execution_count": 185, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(128, 128)" + ] + }, + "execution_count": 185, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "imread(\"data/pacman.png\", flatten=True).shape" + ] + }, + { + "cell_type": "code", + "execution_count": 186, + "metadata": { + "collapsed": true, + "deletable": true, + "editable": true + }, + "outputs": [], + "source": [ + "A = np.mat(imread(\"data/pacman.png\", flatten=True))" + ] + }, + { + "cell_type": "code", + "execution_count": 187, + "metadata": { + "collapsed": true, + "deletable": true, + "editable": true + }, + "outputs": [], + "source": [ + "U, S, V = np.linalg.svd(A)" + ] + }, + { + "cell_type": "code", + "execution_count": 188, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "((128, 128), (128, 128), (128,), (128, 128))" + ] + }, + "execution_count": 188, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A.shape, U.shape, S.shape, V.shape" + ] + }, + { + "cell_type": "code", + "execution_count": 189, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "with rank 1, coverage: 0.6819, error: 8279833.0000\n", + "with rank 2, coverage: 0.7292, error: 4598676.0000\n", + "with rank 3, coverage: 0.7562, error: 3399851.5000\n", + "with rank 4, coverage: 0.7801, error: 2458954.5000\n", + "with rank 5, coverage: 0.8005, error: 1779067.8750\n", + "with rank 6, coverage: 0.8148, error: 1442356.2500\n", + "with rank 7, coverage: 0.8257, error: 1247373.2500\n", + "with rank 8, coverage: 0.8358, error: 1078366.2500\n", + "with rank 9, coverage: 0.8453, error: 929638.3750\n", + "with rank 10, coverage: 0.8534, error: 822231.3750\n", + "with rank 11, coverage: 0.8610, error: 728628.5000\n", + "with rank 12, coverage: 0.8681, error: 645863.2500\n", + "with rank 13, coverage: 0.8741, error: 586921.2500\n", + "with rank 14, coverage: 0.8796, error: 536669.7500\n", + "with rank 15, coverage: 0.8848, error: 492850.3750\n", + "with rank 16, coverage: 0.8896, error: 453479.6875\n", + "with rank 17, coverage: 0.8942, error: 418997.6875\n", + "with rank 18, coverage: 0.8986, error: 387050.1875\n", + "with rank 19, coverage: 0.9026, error: 361310.0938\n", + "with rank 20, coverage: 0.9065, error: 336479.6875\n", + "with rank 21, coverage: 0.9102, error: 314194.6250\n", + "with rank 22, coverage: 0.9138, error: 292879.6875\n", + "with rank 23, coverage: 0.9172, error: 273411.6250\n", + "with rank 24, coverage: 0.9205, error: 255222.3281\n", + "with rank 25, coverage: 0.9237, error: 239045.4375\n", + "with rank 26, coverage: 0.9267, error: 224311.2500\n", + "with rank 27, coverage: 0.9295, error: 210758.7344\n", + "with rank 28, coverage: 0.9323, error: 198453.8750\n", + "with rank 29, coverage: 0.9350, error: 186498.7812\n", + "with rank 30, coverage: 0.9375, error: 175665.8750\n", + "with rank 31, coverage: 0.9401, error: 165195.4375\n", + "with rank 32, coverage: 0.9425, error: 155142.8438\n", + "with rank 33, coverage: 0.9449, error: 145804.4688\n", + "with rank 34, coverage: 0.9472, error: 137142.2188\n", + "with rank 35, coverage: 0.9495, error: 128769.5469\n", + "with rank 36, coverage: 0.9517, error: 120655.5938\n", + "with rank 37, coverage: 0.9539, error: 112797.1250\n", + "with rank 38, coverage: 0.9560, error: 105742.7734\n", + "with rank 39, coverage: 0.9580, error: 99117.2344\n", + "with rank 40, coverage: 0.9600, error: 92590.3594\n", + "with rank 41, coverage: 0.9619, error: 86680.3750\n", + "with rank 42, coverage: 0.9637, error: 81124.5938\n", + "with rank 43, coverage: 0.9655, error: 75750.7500\n", + "with rank 44, coverage: 0.9672, error: 70922.7656\n", + "with rank 45, coverage: 0.9689, error: 66438.1406\n", + "with rank 46, coverage: 0.9705, error: 62045.2266\n", + "with rank 47, coverage: 0.9721, error: 58043.7383\n", + "with rank 48, coverage: 0.9736, error: 54110.5195\n", + "with rank 49, coverage: 0.9751, error: 50288.5625\n", + "with rank 50, coverage: 0.9766, error: 46613.4297\n", + "with rank 51, coverage: 0.9781, error: 43121.1953\n", + "with rank 52, coverage: 0.9795, error: 39856.9688\n", + "with rank 53, coverage: 0.9808, error: 36901.0156\n", + "with rank 54, coverage: 0.9821, error: 34084.9844\n", + "with rank 55, coverage: 0.9834, error: 31307.6777\n", + "with rank 56, coverage: 0.9847, error: 28585.5605\n", + "with rank 57, coverage: 0.9860, error: 25945.7266\n", + "with rank 58, coverage: 0.9872, error: 23384.3965\n", + "with rank 59, coverage: 0.9885, error: 20893.2676\n", + "with rank 60, coverage: 0.9897, error: 18425.2617\n", + "with rank 61, coverage: 0.9909, error: 16010.8184\n", + "with rank 62, coverage: 0.9921, error: 13648.8984\n", + "with rank 63, coverage: 0.9933, error: 11306.1191\n", + "with rank 64, coverage: 0.9945, error: 9001.0986\n", + "with rank 65, coverage: 0.9957, error: 6793.8447\n", + "with rank 66, coverage: 0.9968, error: 4636.5518\n", + "with rank 67, coverage: 0.9979, error: 2494.8293\n", + "with rank 68, coverage: 0.9989, error: 1089.3585\n", + "with rank 69, coverage: 0.9996, error: 133.5367\n", + "with rank 70, coverage: 0.9999, error: 6.6584\n", + "with rank 71, coverage: 1.0000, error: 0.6421\n", + "with rank 72, coverage: 1.0000, error: 0.1592\n", + "with rank 73, coverage: 1.0000, error: 0.0712\n", + "with rank 74, coverage: 1.0000, error: 0.0038\n", + "with rank 75, coverage: 1.0000, error: 0.0000\n", + "with rank 76, coverage: 1.0000, error: 0.0000\n", + "with rank 77, coverage: 1.0000, error: 0.0000\n", + "with rank 78, coverage: 1.0000, error: 0.0000\n", + "with rank 79, coverage: 1.0000, error: 0.0000\n", + "with rank 80, coverage: 1.0000, error: 0.0000\n", + "with rank 81, coverage: 1.0000, error: 0.0000\n", + "with rank 82, coverage: 1.0000, error: 0.0000\n", + "with rank 83, coverage: 1.0000, error: 0.0000\n", + "with rank 84, coverage: 1.0000, error: 0.0000\n", + "with rank 85, coverage: 1.0000, error: 0.0000\n", + "with rank 86, coverage: 1.0000, error: 0.0000\n", + "with rank 87, coverage: 1.0000, error: 0.0000\n", + "with rank 88, coverage: 1.0000, error: 0.0000\n", + "with rank 89, coverage: 1.0000, error: 0.0000\n", + "with rank 90, coverage: 1.0000, error: 0.0000\n", + "with rank 91, coverage: 1.0000, error: 0.0000\n", + "with rank 92, coverage: 1.0000, error: 0.0000\n", + "with rank 93, coverage: 1.0000, error: 0.0000\n", + "with rank 94, coverage: 1.0000, error: 0.0000\n", + "with rank 95, coverage: 1.0000, error: 0.0000\n", + "with rank 96, coverage: 1.0000, error: 0.0000\n", + "with rank 97, coverage: 1.0000, error: 0.0000\n", + "with rank 98, coverage: 1.0000, error: 0.0000\n", + "with rank 99, coverage: 1.0000, error: 0.0000\n", + "with rank 100, coverage: 1.0000, error: 0.0000\n", + "with rank 101, coverage: 1.0000, error: 0.0000\n", + "with rank 102, coverage: 1.0000, error: 0.0000\n", + "with rank 103, coverage: 1.0000, error: 0.0000\n", + "with rank 104, coverage: 1.0000, error: 0.0000\n", + "with rank 105, coverage: 1.0000, error: 0.0000\n", + "with rank 106, coverage: 1.0000, error: 0.0000\n", + "with rank 107, coverage: 1.0000, error: 0.0000\n", + "with rank 108, coverage: 1.0000, error: 0.0000\n", + "with rank 109, coverage: 1.0000, error: 0.0000\n", + "with rank 110, coverage: 1.0000, error: 0.0000\n", + "with rank 111, coverage: 1.0000, error: 0.0000\n", + "with rank 112, coverage: 1.0000, error: 0.0000\n", + "with rank 113, coverage: 1.0000, error: 0.0000\n", + "with rank 114, coverage: 1.0000, error: 0.0000\n", + "with rank 115, coverage: 1.0000, error: 0.0000\n", + "with rank 116, coverage: 1.0000, error: 0.0000\n", + "with rank 117, coverage: 1.0000, error: 0.0000\n", + "with rank 118, coverage: 1.0000, error: 0.0000\n", + "with rank 119, coverage: 1.0000, error: 0.0000\n", + "with rank 120, coverage: 1.0000, error: 0.0000\n", + "with rank 121, coverage: 1.0000, error: 0.0000\n", + "with rank 122, coverage: 1.0000, error: 0.0000\n", + "with rank 123, coverage: 1.0000, error: 0.0000\n", + "with rank 124, coverage: 1.0000, error: 0.0000\n", + "with rank 125, coverage: 1.0000, error: 0.0000\n", + "with rank 126, coverage: 1.0000, error: 0.0000\n", + "with rank 127, coverage: 1.0000, error: 0.0000\n" + ] + } + ], + "source": [ + "for rank in range(1, len(S)):\n", + " rA = reconstruct(U, S, V, rank)\n", + " error = calcError(A, rA)\n", + " coverage = S[:rank].sum() / S.sum()\n", + " print(\"with rank {}, coverage: {:.4f}, error: {:.4f}\".format(rank, coverage, error))" + ] + }, + { + "cell_type": "code", + "execution_count": 192, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(128, 128)\n" + ] + }, + { + "data": { + "image/png": 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kvuWxtkZCc9TF3zKNr5K01mBojkmeJ/dmTKVJGbyMvFa+dkNzNHZ1NrYxPT2i0eFwdMIg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\nUgDKzAdelp9Tkib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DFO4E8HUAv0NELwXwaQBvA3BLSumZxTFfBXBLSWKlXVP1vjYtRZ/+AF7LlBOV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\nSM4+lbACSjw3mwdLZ5CtfmnNnqvR5dB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luxBrX2qd1gBglW95KFpKRT0AHDt2rCJSLC4uVgYDFhstK4I1YMWQIj4cFWZV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\n6fuMeabG3jut/LMC7SZZYJbb2BRNB6I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62lbAGY/F2tZP1zFYW1sraQjy/7W1tVIZOatfK+LVWuXr1Ig4LCx07oP3/qPe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\nVV1WAs6WEzDHYfEHsYKffK71/zruxia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fKlTF4lvRjjwmAVN0LXWwAY6v01vVVV2fAksqSOFSMZGe57ZuPriN/p3yfqwN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\nng7PKcQ6Nr6UCE2+d9W1VuUqTfDb7XbJsCx98OY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490hISNhcjCsp/HsA/wIAFSTcAeC8tZbI7BKAfTEdEbcgwyG5ESmyTEsf9mVV\nSrEtJJKGjpdBUUozB1cBuNFRpl9rfRelg2siqxzHeqTyhuIOQvMZGpd2nktymnGT5x5QNCfVUKS/\nCwsLuUhFLatSi4mYFJTJRJXYtNwHY8z9AE5Za58c8foHjTHHjDHHyG+ekJBw5THuVvS/YIy5D8A0\n+jaFTwNYNMbUBtLCfgCvaxdbax8C8BAAHD161A6OOV2Y3Ilch5WcLsRhfIhtN2rWnvb/kDE0tBEt\nIbYasGYoXQ8jV0gCKNu/rw9fRCP/zXV5mcvQaDScDYHyM0hSqFaran2MUH6LvPd62QLWQ0rb6HuO\nLClYaz9lrd1vrT0I4OMAvm6t/WUAjwP4xUGzBwB8adR7JCQkbD42InjptwB83hjzrwE8DeAPYy4i\nSy55GcjrQFySh8cSYqzpQDyVj+EK3MLP+w+5MGX9Bc61eNk27p7koAAkILufhDY2Hu/P/47CoaRn\nh+v3BK3ykubN4eORY9GyXXl7bU8FWb9g+/btOHr0qPsNDG00Fy9edDkPWog893z5pDp+XNPvQ+9/\nPW1Wo/RV9t2vC1Gw1n4DwDcGv18G8L6yfVQqFdRqNVdqjUcQDvrNRc754g7YuGLGHjXhRepAGUOj\nlroM+I1IodRrjrKuryICGnITxsQ3+NyQIRejtoEPMQaeikyuXMpfuOqqq1xcgtwgtyhewvf/Imyk\n+rpR18cgRTQmJCRkMFG5D91u15VaI5ekxsW1oBd5TrbTztO5MobLImOb1i7kEuKqhSzUQuCSAlcl\nJLj6ETJuho5xhKSBUBRoSJLT7stzAmSwU7fbdcFeNA+zs7POiHjLLbcA6D87XSO3zNPUKu0ZtPWk\nIRS8pD0jX1+j7gGymQbKJCkkJCRkMDGSAoFKhnEDI6AbuYA4fZdT6lhDZChXYFR9XTvH+/LlNXAD\nqy/AyXdPLcS7iOuEjGYx9+T9aHMl36MWEs5tCvTMVAxl586dTlKgkOaZmRknIWil2OV4tXD1svYl\nzWYy6lwV4SfO0LgesNai2Ww6EVruYKyl9BaJYpohaVRLcOilFKkUoSg0HmPvi7fnXpYQUeh2u0Fx\nNnZhjWqAk/378kQ0L4W2hRu1obwFSn/etWuX+03qV2xuBWcUMUQyxFC41yRWFVkPQ+N6xUz4kNSH\nhISEDCZGUgD0TEjf/4F4jsc5QshwGdNXLKUexV0V01dIUlheXvbme/AIvrIRiprBUeOy2j1DRVz4\nXgxSbaDXI4F8AAAgAElEQVT2U1NTrpo0/d25c6dTJeheXJoa1T3IpYGy6y0UiampG2WxEVKHD0lS\nSEhIyGAiJAXiKE899ZQ7JguhGmNyOncR95N7IXJJIUTRixBj8Ay5JPm9uRHMx0k4Fwxl8S0vL7t5\n0zZbJZderIQlqyJzPTy0oSqHrOug7ejEK3BTUBJJAjt27HC7UpFtgVdRpohQvuOTltNA4+S5NHIt\n8JyKGK5eZNOSczNOBuY4kbplMRFEwRiDer2eKa8dG3Ks9VXGeq5BMyqFxrFekXC+fvjiCxX/4Lsg\ny7nh8xK7mKRoriUWaZDqAQf/8HhfFI1I6c+0fduuXbtcaHdoK76Nhi8mJuTp0voY5/6+fmOvjUVS\nHxISEjKYCEkB6FMzvg1XiFNrRr+Qn7is6FXke4+hvKEoyth7aW1CHHJqaionppeN1tPGy+c4FCXq\nUzv4uLvdbk71mJqayqgLwDD9eceOHc64Sv13u92cmF/Wzao9X+iZit7nKHEpo2AzIhuTpJCQkJDB\nREgK1lq0Wi10u12vpOArkhky8MVQ+VjOP6oLs6h9jOuyjKQQupcMCCtCaPtzLb8h5Lrkf6WLbmFh\nwWU7UqQiBSeRjYGPn0sKfHt4n9So6f6hnA1+LCQV+CSnEEbl9MmmkJCQcMUwEZJCr9fLbN0N6Bw9\nVD4rFDxSFLCk6Y/r6e4J2UfKSh0hqt9oNBw31fa7DBWl0cYkuTx/B1o+gSbdyb0kgaG7lGwFO3bs\ncJIBSQxkY5iennZuR81rQeBFfGO4fNH52PdS1l40qqQwznose+1EEIXV1VU8++yzqNVqwY1TtDhz\nSSg0NaPIFReK3JNtNJSd9LLFUHibomrOPvjGH/owQsRM8+fTh8+39aNriBDMzc3l3I779u1zx8g1\nSWpBp9PJGSa1yFTtOYrmQ6vbqMUu+M5x9UHeUyM+43zYZeInfNfGIqkPCQkJGUyEpNBut3HmzBm1\n/mERZ/RRdtmOEOue9AVA+UTGGIOnhhiDpFZPUAMv0hLaxLVsRCM/rkUoapux0v/lprNzc3OuhiIZ\nFRcXF52EIPvi3JgbNzVOHqp0LdvXarVotzddV8Z9rK1lPu6yiE17Xw8kSSEhISGDiZAUer0eLl68\nmMkAlBRR271Ho7wh44+mi/J7hQyARQYozcjmg89w6Os7VurgnFrqoJxrx0JKDMbo+27KcdJ19Xrd\nSQhUDGVxcdFJCmRTmJ+fzwQm8Wfhpdr4X82+FPNuNBuBHD+/JmRnCh0ft63v2lH6KHvNxBCFVquV\niW2X4h5f0LEGwVi1ICZ2YT29EWVzH2K9D7zIyjh+bYmQYVTzMJAYPz097ZKwyKuwY8cOZ1Skc7Va\nLZc6zZPZQmoBhy8Kscw79hkFfaX9Q54XwnqI/EV1L2OujW5f+g4JCQnvaEyEpEBivWbM4ZKCxgFC\nBphQpFqI+47i3godG5eLlKH0NE5tU5hYqcHXTosF4NGFBKoqvbCw4FQF+rtt2zanSpBqQZW86TeH\npiLyqMiQZKjNLd+sVhpNuUQh11WRFKe5SGON2jEYp0BLkhQSEhLGwliSgjFmEcAfAHg3AAvg1wC8\nCOALAA4COAHgY9Za/2YF/X5c3L6PImuGO07ZJYek80XQ7qlxpyIOIBEboBQjNWiFSXztpHSk7Ual\nSTExUZaatMElBeL8ZCvYtWuXK6FGNoW5ublcAZh2u517Lu09Si7On1MLRtLGTf12Op3gewlFucZI\nKUXjKAv+PrX7a/eiNmUlhXHVh08D+Kq19heNMVMAZgH8SwCPWWt/1xjzSQCfRH9/SS+MMWg0Gmi3\n2+oHCmSt0JpIzD8Gn5+9jAGx7MvzjbuobaxnIQY+37h2r9AxH4oMpLIU+/bt2134Mh3jUauycjfv\ni4v2mqdBtg95nXxEIaQihO7J+/IRCl9MwqhqAP8Oyq7NWEMtYWT1wRizFcDPYrCBrLW2Za09D+Aj\nAD47aPZZAH9v1HskJCRsPsaRFA4BOA3gj40x7wHwJIDfBLDHWnty0OZNAHuKOqpUKpiens5IA0TF\nicq12+0cVebuMAKXBjSfuiaKhkRFbawSRYbGUB88tiBGaglxCV4uzaduxcDXjs8t3+yVflMNRfq7\nsLDgjI68UIrc9IYbmLWYhFAJOj5mTZKU49ZUMZ9kyfvg64RLpb4kLJ9xuyzXln0UqT0a5K7nRRjH\n0FgDcAeAz1hrbwewjL6q4GD7o1efwBjzoDHmmDHm2KVLl8YYRkJCwnpiHElhCcCStfaJwf8fRp8o\nvGWM2WutPWmM2QvglHaxtfYhAA8BwIEDB+zq6iqstTk9kwKarB1uH0bnms2mc28Rzp07l6sMzANh\ntI1MNbeSpMY8Np82vyW02+1gWrcE3wjWJzVw8OOyyrUEzRGlG1P7arWqVmDWbBA+w16r1XJGROL2\nW7dudcbE66+/3h0D+nPGsx3pL/9NY5PQCqpwKYV+0ziMMWoFayCbn3HmzBkAwJtvvom33347075a\nreaqYVP/a2trbpw0xzfffLN7l7Ruqa96vZ6Tenu9XpTUo+H06dMAgLNnz5YulkPvJxYjSwrW2jcB\nvGaMuXFw6EMAvg/gywAeGBx7AMCXRr1HQkLC5mNc78M/AfC5gefhZQC/ij6h+aIx5hMAXgHwsaJO\nrLXodDoZvVAG3zQajdwW47VaDaurq5ljZJsAhpyIc1e5F4RWXFTT/YgTaLo6D8/mz0SQFJ3GLO/v\ns0zHur46nY57Bqlf+zavjQmw4ZKX5Nq7d+/GddddB2DIkTiHpGfV5kPTdYs8DLIdn7+QW5Pm5eWX\nXwbQ32tC3p/C7YHh++brke5J6/DHP/6xKzC7Z8+ezBi4m5VLa6OWpiep5vLly1EuSY6zZ8+WutdY\nRMFa+10A71VOfahsX/JD5C4Y+isXa7VazaQLA1nRXH7IlUolJ2L6fMdSzONiKqklfKyh4jAS/H4x\ncQqxRIGIKzD84HikoKZ6xLhouaolRf4tW7a4GARSLbi6IROc+DvgEY3yXlq1Jw2c+GkGY9kHvUeN\n6PCPVjIPXv+SnuXs2bOuX4rYpP/X6/Wc0Zc/e1lwol7W0OhjCD6kiMaEhIQMElFISEjIIBGFhISE\nDCYiSxLo60lauCvpT7x8Ftc7Zabb2tpaTr/nepxW5VjqsfIa/n+e0Ufw7Zkon0X7f0zYa6wOaYzJ\nGc98e0uW6Zva8HoNNAcXL17EuXP91Ba6N9fztfvLPkLj4YFkms2lqPyebEdj5LYoLadCjpsHzxF2\n7NjhSspRv9zQSAitv1hQ/2tra4WZm75rYzERRIF8zPyDk3EKzWbTGbLWM05Bi9KTBAoIxym0Wq2R\n4xT4IvEtmBCx4qhWq24ByDiFWq22rnEK1NepU6dyHy2PUyCfPjfS0bX04RSViw+lU/NalNJwyT0x\ndA/ylJSNU2i327k4hXe9613uXUovC49T8KWFlwEZMvnajCUKVOEqFkl9SEhIyGAiJIVKpYKZmRms\nrKw4yUDLYGs2mwCy8eWXL1/O9DUzM5OTBjSpgIvEhJBYxuMh5HktTiGUOq1VXZbXcHDpoCh1muZI\ni6bTMGqcAkkkly5dclLJ+fPnAfT3cQCAq6++2sUukIRRr9cd96Wx8uxY4sZcfOf1GoHsO+Mqiy+X\nwVrrzlHW5tzcnJMaYvIitGzNqampXCyCnDP+m0ssZbF//343/rIuSZJyY5EkhYSEhAwmQlLo9XpY\nW1tTDU9cf5KcnHMRzRilZVCGdGh5XF5LfZZpL3/LcWl1CUJ9h/RIbfNWLUirSBfV5oj+Sm7darVy\n7cnOs7Cw4CQE4pC1Ws0rifB7hza39Y1Zsz34+uX3DWXH8rUm+9AC6rjRWlsTo0Y0cltHWUkh1vZA\nSJJCQkJCBhMhKVhr0Ww2M9RY6v6+Eu9SeuDUXivqqoXCynvJa+Q53zPEngvdZxwUSQoatGf3wRdu\nTb/JRnDx4kUA/Xh9khCIQ/JybNydrBWEJWgFVuW9Q5IQ/z/vV/NEyWu0daVJA6H1EpJeY8Hfa4zE\nx9uUlSwmhii0Wq2gQYQbkvh1obTnmMmLMbQVtdcQW7E5Jk4hdiHxdlrxj1AREQ7fR6URUB7nQcfI\n8Hj69OmMmgH0azUuLCwAyBofZTp16OPVyqDFvrOQOhrLFEJEYT3WjoayFcDHIURJfUhISMhgYiQF\n4mShElmaGB4KGpLU22dULMttYhDqS1OFQtdoxjEftOhMea5InPRJClwyI2jRepRa3O12nYRAqgWl\nyANDV+709LRTEbQdoqTEx0VobmiO2UVJcyFq7z/WUFuklsUeL4K2U1rZa2ORJIWEhIQMJkJSqFQq\nmJqaUilwSA/2SQo+Y6V2zKdTh9xmvvHEwsctfP2E3JscWvDNODsLyb60+ealzmhsFJzUarWchMBD\njrmEAGTzWmSRnTIlzcsYh30GOJ+NQHMxhiQGbRPc9bApjNJHWUlhYojCli1b3AICdN++9kGHLPsS\nRR9dKKKR4FtMPn91UX9lrf4haKI8N86VXRyaXz40Jvl+2u22IwYUeTo1NeVyB3g0Is8t4eestY7I\ncOKkvSufesTbx2wew/vgf0OqZ8w78vURgxgVt+jaWCT1ISEhIYOJkBTq9Tp27tyJ1157TZUQ6K8U\nXbV4dI0aa+5K7XyMpBBrWIoxRhWdI8SqADwWX6JWq+VqXBaNSRr9tNRivveGlrIuDYLLy8suO5HG\nwVN7SWIgFcMYk8t94Ndyzh/jptTKt/FzPvUylsOH1A3f+iuDca+PQZIUEhISMpgISWFmZga33XYb\njh8/7vTikM5aZODxtdcCm7Q+tGPr6a4sk7Eoj4di58eRcLT5CNlJNOmF5zcQZGXtlZUVl3FKEsOl\nS5dyVZGpBsDs7Kzrj9fa4MFTNLZQ7oO2FmKku5D0WNS/dm5Um8JmbkU/EUShUqlgfn4e3W43RxRC\n4ZpFIZ8xH7K2ONZbRIslKDFeiVBfzWbTe95XwCWkToX8/tqYuFGTX8+P8Q1R6CM+e/ase++kNnAj\npBYzIAlAKDnJR/BC52NQ1LZMXEMRYmNMQtfGIqkPCQkJGUyEpGCMyWxUCuRFWC3asSjGYD3dfUVi\nZxl1o+z9tUg7Da1WK8flQzEdRYg17IaeXY6Dv0f6e+nSJSchkMTAr6PybpqqUOSmlP8PSUbas/A+\ntXW1npGuG4XkkkxISBgLY0kKxph/BuAfArAAvof+tnF7AXwewA70t6f/FWtty9vJANZazM7O5jbq\n5ByGt1XGEuxbtivKgRg3dn0cbhLqK1S4lW+CKst+8crXRZzD56LlOyiFisCGgoK06tnNZtOlW0vp\npNvtushH+lutVl07XqIvVOos5GLk49HWG10X41oua9sqi4m2KRhj9gH4DQDvtda+G0AVwMcB/B6A\n37fWXg/gHIBPjHqPhISEzce4NoUagBljTBvALICTAH4OwP85OP9ZAP8XgM+EOqFQ1sXFRZw6dcod\nK4IW0BRyL5a1HxQdGxVlcx94+5CkwD0MMbH7sRID1+XL1H/Q6g1oxUubzWauRDp3P9JelbyA7KgF\nUEdFkXSq2SJGtTOtN8red2SiYK193RjzbwG8CmAVwP9CX104b62l1bkEYF9RX7TY7rjjDnz1q18F\ngNxGptba3Oaw3F+tiesyHdf3EssaJGNyCIp8+oSYfR/4hrahj2Fubs7rL9fceEWGWlmoRXsmnxgO\n9N+PtkeBdFnOzc25dpTnQDEMKysr7hxtvLJnzx5HKLiBklQJOW5OSLVEq1GNsdwlrkG+g3EIWcgF\nvN4YR33YBuAjAA4BuBrAHIB7S1z/oDHmmDHmWNmtshMSEjYO46gPfwvAcWvtaQAwxjwC4GcALBpj\nagNpYT+A17WLrbUPAXgIAI4ePWqB/rbm7Lxsn+tDE9G0a2JdUjFYT1djLHhffM8ICR67L6+NlYx8\nQT2+64o4pabeSYlFMyLT31arhdOnT2eepVqtOq5LOyeF3Nk+yPURimjkv2PXkOxjvdWHjVqL47gk\nXwVwtzFm1vTv+iEA3wfwOIBfHLR5AMCXxrhHQkLCJmMcm8ITxpiHATwFoAPgafQ5/18A+Lwx5l8P\njv1hTH/GGDQaDacjSl1U4zBlJYVxKHWM7uhDyAYRY0TkXJCKomoIbSTKA36KxjvqPMnrNJ2bv0f6\ny12Mcj9Iay0uXLjg+qP2NCdUBJbPXcigGuN21q7V2o5S8m7Uud0oaUPDWN4Ha+3vAPgdcfhlAO8b\ntU/aSETGx/MU3dgEkxhxl/cRii0ILabY3ADt/1x0DnkWCLwQjYT2YYwSL6EZKX3QznEjZIzBk6sZ\n0gjZ7XZzpeM5EaFt6biRUBpB+W7Z2nzwD7+M0TlU4l1DUazDRiFFNCYkJIyFich9AIb+69tvvx0A\n8O1vfxvAkDtwlDX4hM7Hinmcm5T192tRegRywQH+jUAvXbrkftNeCRq4mhGjasVKONqzazkBsVxT\nng9tGwcMXbJ03crKCt58800Aw01tr776atx8880A8irF+fPnXX+knnKJT7pSixDjEvQZt9ejZuZG\nY/JHmJCQsKmYGEmh1+u5qEYAuS3peV49YT30s7IuJ5/eGeLCIc6o7eokwY2LxAU1+Da/9SE2opH/\nX5OSfJzT9zyhCt3aNWRA5RxdFmqpVCo4ePAggKHExSMxtaAuTRosM39FEY0aroShsaxLcmKIAqXU\nUqzC0aNHAQCPP/44gL7hkYyP3CgVG8/gO1d0rYSv1HdIpeAqgjzH1QFfRCMZX4GwMbLX6+UqM40j\nrvLQZOpflo7XVBatlmIoFiBUIIUbIXmkpIxafPvtt/Hd734XANQqTjRvy8vL7h4yQaxWq3mjODUD\n5Sh7SY6KcaIYk6ExISFhLEyMpAD0qSBxOlIjiMJzbqu5kDT3WZEhzddGO15W1I69lnNyEokltGi9\nIsRE2MUi1iWpGSa1cYWku9C4eb8yrqHb7eKNN94AkM91WVxcdOqoNo7QeK9UFKLvuiQpJCQkbDom\nRlLgse7A0FhEhjWtKGlRVeSyXHU9Ix5D3M9nF/AFJnFXZVF0ZKybbFyUzYPgbWI4NG8fE+zU6/Wc\ne1LuMrV3795cey6VEsruoLWZ2ExDY5IUEhISMpgoScEY47go/SUvxLe//W0XA8+lCtqXkBf6lBZk\njlDWHqeokotwS7zsQ7P68//LnAReH4HbEfhxDq4PS0+GHAcP7QWGc1CtVtW8Ai3wSBZb5V4R2QfP\nqZAhyrz/UIFVHqKshUVL7wPn6LwUPM0T7YRFNobV1VXs29cv63HDDTcA6NdwkJJZp9Nx96d+NY+Q\nZtOS4+aeMb4W1iN4qay08BPrkqQHpUmjF0sGx+npaTW6MRRNF3IryTby2vUUtTUiQuAuMl9EI28f\nWlQ8xp9QFGUYa3iltlL0527K0LsIxQeExqONjbehD65areaMifTRLy0tuWP79+8H0Ce0GxFdyOdH\nG++oKqok1GWQ1IeEhISxMBGSAnEPXnGYqD6pBzfccIOj/MRda7VappYf9UUg6sqjI6U4qGXyAfnS\nWVwUDPVB4KqAVB+4ysCNjqHUZ0Jo2zgu/lK/PEBHqgM8CIgb4uRuTfQsnU7HqS88I5F+k5GYvwtN\neuDGPuq3qAI0kJWYpGTJf0tppt1uu8jHp59+GkBfYiCpgVeJpjHJ5+TgwUu+Hc1arVbO4CmfoQxo\nTjX1NfbaWCRJISEhIYOJkBQImr5EFHt+fh5zc3MAhpIC585aBWHNbSW5COcOITdikV4oJQvOHSSl\n5rkMRftZaH37wMes1SWIdRlKgx6XCrSMQsn5tXmU70Te0/cssbYQPm5ZV6FSqTgphoyPlUrFhdTT\ndbzwrWbQDUkNclzcvjOOPYCgFcCNtb+UlRQmgiiQ+F2tVnOeAJrQbdu24bbbbgMAPPHEEwD6KbHS\nul2pVHJbj2kEg8A/Fm23ZAIXg7U+JIiAAfm6iqQSyXv6EPI4cFQqlYwoDCDjsSF1QNsdmsBFfjL2\n0lwsLCy4XI3Lly+7c774Ch8BCBkktfbSkOnbdFbzXAB9NUh+7G+88YZ7PvJMHD582OWZaH3xtGsa\nh1QlaS3U63U3v3zjnFEN2Npu7DF9cY9eLJL6kJCQkMFESAqEkN/XGOO4L3FDn6tOciBe2k3zwWvV\nhX0il4/7SRGfcxCZ0+Cj9j5xsIzIyNUFICtBhTIWtftJI2673c5xHU2N4GPVclJCzydR5MKUbbV+\nuWRBz7K2tuY2HqJn2rNnj1P75B4jnU4ntyZqtVouFkGTTkgiAUbf+yHWpauh9MbCpVonJCS84zEx\nkgJxMsmdOOUm6n3jjTcC6HNg2kgmZMjSXFmaS0uLupPXcTceodFo5NyJnDvIMXGbQiiKkqBFFGqo\nVCpOZ6a/0o7AUcRxpB67trYWzD+JLYIj55ZXfdbyImTEJLfrcHuLtoMYXUd98Db0jkhiePbZZ10t\nhoODgi1kjGw0Gk7i41KBrMnAObo0fGrPHgtuHysdjFRSUpgYogDoFn5u7aaPg17U7OxsjijwBaCF\nKst++YRxC6+cSP4i5DntQ9WKeWh9xRyPhZYOzKsWSYOdz+ov1QvuvaGPsKiqEUHOd1G7kCeCQ/M+\n+CJXfXtaEog4nDx50s0RbVFHUaY82pQTHaluEDghHyX1XUILTd8oJPUhISEhg4mQFMhtoonPMpUa\nGOZD3HDDDc41psUuSK6mGduoDByHz3VJkDH2QD7tmasTvkQnCZ/6EOuGqlQqrvIz33jV13/ZfAhj\njOuf3gGfU+k65TtM+2JKfM/H/8o9QHxGU9/z8bVF76lWq7k1Re1WVlacKvH8888D6FeJBoADBw64\n90hze/nyZTdX8h3znBCOcbn8KPkaZaMok6SQkJCQQaGkYIz5IwD3AzhlrX334Nh2AF8AcBDACQAf\ns9aeM32S+2kA9wFYAfAPrLVPxQykiILy88SR5ubmXDAND7QJccBQpGKMTl+tVnNGxWaz6SQWQmgb\ns42ENG7x4C4taChGv+dGWS0ilCCf02cLiHFThjAOt+XzIUu68WCkkydPZtrPzc25ICcueYbS9H02\njlGgFcONjWjcCEnhT5DfYv6TAB6z1h4G8Njg/wDw8wAOD/49COAzpUaTkJBwxVEoKVhrv2mMOSgO\nfwTAPYPfnwXwDQC/NTj+X22fhP2NMWbRGLPXWnuy4B7qPpGyDYEXdz18+DCAIWU/ceJEjiOSZFGr\n1Zw+GMoJsNbm9GOSDqanp3PeBM0WwO0OsW68GK9EiDvwrD3pgdE8Kr7+fHPPQ31lgJN8Fj4m3p7f\nT3v2kFdBm58Q19TaawVg6O/s7Kx7HirtRuuAt9+xY0euvQx3rtfr7tn5Who1eEm6W33PJzFKmPOo\nhsY97EN/E8Cewe99AF5j7ZYGx4JEAci/VCn+drvdzMcN9Cf+wIEDAIa5BqdPn3bx/oTQRxUygHFw\ngxmPQaCx8r0ZZL+SaPherM+IpIn2Gnq9njN4kUGNuxW1eP6Qy1DLHZHPyRc8xV8UVXbSPvJQnELI\nJRnzYfD3yYmmjHjl6hE9C727paUl96yUcn3DDTc49VXuBr7e1ZZo/XU6ndLqyKbnPgykgtJKkzHm\nQWPMMWPMMYo1SEhIuPIYVVJ4i9QCY8xeAKcGx18HcA1rt39wLAdr7UMAHgKAo0eP2sExfl62dxSf\n188jCkoUu9FoeIOFeAAPP6cZyGQf9P9Wq5UJTKJz0iU1aqy/hjKcgeYmtGW9ZuiL4bzW2tw+HNxg\n55Mw1hs+CSPGxapJKZqxkOaRjvFNbWkO9u7d69ZdqOTeehiaNYNx2WtjMaqk8GUADwx+PwDgS+z4\n3zd93A3gQpE9ISEhYbIQ45L8M/SNijuNMUsAfgfA7wL4ojHmEwBeAfCxQfOvoO+OfAl9l+Svxg6E\nJAFfwQ5e3orH5JPuRpz6uuuuc8YwCkThGYO+AiL8ntVqNZOfQPcHkLMnAH2jopQseA2F0Fb0/LfP\nCMWPhwpmcK5N+2VQsdtWq+W4nxbMxTkuzY0MGpqfn3fzQpICl8ykcZNzby5NyHsWSRSabUO6RHmI\nt0S321WlGfleWq1WJsuR9z89Pe3e6ZkzZwAATz31lKsOfc0112Ta83USKrgTC5pvn40l5tpYxHgf\nfslz6kNKWwvg10uNYHgtAL+o1W63M4VLgGwCEF2/b9++TNlvYFhtR4uPb7fb7hgt+KmpqdwCo5fc\narXUcYQ2dg0ZN2OIQmxEY7fbzUWAUnstKYxDMz7KZ2k0GmoyGIHmKNZIGEKRGqPNqa9fjTgBehl8\nSRAJ9Xo9Y+wDgOPHjzs1jYjI1q1bAfTVWc7QCKN6H+ieMXU8fdfGIkU0JiQkZDARuQ+EEHfVxD3O\n5env9PS0i1eXpcPOnz+f8yt3Oh1HfXnGm1QTiMLPzMyo6oDkbLyNpNRaBWLtmQllDHbElWRMvhYR\nyjex4fUs6VnlRjutVss9C3fnSSkvlKbt49qhuBTZvxZZyc9ra0eOzdph6jTNwczMTG4TGOqLG7Xp\nWK1Wc6rEc889B6BvfAT6pd1o/fH5HhVl3YrjXJskhYSEhAwmQlLQost4vD1BRtFZm99ujBsrZfk2\nHtvOM+h4zQGgzxFlLgONp16v57ialm8RIwFIxLjUisA5G40XyOrLRRGSshoyjwyVVYU1aaOof43L\nFz1PzHkpNYaCtHixHL7WaO3IcnbciMsN3lR45a233sr0v2vXLidp8QKuZd2D8tlGub6sYTJJCgkJ\nCRlMhKRAcfkaRSNKzS3f/K90LXLPAUkKN910E4A+xT5x4gSAoZ43OzvrJAnudpR6Mbeya7qhtBto\ngTAEXwisjwvEUnqttBwP4ZV6NS+HrwX1SF3YV2eibP5ByBWpcftQPoTWrwR/l+Qt6PV6uTwYLTCI\nS5TcY0XX0dohiYECnNbW1nDrrbcCgMvPAZALfJtETARRAIbGIynm8dp62iLStj3jHwIwNP60Wi1n\nXAjiE2QAABHiSURBVKJtxLhbk15Yu912Jd8ItIC0qr7aAo1xNcprfYao2IQoboDTUqflB1e0L4NW\nDEWL/vRt18bdhOO4JrUoVPnb56ak55TJScYYR+i12AJtQxm+3R6BXL+y/xMnTjhmQG127NgxcnRj\nmVwP37WxSOpDQkJCBhMjKfhEQi2OXsu44wY2n3uL1/WngKalpSVX/JU4QaPRyHFRHt0XI85qQTJy\n/Hxs8rg2/iJoBttQenKRuiINhzzaUXJSDk0lKlItyuQtaM8S6kPLkuTRsLzqs5RQqX+uJvE+SOWU\n2/RNT09jaWkJwFAtvfXWW12G5SQjSQoJCQkZTIykII1YktN1u91cARGuz/KgJBlkQpR6YWHBhaGS\nxHDp0iVXf4FTecnZeH0CjSPJY9yOIPeS5MEkGyUpaHYDTcIJQUoKXOLh10pJSCv/Hgo2Co2lyKjI\nr/PZNngffO7pncpAL+0+vIANl15lmDOdm5+fd4FNr7zyCoB+CD4F1pXFOC7JspgYohDaZwHoLzTN\nHy4Xv7YNHHkhGo2Gm1RKGOIviYhDs9nMfcj8Y5OGQ81zwr0RsZuklD0uwYlkTNKR72OT12iRilyN\nkB+j1he/Z5noRZ+KoRnefIZGfk++hrSt4XgehOxDu6fMs+Hrhtbdtm3bAPQrhY1acCUZGhMSEq4Y\nJkZSkK4nyek0VyO/hh+T+z0QxeaRitT/tdde6/YwoBiGpaUlteSaD9wVSAjtE+ErwBETpxCi+lxS\nkOPQxGxNvOe/pVrgi+b0ie3aM5RVkTiHDvWrqU4E/n54pKJMj19dXc1Jo/yvloJM0gZdR/EK1WoV\n1113HQDglltuAQDs3LlTfcYy8KlT64kkKSQkJGQwMZKCzwjGXUTS0CjPE+T+fkS919bWnLRBRqXp\n6WknSfBtyqWkwDmIxi0lNP075rmLUMQlfFzVZyANcd9QABS/XuZDhMZYNmpzlNwHCT7/3AjNIxOB\n/nqR9iKt8jafF233KqBfdIUiaakACzBci2URCtKKvTYWE0UUQoakTqfjxHDNqswXJk+AAoYVmCqV\nijMwUlqrtcOdg6l09+rqai4hioyQ2nZgXIQmcCt3yPuwnrX8+NhojmRJdgAZ/7w0JvKkIDmedrud\n272ZF5jRiEJsnIIPReIyXyc+AyZ/P8Qwut1ujvDPzMxkanHStfRXJs5Za533gbxapJK85z3vcZvH\nEPHRYmhiEatCFl0bg6Q+JCQkZDAxkgIZlCS34VxIcqler5cx7AB99w9RZqpPyIuGSE7AXZgUo37d\ndddh+/btmfH98Ic/BNA3QmpJLVJ64NRcGhq5uzJG/B0lDZvnatB1WuqvFkcgcx7oXL1eV8uUEQeV\nojF3V4Y2YQHyUoYmLmsSIjea+iJH+fyRdFCtVt375kZIGeVIa63RaLhnp/dvrcWhQ4cAAHfddVem\n/eLiomvPJZJRi6XQmq7X66XdmlJSLUKSFBISEjKYGEkBCGfV1ev1TIYb0KeenJIDfapMlJHakR2B\nuyu1qEh+L7IvEMhY1Gw2c7qoZoDjHDXEHbhhyycFxJbxMsbkXGS+TMiie1J//G+n08n112w2VWkg\npn95n7Lj4e1DEhfPktSCrniaOb0PaT9ot9s5KengwYM4cuQIADjJksaxtrbm3gHva9SSbL4o2LLX\nxiBJCgkJCRlMnKQgKanMPgOy1lyqe0Dnz50759rRvoe8xJYWwqvpp5K67tq1C0CfA2ieiVA9/1D5\n91A2pXa8qEQ49UfSDOnNPEycB/BoYcW8NgXHyspKrn5As9l015JHh8D792W50l/J/TSOqpV748FZ\nMudFA9laer1eTtfmRWu5hAD01xq5rqmP2267zUmQoYI0vlDtMuA7c5WVFKRNq/BepVpvIMhtJEVQ\nmsRms+leGBl6tm/f7l4CGRW5S5LAfclaHoIUQTW3I6kn1113XU61eOGFF/Dyyy/n+iWEiAI/F2No\nDKHX67lnpQ+U/t9ut3MflS+i0bfR7vz8fE414/kkodwHbSGH0ro5QrkSWl+yHVd7+PqiZ6F322g0\nHDEloynN30033YSf+qmfAjAkllu3bs0YrDmq1WomHyc0zhjErJOYa2OQ1IeEhIQMYraN+yMA9wM4\nZa199+DYvwHwdwG0APwYwK9aa88Pzn0KwCcAdAH8hrX2L2MGIl2SBO4u0sRU2gKcxLf5+XlHyWUO\nBJDnfto5LopK1Go1lytB2L17d0ZtAbJqTChLUou2kyjjkqTz0uCoXatFZ2rcnXNZKcFVq9WoTMyy\nUY6ayB3jytT68KkiMkJ2dXXVcX56x9Tm0KFD2L17N4DhnDabzYyrkINLZjwbs6zoTxgnyK2scTNG\nUvgTAPeKY18D8G5r7W0AfgjgUwBgjDkC4OMAbhl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l8plpRGatVnMqSOieaoRqWYwSP7FmUZLGmA8BOGGtPTzk+XcaYw4ZYw75xOaE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\nVz53eS3Dgt75In+T0LmxSOpDQkJCBjFl4/4CwIc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xClwpJlO6EWSuBh98JkMaQ8gUGFLKhriJWFNnGXzz6+N0uIcp/U1xGZQIhjiG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\nEsn4GDjXKDkQ7oRGz7VmzRoAwE033VRwnms2mwV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klLMyD5Iq7kOUFCIiIlIYCEmh1Wrh1KlT2Llzp9E9SY+W9EJferVQr0dJmnD9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\n8Jl2u58H8IDWej2AB9p/zwY+C+DX7O+/BPC3Wuv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z48LCQr7FvWRdlj0qms1m0JRa95mG+KhQ7EOVuTLERfQDvdSXnJcSEhJ6wkhI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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "for i in range(1, 50, 5):\n", + " rA = reconstruct(U, S, V, i)\n", + " print(rA.shape)\n", + " plt.imshow(rA, cmap='gray')\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true, + "deletable": true, + "editable": true + }, + "outputs": [], + "source": [ + "plt.imshow(data, interpolation='nearest')" + ] + }, + { + "cell_type": "code", + "execution_count": 164, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "13824" + ] + }, + "execution_count": 164, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "128 * 128 " + ] + }, + { + "cell_type": "code", + "execution_count": 165, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "-2560" + ] + }, + "execution_count": 165, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "- (10*128*2)" + ] + }, + { + "cell_type": "code", + "execution_count": 167, + "metadata": { + "collapsed": true, + "deletable": true, + "editable": true + }, + "outputs": [], + "source": [ + "from PIL import Image\n", + "A = np.mat(imread(\"data/noise.png\", flatten=True))\n", + "img = Image.open('data/noise.png')\n", + "imggray = img.convert('LA')" + ] + }, + { + "cell_type": "code", + "execution_count": 171, + "metadata": { + "collapsed": true, + "deletable": true, + "editable": true + }, + "outputs": [], + "source": [ + "imgmat = np.array(list(imggray.getdata(band=0)), float)" + ] + }, + { + "cell_type": "code", + "execution_count": 180, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true + }, + "outputs": [ + { + "data": { + "image/png": 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SmLyERAqTl5BIYfISEilMXkIihclLSKQweQmJFCYvIZHC5CUkUt5UxoRnn33W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\nCYkUJi8hkcLkJSRSmLyERAqTl5BI+f9TQAmoLqKcoAAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "imgmat = np.array(list(imggray.getdata(band=0)), float)\n", + "imgmat.shape = (imggray.size[1], imggray.size[0])\n", + "imgmat = np.matrix(imgmat)\n", + "plt.figure(figsize=(9,6))\n", + "plt.imshow(imgmat, cmap='gray');\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 181, + "metadata": { + "collapsed": true, + "deletable": true, + "editable": true + }, + "outputs": [], + "source": [ + "U, S, V = np.linalg.svd(imgmat)" + ] + }, + { + "cell_type": "code", + "execution_count": 183, + "metadata": { + "collapsed": false, + "deletable": true, + "editable": true, + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(250, 150)\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "for i in range(1, 10, 1):\n", + " rA = reconstruct(U, S, V, i)\n", + " print(rA.shape)\n", + " plt.imshow(rA, cmap='gray');\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true, + "deletable": true, + "editable": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.0" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}