From b558c45478b4d26252bc1bcda1f311b939ba182a Mon Sep 17 00:00:00 2001 From: Jan Chorowski Date: Thu, 16 Jan 2020 14:08:19 +0100 Subject: [PATCH] Lect 12 --- lectures/12_PCA.ipynb | 1615 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 1615 insertions(+) create mode 100644 lectures/12_PCA.ipynb diff --git a/lectures/12_PCA.ipynb b/lectures/12_PCA.ipynb new file mode 100644 index 0000000..3da1e4e --- /dev/null +++ b/lectures/12_PCA.ipynb @@ -0,0 +1,1615 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "name": "12-PCA.ipynb", + "provenance": [], + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "Os5hAtLSOaT0", + "colab_type": "code", + "colab": {} + }, + "source": [ + "!pip install -q gdown httpimport\n", + "\n", + "![ -e mnist.npz ] || gdown 'https://drive.google.com/uc?id=1QPaC3IKB_5tX6yIZgRgkpcqFrfVqPTXU' -O mnist.npz" + ], + "execution_count": 0, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "VTtfvQR6Km9e", + "colab_type": "code", + "outputId": "1d154ba4-49d2-47a2-f0c8-e9de51fb341d", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 107 + } + }, + "source": [ + "%pylab inline\n", + "import sklearn\n", + "import sklearn.datasets\n", + "\n", + "import matplotlib.gridspec as gridspec\n", + "\n", + "from scipy.stats import norm\n", + "import seaborn as sns\n", + "sns.set_style('dark')\n", + "\n", + "import httpimport\n", + "with httpimport.github_repo('janchorowski', 'nn_assignments', \n", + " module='common', branch='nn18'):\n", + " from common.plotting import plot_mat" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n" + ], + "name": "stdout" + }, + { + "output_type": "stream", + "text": [ + "/usr/local/lib/python3.6/dist-packages/IPython/core/magics/pylab.py:161: UserWarning: pylab import has clobbered these variables: ['norm']\n", + "`%matplotlib` prevents importing * from pylab and numpy\n", + " \"\\n`%matplotlib` prevents importing * from pylab and numpy\"\n" + ], + "name": "stderr" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "2lQB34CUKm9s", + "colab_type": "text" + }, + "source": [ + "Let's generate some data first:" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "n7pOyHmcKm9t", + "colab_type": "code", + "outputId": "2cba80e4-bafd-4934-b4b1-80f2736e6e9b", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 283 + } + }, + "source": [ + "X = np.array([[1,3],[3,1]]).dot(np.random.randn(2,20))+[[1.0],[1.0]]\n", + "Xcolors = (X[0,:]-min(X[0,:]))/(max(X[0,:])-min(X[0,:]))\n", + "Xcolors = pylab.cm.jet(Xcolors)\n", + "\n", + "scatter(X[0,:], X[1,:], color=Xcolors)\n", + "axis('equal')" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "(-4.731280299877971, 8.175711099481958, -6.0333234992675004, 6.876693163168702)" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 10 + }, + { + "output_type": "display_data", + "data": { + "image/png": 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" + ] + }, + "metadata": { + "tags": [] + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "hpE1BnldKm92", + "colab_type": "text" + }, + "source": [ + "Now subtract the mean and normalize the data such that each dimension has unit variance" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "rOmDY-QrKm96", + "colab_type": "code", + "colab": {} + }, + "source": [ + "Xorig = np.array(X)\n", + "X -= X.mean(1).reshape([-1,1])\n", + "X /= X.std(1).reshape([-1,1])" + ], + "execution_count": 0, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "QF9Qg2iNKm-A", + "colab_type": "code", + "colab": {} + }, + "source": [ + "#create a grid\n", + "xmin,xmax = floor(X.min(1)), ceil(X.max(1))\n", + "xg,yg=meshgrid(arange(xmin[0],xmax[0]+.5,0.5), arange(xmin[1], xmax[1]+.5, 0.5))\n", + "mxg = hstack((hstack((xg, zeros((xg.shape[0],1))+nan)).ravel(), hstack((xg.T, zeros((xg.shape[1],1))+nan)).ravel()))\n", + "myg = hstack((hstack((yg, zeros((yg.shape[0],1))+nan)).ravel(), hstack((yg.T, zeros((yg.shape[1],1))+nan)).ravel()))\n", + "G = vstack((mxg,myg))" + ], + "execution_count": 0, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "SMsKyyOrKm-G", + "colab_type": "code", + "colab": {} + }, + "source": [ + "def plot_marginals(gs, axis, data):\n", + " if axis==1:\n", + " ax = subplot(gs[0,0])\n", + " data = data[1,:]\n", + " else:\n", + " ax = subplot(gs[1,1])\n", + " data = data[0,:]\n", + " xx = linspace(data.min(), data.max(), 100)\n", + " yy = norm.pdf(xx, loc=data.mean(), scale=data.std())\n", + " if axis == 1:\n", + " ax.plot(yy,xx)\n", + " ax.invert_xaxis()\n", + " else:\n", + " ax.plot(xx,yy)\n", + " ax.invert_yaxis()\n", + " ax.set_axis_off() " + ], + "execution_count": 0, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "yynsjN2RKm-O", + "colab_type": "code", + "outputId": "9816c39b-b3f7-4df8-862e-92a558e90ed4", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 283 + } + }, + "source": [ + "if 0: # If true, will plot marginals of data\n", + " gs = gridspec.GridSpec(2, 2,\n", + " width_ratios=[1,3],\n", + " height_ratios=[3,1]\n", + " )\n", + "\n", + " plot_marginals(gs, 0, X)\n", + " plot_marginals(gs, 1, X)\n", + " subplot(gs[0,1])\n", + "plot(G[0,:], G[1,:],color='gray', alpha=0.5)\n", + "scatter(X[0,:], X[1,:], color=Xcolors)\n", + "axis('equal')" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "(-2.2002649726160857, 2.205564424937798, -2.2, 2.2)" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 14 + }, + { + "output_type": "display_data", + "data": { + "image/png": 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" + ] + }, + "metadata": { + "tags": [] + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "mpOCI-6AKm-X", + "colab_type": "text" + }, + "source": [ + "# Theory of PCA\n", + "\n", + "We will describe the PCA algorithm in two phases - first, we will describe how to compute the first PCA component. Then we will generalize it to more components.\n", + "\n", + "## Only one component\n", + "\n", + "\n", + "We want to find a projection direction $v$ that will capture the most of data variance.\n", + "\n", + "\n", + "The projected data is:\n", + "\n", + "$$ v^T X $$\n", + "\n", + "Let $ \\overline{v^TX} $ be the mean value of the projection. \n", + "\n", + "The variance of the projection is:\n", + "\n", + "$$ \\frac{1}{N}\\left(v^TX - \\overline{v^TX}\\right)\\left(v^TX - \\overline{v^TX}\\right)^T $$\n", + "\n", + "By noting that $ \\overline{v^TX} = v^T\\sum_{i=1}^{N}x^{(i)} = v^T\\overline{X} $ we compute the variance of the projection as:\n", + "\n", + "$$ \\frac{1}{N}v^T(X-\\overline{X})(X-\\overline{X})^Tv $$\n", + "\n", + "We will call $ S = (X-\\overline{X})(X-\\overline{X})^T $ to be the data covariance matrix. \n", + "\n", + "The 1D PCA problem is thus finding a direction $v^*$ such that:\n", + "\n", + "$$ v^* =\\text{argmax}_v v^T S v $$\n", + "\n", + "Since we only want the direction, we can constrain $v^*$ to have unit length: $v^T v =1$. To solve the resulting constrained optimization problem we will use lagrange multipliers. The Lagrangian is:\n", + "\n", + "$$ L(v, \\lambda) = v^TSv - \\lambda(v^Tv-1) $$\n", + "\n", + "We solve by looking at the gradient:\n", + "\n", + "$$ \\frac{\\partial L}{\\partial v} = Sv - \\lambda v $$\n", + "\n", + "At the optimum the gradient is $0$, thus:\n", + "\n", + "$$ Sv - \\lambda v = 0 $$\n", + "\n", + "Therefore the vector $v$ is the eigenvector of $S$ with the largest eigenvalue!\n", + "\n", + "## Multidimensional PCA\n", + "\n", + "The reasoning above generalizes to many dimensions. The general solution to the PCA problem is to project the data onto the $k$ eigenvectors associated with the $k$ largest eigenvalues.\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "qeYoCohbKm-a", + "colab_type": "code", + "outputId": "ff82e957-335a-4d8a-a460-c96ef4bdf360", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 52 + } + }, + "source": [ + "#Compute the covariance matrix\n", + "\n", + "S = 1.0/X.shape[1] * X.dot(X.T)\n", + "print(S)" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "stream", + "text": [ + "[[1. 0.64383629]\n", + " [0.64383629 1. ]]\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "XTNa385CKm-m", + "colab_type": "code", + "outputId": "f9846192-f432-468a-ca7d-5333d9750237", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 69 + } + }, + "source": [ + "L,V = eig(S)\n", + "eigorder = L.argsort()[::-1]\n", + "L = L[eigorder]\n", + "V = V[:,eigorder]\n", + "print('L=',L,'\\nV=',V)" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "stream", + "text": [ + "L= [1.64383629 0.35616371] \n", + "V= [[-0.70710678 -0.70710678]\n", + " [-0.70710678 0.70710678]]\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "3d-hmnbMKm-t", + "colab_type": "code", + "outputId": "e8a72ba7-4cee-46e0-d483-db6ae1cfc09a", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 335 + } + }, + "source": [ + "scatter(X[0,:], X[1,:], color=Xcolors)\n", + "plot([0,V[0,0]], [0, V[1,0]], 'r')\n", + "plot([0,V[0,1]], [0, V[1,1]], 'g')\n", + "axis('equal')" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "(-1.5311543411130317,\n", + " 2.141785304577779,\n", + " -1.7897953911031323,\n", + " 1.9370802817980646)" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 20 + }, + { + "output_type": "display_data", + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [] + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "LTjbYLghKm-x", + "colab_type": "text" + }, + "source": [ + "Rotate the data into PCA space" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "8lbTGjXnKm-x", + "colab_type": "code", + "colab": {} + }, + "source": [ + "XPCA = V.T.dot(X)\n", + "GPCA = V.T.dot(G)\n", + "VPCA = V.T.dot(V) #this will be the identity matrix!!" + ], + "execution_count": 0, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "hAj-CDdyKm-0", + "colab_type": "code", + "outputId": "3455ce5e-01cd-4dec-8425-ffb884518967", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 351 + } + }, + "source": [ + "subplot(121)\n", + "axis('equal')\n", + "title('Data space')\n", + "plot(G[0,:], G[1,:], color='gray', alpha=0.5)\n", + "scatter(X[0,:], X[1,:], color=Xcolors)\n", + "plot([0,V[0,0]], [0, V[1,0]], 'r')\n", + "plot([0,V[0,1]], [0, V[1,1]], 'g')\n", + "axis('equal')\n", + "\n", + "\n", + "subplot(122)\n", + "axis('equal')\n", + "title('PCA space')\n", + "plot(GPCA[0,:], GPCA[1,:], color='gray', alpha=0.5)\n", + "scatter(XPCA[0,:], XPCA[1,:], color=Xcolors)\n", + "plot([0,VPCA[0,0]], [0, VPCA[1,0]], 'r')\n", + "plot([0,VPCA[0,1]], [0, VPCA[1,1]], 'g')\n", + "axis('equal')\n" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "(-3.1112698372208087,\n", + " 3.1112698372208087,\n", + " -3.1112698372208087,\n", + " 3.1112698372208087)" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 22 + }, + { + "output_type": "display_data", + "data": { + "image/png": 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8Ph+KokR5VhJJV6TIJZII+P1+li1bxoIFC1iwYAHTp0+P9pQkki5IkUskETAajbz11lts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\n71Ee/meMm0tTu5e4RBKkuRnaN7QoLgY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" + ] + }, + "metadata": { + "tags": [] + } + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "k0zIWuAlKm-6", + "colab_type": "code", + "outputId": "c7bd622f-7546-4d6c-8e89-23300b909fd0", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 285 + } + }, + "source": [ + "X1D = V[:,0].T.dot(X)\n", + "scatter(X1D, np.zeros_like(X1D), color=Xcolors)" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 23 + }, + { + "output_type": "display_data", + "data": { + "image/png": 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" + ] + }, + "metadata": { + "tags": [] + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "MLSiXCsaKm-_", + "colab_type": "text" + }, + "source": [ + "# ZCA transformation\n", + "\n", + "We can think of PCA as of a rigid rotation of the data. In the PCA space the marginal variances are different for each axis (they correspond to the eigenvalues).\n", + "\n", + "We can normalize the variances in the PCA space to have unit variance along each axis by dividing by the square root of the eigenvalues. This procedure is called [`whitening`](https://en.wikipedia.org/wiki/Whitening_transformation) and results in a data representation which resembles white noise (all features are normalized to have mean zero, unit variance and are uncorrelated). \n", + "\n", + "The PCA whitening is not the only possible one. In fact, any rotation of the whitened features will also be white! ZCA (Zero-phase Component Analysis) searches for a transformation $Z$ such that $ZX$ is whitened and $ZX$ is the closest to $X$ in the least squares sense.\n", + "\n", + "ZCA is derived from the PCA:\n", + "1. Do PCA whitening: rotate data into PCA space, then normalize variances.\n", + "2. Rotate back into the original space.\n", + "\n", + "$Z = V \\Sigma^{-1/2} V^T$\n", + "\n", + "Note: $Z$ is symmetric, i.e. $Z=Z^T$" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "fOyeMOU1Km_A", + "colab_type": "code", + "colab": {} + }, + "source": [ + "Z = V.dot(diag(1.0/(sqrt(L)+1e-4))).dot(V.T)\n", + "ZZ=inv(Z)\n", + "\n", + "XZCA = Z.dot(X)\n", + "GZCA = Z.dot(G)\n", + "ZZCA = Z.dot(ZZ) #note: this is the identity matrix!" + ], + "execution_count": 0, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "KPeVY-zWKm_E", + "colab_type": "code", + "outputId": "7f29a952-b205-4105-e4c3-9ed343cf37db", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 583 + } + }, + "source": [ + "figure(figsize=(8,8))\n", + "subplot(221)\n", + "title('Data space')\n", + "plot(G[0,:], G[1,:], color='gray', alpha=0.5)\n", + "plot([0,ZZ[0,0]], [0, ZZ[1,0]], 'r')\n", + "plot([0,ZZ[0,1]], [0, ZZ[1,1]], 'g')\n", + "scatter(X[0,:], X[1,:], color=Xcolors)\n", + "axis('equal')\n", + "\n", + "subplot(222)\n", + "title('Step 1: rotate\\n(PCA space)')\n", + "X1 = V.T.dot(X)\n", + "G1 = V.T.dot(G)\n", + "ZZ1 = V.T.dot(ZZ)\n", + "plot(G1[0,:], G1[1,:], color='gray', alpha=0.5)\n", + "plot([0,ZZ1[0,0]], [0, ZZ1[1,0]], 'r')\n", + "plot([0,ZZ1[0,1]], [0, ZZ1[1,1]], 'g')\n", + "scatter(X1[0,:], X1[1,:], color=Xcolors)\n", + "axis('equal')\n", + "\n", + "subplot(223)\n", + "title('Step 2: scale')\n", + "X2 = diag(1.0/(sqrt(L)+1e-4)).dot(X1)\n", + "G2 = diag(1.0/(sqrt(L)+1e-4)).dot(G1)\n", + "ZZ2 = diag(1.0/(sqrt(L)+1e-4)).dot(ZZ1)\n", + "plot(G2[0,:], G2[1,:], color='gray', alpha=0.5)\n", + "plot([0,ZZ2[0,0]], [0, ZZ2[1,0]], 'r')\n", + "plot([0,ZZ2[0,1]], [0, ZZ2[1,1]], 'g')\n", + "scatter(X2[0,:], X2[1,:], color=Xcolors)\n", + "axis('equal')\n", + "\n", + "\n", + "subplot(224)\n", + "title('Step 4:Rotate back\\n(ZCA space)')\n", + "plot(GZCA[0,:], GZCA[1,:], color='gray', alpha=0.5)\n", + "scatter(XZCA[0,:], XZCA[1,:], color=Xcolors)\n", + "plot([0,ZZCA[0,0]], [0, ZZCA[1,0]], 'r')\n", + "plot([0,ZZCA[0,1]], [0, ZZCA[1,1]], 'g')\n", + "axis('equal')" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "(-3.6857433037753884,\n", + " 3.6857433037753884,\n", + " -3.685743303775387,\n", + " 3.685743303775387)" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 25 + }, + { + "output_type": "display_data", + "data": { + "image/png": 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lmczMTCoqKsSRe4JOR1pamsspp6aMHz+e8ePH88ADD3D48GHMZjO1tbV8/PHHrF+/nv37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7GxgUmT8jAYos+taDBjMlXR2NiAJEloNBrk8s69RpVKTV1dLe3tbQH5kl94bE1NNRqNpkt52Qvj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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [] + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "GqEUo3O6Km_N", + "colab_type": "text" + }, + "source": [ + "ZCA Whitening is useful for images: the transformed images have decorrelated pixels, yet are close (in the L2 sense) to the original images." + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "n2HuWb7EKm_Q", + "colab_type": "code", + "colab": {} + }, + "source": [ + "with np.load('mnist.npz') as data:\n", + " mnist_train_X_flat = data['train_data'].astype(float).reshape(-1, 28*28) / 256.0\n", + "mnist_train_X_flat_norm = mnist_train_X_flat - mnist_train_X_flat.mean(axis=0, keepdims=True)" + ], + "execution_count": 0, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "w2wFqVGTKm_X", + "colab_type": "code", + "outputId": "49184c47-718e-4d61-b822-1004b298ac28", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 248 + } + }, + "source": [ + "plot_mat(mnist_train_X_flat_norm[:25].reshape(-1, 1, 28, 28), scaleIndividual=False, colorbar=True)" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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rVbNYGdgMqJjbYD1n6iqVX9tROWRvH+66Lv58m1ohfae/HcuxieheA2VESBhx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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [] + } + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "AnoUDmQwKm_f", + "colab_type": "code", + "outputId": "45c40fe2-1247-4ea2-cd7a-c0c5139bbfba", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 35 + } + }, + "source": [ + "S = mnist_train_X_flat_norm.T.dot(mnist_train_X_flat_norm) /mnist_train_X_flat_norm.shape[0]\n", + "S.shape" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "(784, 784)" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 28 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "8GgNU1fUKm_h", + "colab_type": "code", + "outputId": "0f16a1cf-b038-4c58-9be5-0aa0972c242f", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 269 + } + }, + "source": [ + "L,V = eig(S)\n", + "L = np.real(L)\n", + "V = np.real(V)\n", + "eigorder = L.argsort()[::-1]\n", + "L = L[eigorder]\n", + "V = V[:,eigorder]\n", + "\n", + "L[L<1e-2] = 1.0 # note- the zero eigenvalues cause a problem!\n", + "\n", + "Z = V.dot(diag(1.0/(sqrt(L)))).dot(V.T)\n", + "\n", + "mnist_ZCA = Z.dot(mnist_train_X_flat_norm.T).T\n", + "\n", + "plot_mat(mnist_ZCA[:25].reshape(-1, 1, 28, 28), scaleIndividual=False, colorbar=True)\n", + "plt.title('ZCA Whitened MNIST - note that it looks like edges!')" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "Text(0.5, 1.0, 'ZCA Whitened MNIST - note that it looks like edges!')" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 29 + }, + { + "output_type": "display_data", + "data": { + "image/png": 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mmetHuisOjSuWnHyhnaegpV5HQQkyHPMas5m+J3XfHCLKOblHscUS+EL/dktH\nFSnLo8ywAxvIoXZgMn31WcBgA6ev4a8IJaj2dHtLHN0/Y32HA/K9JfjnVTkN2zTDvTSWYUO2hDHx\nTg4zBNxtJUJ7Jwzcer691uAJrS3UeoV+7xA+Z/T45NFz2cPlwUSSqTlN3wjf5afxHlr8Hq7M6yOd\nlBDUyQQVhqhOqR2LedE70qcvFDsIne1ODimOumiXmmmWYLG/p23CS604XZkYpXE9IzqET4nQzDqQ\npLukotwX4UYMYoewv2HFMNiEr776aq6++mpAnzp0zz337BYDhn2ECUeIECHCHkWUrNE3wrCXIhtw\nmW2z1u/h11v04X4T84r1ccmnxzdzzofavPBXWcpvRBP72zr6oNN2+dYLZcxJ1DHB1bvvRsvnI34y\n3NE9AVkh6NlO8tgZgr05J3RsY56C+pUy4XKB1NSjPHLYPBFzODGjZetG22aN7fMvvg5hSZbmOLan\nhufiOc7r0fRtiQua/DSjpJaEYwoyohA32RccBYkiGX71O9W84TfyidgBAKyyfQ7wHHqEokXq61rx\ncRCMMjbrPIptwmOUssK40qtyKbKZbl6Na2lvnK/V9PVOQdW3+lEPJVqt9gVhaJQDlPhQYY7aKVGC\nFulT7UvWWK55ls026TPOaAXTe1wabYcxbo53zIkKHcplBHYYgugjiFGgrS8oTKJPYE5C01dVFL7R\naimW00OPr/trildGlZ+n0db99Vfb432/g/tEBwCfU+OwHCBbwkZHL6MYLpUexGUQgaL/3zuOYEd4\nKD3PikLAMvj02PqLFuExyXPYL9HOo+jIGkvB8RmfCaX6xPO7/BQHqVK67CT1xma+jFJyKscHtu7j\nciW1qi8K/dVXqJpgx8SUYJ5YQiccBf2ZM+aKHD6TJ+lIlsaVo9mq4pSZ+9N4tAtBnW+FETG2KiSU\ngPZz2Ig9Fy88zGnLM2bMGNApKv1h7zNh838loDavP0kcfFvRaJax7dg8kF/LpGVjGBPTNrlNQhFX\nNifntAr+ctzlduVRqwStMnB0+ThINhpG5AI1QvbKIupLHfPDBasXSFIJqgzfcyksGIBPZBxWODaH\nuCCNNfdutZFP+qNpy2mm8rOWOKOkYp3XzSjT0PRWaE9Uhyp8lwl52lVej0CbOeqrupATD9b0+Ovo\n8jLUGKKfFy1Mk1X4wAjj+Fov84xQheHOoShXkoQSvI8+l61BluN1pVgc14xmrl9BlYKsLLx3f/Ap\nmCQCHqdD0wRxitRiFDkTkgdQ4ymWyAznZnR/tUuLDbaizLN5R2qmMtMrodpTrIgVnpUcoIM1LwqZ\nWhkUNb4Mw7022oo0PgerJMmjAQgAACAASURBVEdl9VtWWt1sJc58SzO5E/1KDlBVJKU2AY3O5Xk3\n5lAtcjxhzDmTvBiuKGRpBsylv40rQDClkgriyNBHUqEsZtFBZXWa07bqwagZ0U3jlnL+y9P9VSHg\n6KzgtbikydNrYj88rJggZUw99Z6kXaodsuj6QnEmZ/EmhlLkhQh/TylBk/DI4vOnVfrU5DrfRQKf\n9LR5aYkq400nR6ksxJonlOjl+9iTcqoClL9HWPtuY68zYdCMrkcI8sbuVOIrJnoxus3KGuEJxjvV\ntLuShpFasjy9SfGuiIcLcoSy6RSCMl+G8bL1vk1WFIz8CQTWIIPBg4yscq/AXFbZHikko03UQClZ\nqjyLg51O3lN67z8qVkuz8pmf1NO9DMHRPR6vxHxiiQI7OzwnWGxiKdfZOhZ6VwxFoiXm6gPTiCOO\nAaBuv/dJbU0w2URLjEqUkEWRFh6OGeKxvkOX0BmEACkl2d+VtFrgGgnBQzChpo2qbv0OaQkjcz5p\nw+jSUoQxnbtCIMkHNlgLQU8Rw035Oolgg+Ux3tXfvuN4bPMzlBib5ybLYUYmz6sJm1Lj3Y8p2GKL\nMMsuJzSDjw/A+qooxHlLdGxws1WIsa1XDofkFL5p6wknie0ITva1k9JS8ILVzeWGM77jlLB/3ufZ\nWJKAlcQUbLMKz0kVRQHsCgJBTBUiPAKNMGBKqyyfn8k4Y1vKWG3pMe5sKWViLME0Y9iekHP5S9Kn\nSlmsNZrLQfk8aeUx1dWLJGM470Dmf/ElvtD9V5w8tb2jbqxvkbFi3Ce3AvBDJ84Cyjk5q1dNq1mn\nlX5hDuWNRB5shkHc8B5JlY/SlvuGJEjdVTQb9SstFBU+bDLTcCQWR4gUd4nNVK3T4WdHHbSZ2Loa\n5mfXAHBiYixlQaSEmR5dQtEuPEYaaTCojVA8FAMZ72CJbzazcCs5jjISLsBWEePxWA/PEGeieYcp\neYcVdiFlepwr2WopOrwMXR3acfihHWe0W/BetwuPVFEWWV/95QmwSiWyRp/G3NURZ3N2I8RGATDV\nT+IoaJWSZqMFlCubWl9Qa5w0axwtAa4jyzFCS3eVvofvCSoM02vCY6SUYR9Zin69TcG7SArefaBX\nREVWKJqkj0UhrTuF5MpcGY2WHV7/bsxhA1lOzOoVvCKmcFGh9CsoZP31J9lZCOLGiesgKfd93jVO\ny3k9Fily1JamWWM2oHbhc3xG0moZ7cJOE0PSrDQtPQK6pWAxHczxtCMzIzUDCQxgjhqY41eGb6OR\nNlJ70H9t5I26r5is4uZ9EvSgWG/G94OkT5OfZXo+xTazquuS3dSpMjYbrrtVuFQrO2R6g4GjRJgJ\nGDDKYDPcLDxGK4uDXYf3zXvU7t9J5/pSYpZJQ0eRMNJ9YNaII0j4hbHLiCA9e/hqvPRCJAlHiBAh\nwl5C5JjbNYKdMLCBtQlFBSIk7kPbo8JIuffEtU148rY430p087w7HoBVyuMt1cFHRHlBAhNa7Q7S\nSLNCO4ikGHxAeI/UCQ4A+6kY9SpH3jzn4aSgEocDfCcMt2mzBClkqMKtsD3iCMZTiW2brPsslIs8\nJUa66RJ+v3YxH+1czLcWrlybSbGlq5UFo7XU3aky1OJQ71thONA24bNW9ODFDH1+lsNlBWf3OKFz\nZ5mo4M5sJbVGc8gIRaslwnco9xVdA1D9i6XhAClVsCF2SkW9b1Huw5O2Ni+NJ0m7sMgak9QBOY/n\nk4oD/RgdVmBbVYzwZa/6Ca1hENmu6SoOs0r4kBGCDhNze+zUrbz3Zi0v5Kp4P6m/G6FsHo9nwrlz\nfbyH5o4SltlW+G5/cnqYpspD80GT7VOmCrbmIEW3P/U/iKkOQr46pKJb+MQ9vQI+4idwFDRafljg\nqBWXw/04B7q6l7PS4gPbYnkMjs5oXS9j2ZQ4BU2mQlmh32Aw2mBQvS2YBxmhSBTF+KaEZIPlckTO\nohsdoqY8QRqfLlebl8qEYKPxBThFY5WRBXOEA7hDqGkxYERMeOeQSntb40pRYvoobQnapeKQvJ5g\nb8Rc9vcsPks9t+dWAXB39zgupIspSjPl/TMx8skULbhkjfV2rG/hU4hD7BQ+jrAG5JQI1CFp4mIz\nomADm54VtCiHDSYw/gO3iXOpJeWrUMV1hQ7SbzeLZoSymJjzWeLkyGT0xKx1PSxZmJQVSuroAnZR\nJB6tCmdaHMq72wFI4XLSyClsVpq5b/G66ZAlLFYZjqEGgAmuZJQsZU5c19UYMb4baXfzx7fH8kpW\nmyOmyG6WeRmm+DXmWTpDq2DL1Ux5VxuYohD3GkQxuGgmHIxDidLFcD5w8hyudOLF9IzLOtthi+FY\n82U701UlJUqwxtJPrPctHTkQOL6M6WagSysYUxtosQr3CRvejiW4rvlFjqg6AICr/VEcqWIkzFWr\nMxX8NpHj0qzu4/tsqBExRrmC5cYxl0cREwWbTWA7tQfAWKQqODLjSiBDC7Huy1estInC0X3xUVXJ\nKeVNvN+sx6rCV6Q8SVZC2sRV/7fs4SMiwdHGLlvh+2QErHdk+KyBqv0+BWd1XvSufjfSE3RZgrQU\nSMOYla+IIU2sg34319jvC6U2hREqdDslvmbEe8xoMIwFfIYTe50JQ5AxJ8LSkCM8wQe2S8zYB0co\nm6VWlulunLPjBwCwmTw3KsEFSidHTKloZV57OS8mbDaZ3ThvKWp9K7Qhtor+bYfbw0dPHiEEVca+\nO4oe1slkWHjnDFWLB7wR80Ip0hd6MQXB+xmhWONIlnStxSs9EIAYilUiGU7KGr//2lYKPaEz3Q6q\n8UMAJo9v5rf1Pqte015xIUo4oKGN5a/VMLpuCwBbt6TYmCvhN1I7mrYuLyGP4uH2V/h2jXbwVafS\nOJ126DgpVZqJBDbOEuVhKdmrME9ffZanUIFMoO3+QYZalSdYZ/kkkZzj6OJKD1NFrQeHZPU1LYly\nxuclG2zFaNOnWaHbCJh5adGcGQxcjC3ZvNfqN6uZJTt4pqoBK9BklEu5lWMZpebZghNdG0ztsHfz\nzXxJjOGvthdWmatSlnYKFzHTgW4QgkIm4UhP4QrBWsPcV6CjQ74jPXpyegMvTbSysbmcV/SQ8wmv\nhz9YKRQwwagKs6wRrFQ9rIglDT02LcLDxaPcrIQS+re/BptqsHYqfNGrVva2IkEiZvwJvufiKEGz\nMGnLQBJJiQ+tMugf/f9gPD2htd89EqIWmSMiRIgQYS9jGNKW9wT2CSbsKL3TNhmjU70LY32bLrNF\nT84psjGHjbaObQWwRYxSabHUuGwXZhNcZWeZkUngGHPEQwkdolXr6XayQtvrdLlBjcHsuM3CBL2X\nZJE9CV5EmwOmygqSSpscApvbIquHg0SCcUaKSwvF+zLDpeVHUF7aDMB7bSlej7lhBEWFSY7or4iJ\nD/y1tYra+xcCsHZNFYdObAudv1nPYfGrI3kiCVuatbd/g+rgkIRDu7GDHkmKJulx7YhjOMnVJp01\n2yqpSuTZYuS3Ok8rxVWm/3SCSKEsYl9QJnypwojCnnmn/Uw4lQTSwqch77C+R9PXlfA5Pu/ycxO+\nN0klWW/raAgRlnJUVPgCk/OhS0UqEaqz/SG4zBM6FjcoxvOIHeNCq50DprWzYYmm5wW7hA/I8XbP\ncgC+JyexNiZ5V2jRc4ysYDOKCiWpKCqSkbVEWLQ/eNZAUFzKNSsEm2zFB6QBqMDhwoyCZJ6fmPCz\naj/FB7EOmrI6prvWGc8hWZ9y5TEqpe3spxzexV1LxvCe0JL0ak/b/ifb1ZSYWAd/ADHDhaL3BTOL\npaAmCF00kRw9ArpcrSkIYVOODKNfDs65/CXWSb2sCplOq1RUe4KcIcBRhRotwx4doVQUHdEXBPoI\nm6yEZUKbEWJWnJGu4gMTaLo8JihRerBbjepS70mEZfGBUdWWZhqx47W8aVt8MqVjFUu7q1GqUFsg\nsD8NRinx0Vk8Cmj09QTzlCTuKyqMqjUhD82WYI3ModOodJhYVsAKkxG2xu9mGuV8pmoL7zbq3P7l\niYKNFHQSRt4aSMwrNNkWT/5ZZxT+LtbBqBdHsMbSi2+0Y9NJlnEqyUe9FADtVimOL+gR2gloozOo\npmR8PpRa5V4bh0nYYWEiZcK/Up7usRwWA4GPVsUrzaTfZAs8FLWm3Xcdl4TSBfDfiOspeHzGI48k\naZ4x0pO0Ss3kgkpmSSUo81UYT54bgoM1gKVgP7OhrxQ5/ttLsPr1HGMtPab1KI5UpUxNHATAtOot\nbN42MhQUppACBft5gtV2kGSk7frG90leUGTZ7b/PArV8iZ1ls5/mJHR26EdFB1Wjulm2aQSW2aSq\nlc2BVhlX5HR4XEU+TUVplvluJQemtcmpZHWOz43ZRFuTNkc85Y/CUbBfzqfV0u/eIwYmiBRvEh1C\n9ar412WK7iSVYKyjnx2raCPVKMJwuWNqmqlsLcfxCefXJlsnQgVV1FwTj7yn6gqryByxc0igRCnK\nXKiLaQbWIn3apQgncJvw2N+3qfAF64yT5iWrm5EizldMoMEmMYFleUFb3MMzHuMWlacWiyY7mCx+\nWDS9v6VRXAFMoBd7ENGbdy2WJiQbPM30umQJJQr2U3aYCttiKTaLPEkznY6ngpNo5y9bR/JATKd2\nzqCKWlPeD3QEhkv/m4Qv9ARuNLZvFGSVz2FSL8iJnsU2qRdJRyhlCDZLLzy5okcomoXLBifGISbJ\n41UpqfPtMMlimxFHeozomUUMWLIDwhjbJuGFJSsBmlWOWw5qZunSkaw3acEtlsVCu5NjlU7L3WYp\npNl4A6bmodhiFxw7ttD9pSfxrgkTFCa7i96MAxvsISpOyoeDrUQYR90qdULHSlNAfk1jFfvj8bCj\ntZgzZB09QrHFVqFuEDdx6EFSxGCWfLooxXyzl+ZoWcVnD1+naVmd5I6WWjqTHnmTWLOSHo5xSxiV\n0NrY+7lyHnMVjV4TS0wRqefaK7moOc+kY7UEfMlBJYjKcvJL1/DM07o86HpHDmgj63XqiNAJT2Vm\nkThS25V7hKLD13Ppj++NZZqf4dm43vTTXTHmuiW87uQ41MRaBz6TwCGfE3pcBrbVDwGRJNw3fDQj\nPtbUXVhvO7zvuBxrZvPymMU6y6VJ5ZiEnmDnZpNMjHfSadQqVwgcpTgvl6Upo6W/ioTFSFfQZhZF\nOYUKToMdji58YuaEiZJkjnHpUsptPcE2Cl9XKVOCVy2tQq5zOzjRrmVmRs+wCpHmVbuC34ktHGSc\nY+NdSZssePtbLT2Z++NzHjoJpUNpqWieX0HKL0RvtFpaKumUilaTIXeAZ/eSysbnYb2jGJP3GF2p\n05a7MikSQoYnaXhCS4xdwRk6A5Tq9MkQig5zeQrJ6LzPa8YTs97rpGllGc8nbE7M6I3kDwmbcaKE\nCpPHmrYLh6DWGM4fVLELQhA9gKJawv3BCpnIjufWtVtmozIXdQhFTElecnW50FOowkFRJbU5otyD\nVltRrgQTjSOs1dLV+YJQs4GmB7uicCoKwAVeFZO9NO8urgPg+04Ha7PLOat0EnOzev4fXNpORw7+\n3WyQvtNJnUgwR9XxtqmUt8br4jqZZ/brOpX48yu2UFrXxLK3a0NJeKCQ2yWeJJQItYI0PgkhiCvB\nMZaO1vjAUpxY20Lc1H9ZnK6izPdZLbs4lEJ52YxQlATp3abP9sjxRkpFR95HiBAhwl5FJAnvHB7a\nnrrZFpQbx40PtKk8z5gC7gptAxtNnLlZbQO2pc/TqoL2uN7dTsjkSWPxjF1CozmHbn9fK4phnGvR\nCcMDCVAHiAtBj6nDUGYK4LR1SUpQnOpr9X+pnWOR184xVg3nmQI05VSxzYM1psJWs2WxkSzzVC01\nRuXtkr2PvM+jcIQYUMEXSwlqjE261vX5a1yQMW+laZWM9CRYlrle37fR9E2VsLGEoNW2aOvU0tVU\nmaDFUiQNQSlfhI5CTL/1J0sEoVaeAMvQs58naHQEW439/uvufjTmPapjkoljdNzyxuZyjnNL+SA8\nP06GyQ5BQSYHEaqu4cMGcV7a9tJvIAt2CUWP0KF4gZNvgitpshRHSG2/T4kMzW4slHLbLH0iSZP0\n+SAWSHI6pToINAz6vL/hVCjSQtd/BjitYT1taxIs7NQp+h9jP86qFsSTzTRv1Vqe60qeiiVpcnUI\n4hnWSLqUT5OlONwkSEwSVbwgO1mitPOusbWKRJtFMi6oMDGz8QH0n0RrD4W6v0CRlD/Wt2iVylyj\ne/lPPWs5a2MdDaZew7sxh3mTN/DaqlHETaaIUjp0LYxZpnCi9R4JUXOj6Iidwhe6CMs6keNdpW2l\nFTLBoVSw0SQfCODr8U6yWZvH4uXhvTMy+XBh/Tbh0+R3c7AoD5mvVLDBLtgUY4MwRQRTM+Hro3aS\nlmSE6S6fLBucwikMn8z4fGjtR96DNUGhEk/SVuRkaxIuH3HjVPqK1U6BglJfEN+uYHZ/9DlKUIXE\nNos2J2ADOWqNdfLQvB2qih2mh3xLUuvL0LQQFOJO+Ir6UXqR5ppKeUd1ga0X+mhXq4bZIhvnQPrO\nRmeJBaYfqeB9OxceMPmRmmZebt2PMXmfFxq1bXKs45tShhouem7EtntgWhYKrVsDiHENEMRXF79H\nsCTjShcbFwpc02+NtjblHJXXfbrGs6gjS7evzSeOMdUUM88gHj1gvkHM60AgEGGVt3y7JFmWZ1qz\nKXB/+FYybTbPNo7kZUc/f42f5WDL4+NS919LkEknfJLGnDTa9ZknC7UjNok8LSpHlXDCOisDQdDH\nwTSNmfhxt6ikaLvwOMCziZs44f1j1SxRKSZ72kbsCm0N+FB1YZnys2M9iS0K5riY2oMHfUJkjugL\nloIqJUiJOHnb1ArOb+MjXhVXjNFOh5Vrq3nVrWGDrTjS2I3bLYuHEz5tpoLVeJIc5yfoUYWF2yWD\nlMsCk9NZTIODA5QqSTrM9FEclsvzgpHUF9o2lvJoyBUSGTbZgj/4TYy39KZRhU2T5dNcxJhTSuBQ\n0JIGIwEklY4YAXCFYjSx0OscU4pG6eLghBEAOaGZ0FYTZleJQ0zpFGBpuEbKB8eW4dlm7YZhD+QU\nhmL49C7202UYfp2pFdy0LYVvCUqVxy8tvQHMUdV0SMLjqnJCV9yCwlFPQWpvmOlm/jPYcCabHaXi\nrNAnPQT25g7hk1CSJyxtL79OKupGd7J1tclKTNRwaF4yMyPDaI0tts4EDM5eUwOw7+tX0OUmuwwj\nfXDtGPZzFY5hTo3vj+Hf/RWMjm3jo0rbXKtkJSVKhrV5YwhqTJLTRhOR0y0tqrzCEVflVowO6aAU\nvVKH+0PQ74GttkSJMOEFAien7FVhr0zGeIUe9jebmK1A+YKxsiQcV2nePdhUizfGPYLIHBEhQoQI\newlKDVuIWjab5dOf/jS5XA7P85g3bx5f//rXh9zeXmfCEij1FVMTbXzxDP2dSNWw9v/a+L/NujTj\nOOEzRXZg5ctoNzbOh+0O6kWSj7rGRgassH08CmmuDvr8sOL9b7DD4AlNY1IJNgstUvwiLjlUOZyY\n0apWTSJDaybBMwmHRb5Ow/2IqOQsUcsEI7mvillhbGVxWUeXoZ+plTbttNvQgyIvA8++lqz286DN\nSLNbhYcnJJM8LZk4Cpb5Hczyyqn8mLZ7zn6omS09NXSbXuox9TL6O4WhGAoT3C8KRdS7hD6Ms91E\najSS4BCli6YHNtYSX4elFWyUih4jgQWFYhK+PjdtV4egDgRCQbzoc1Be0TFhVqBTyNNCsSavx7Ok\nrBTfEzQkRpl3yLHFgXEkwmSNtNB2UWnsrf4ASzLaykTumOCsZumzJu7TrUwZUmwuYCL1rmC9iUku\nQRfkD6TnDIpSYTElb9NuBmyNlcez7LBPy33tSxjMIZ8QFBgSBHpa0F9BqGCZEtQgaRU+40x4aJlt\n81e3BcfULjm3tpGyY6s56tc224q0waTqXbRnj8qqwyQJx2Ix7r33XkpLS8nn81x44YWccMIJHHnk\nkUNqb68z4aAqGICs0Y4uOe9sxk9fzUlXvgTAX5wK2vxynnG6w0U7TZUzJgfLTMEcB6j1tXoW2JiC\noO+hZN8EtwRMu0QJJpqlmzX1C36fDKqWxbESMAKYZyZdyoUNts/bCT0pLaXDmYQqFCwJaqcGdUUG\nuTbCuhRZoQcysPPVuYoOy+pV12BKXtJoE9afLUFyoCijApfs29q5s651JN2JwjZlA/1HVO8IhVZh\nA+adUoI4TlgrYLzTyaSzXToWtzFps3Y+NSrfZOcFbWhmkZaFTbS4FkXwnMEgfDOh7w2YebfUqnaF\nL2ixAlOM/n+dsV++0F3FadUbudbRzsUH81W8p7rolB5xUaispkMMC7bwgcJRoig+VlDtS3Km3SCh\nYb3ts8VQPZoYXcIPGWwSwVapKzwE5rhqZevsxKKMNCX6P25pZ5CAHZ6SrGsBl4XmL308VBDzD3Ck\nF6fcruU3trZhr90iOfT/bFKOH9b3DjJlwyPOBknToKAYtrRlIQSlpTrByXVdXNdFiMGvkwB7nQkr\noFvCS7kqlt1pdvk75vNe3OZFM1VqZYY5bpwTvFI2mSLRNb6gxdL2WYAxriSuFBvsIkM/hQD64ucN\nlr7iExlAT7qcgIRhegli1JgShoEHeYutJcdgaDwBHShkUTTE9p0/lIUB2qPsFHmrOyzt5U8gqDQR\nJ2mpK18dZirTJZTizzGPW+M9VCzVknAyoSiHsLjL7mYuWUXsMo9itdCaw1vCYtTvS6hUVUw2K3Bs\nzqPdEmw1neIobVe2VWGRBs75ocozITM3f/nQIaQdpErANiOt1yiLQ7KK1XEdF3y3t54Zm8uYdPtc\nAL751pss+nGMVbYdJmcEm+tQU26LT66AAjP3UDQbuurD0uo6tjhlInYcpUutdkjBSLNbBYV2gvkb\n9ONQyCt+Jw/9rlnzpa30OitDsMmMX1LBYa7FahNLL61ySpRFjZKYRFF91h+9j1Hac1ADloRbWlq4\n5JJLws8XXHABF1xwQa9rPM/jnHPOYd26dVx44YUcccQRQ6ZsrzNh0J2fFbDZ0dMvj6RJeFQZybOO\nmFHztJoIetJlRSFwv0dCDwJfFCo6BQcJFj9ndxAsEgtBTNErqsFHZ5gFJf5SSpLyC9KbTg/VKZmB\nxDNUKT1AWG6zKNg9oLPCh5GqIPNstPVpEXFjzilRgkpsXJEgYUoflitL18MdgiS3M9qC3rEQVClB\niam74AqwfU1DEHLWaltstlQY4lSCCKV4WcR8hy5v7Ihgk3BMVEaXKER0lCg9l4JIgxqrlJWZciY8\n+5y+2baIid7za3frHRRrX4rem6wlJEklQm2iSyhSyF7PD2oZBxEZWnrdsf3dRcDMA4k7oQSVniIr\nBNuCBA6hpeWRnqYwJZN46MSa8MBVsYcqpu0MauBnzFVXV/PII4/s8hrLsli4cCEdHR1cdtllLF++\nnIMOOmhIpO3RiJAIESJE2Gfgq4H9DQLl5eXMmDGDF154Ychk7ROSMBRUxAAjlcVIk6IsFWw1Yl4Y\nYC8LhWKgoNIUV7Aabmw/PMVShh9K5QXprbi6V6Dg75GzswyC/vOEPq+rs8gcYqHDv4LuSQMjfYta\nYSGLjHFDsRf2he3bcYokT9AhTh1FYoCFoEwVtJid0TGc3ReMRVAoXyp9nmHw20ZbMtrEnNfKKtY7\ngof+N1W4x+59dt5wIXjHMGEILQELClJuXIleiRYKXZBJqj1DUzGkKsxn0H3RYpxtxTT1FI2t1jYC\n8wq9/v83wzBFR7S0tGDbNuXl5WQyGV5++WUuvfTSIbcnlNpHy81HiBAhwjDBW7uc9M1XDOjasjv+\nsMvfly1bxnXXXYfneSilOOWUU7j88suHTNs+IwlHiBAhwp6E8oZHEj744INZsGDBsLQFEROOECHC\nPwMUUcZcMW4d+5m98dg+cdX634T/3ldp21fpgoi2wSAaz8GjmLbdQsSEhxd9+R72RjcX11Yopqs4\npGrfHP69h4H0y3A6CYcD28+57UPm/ha0DsTntrf6TFBwnAdhdsVrIwih3Bu1zJRSAw5R+1vj74IJ\nBwVERFF1/7gqeNlBv4ilFF5RWqsrepeKHO7BD4L9c0J780soxHH6BEeDa/wtF+vOAkR8dH8V0xdU\nJEsUebQzolAgx6F3Wc3dobuYJJtC4kUQRx30VUBfyocSX5GRgu4gyUDo+7avhra7CPqruDgQ9C4w\nXpx0E1zrmJT4bFGJR2cYI2DcomdJdDxuEFcdU4qcEGE2nKSwHoKIkzw6Zn6PFEmnd6abRKeVl5pn\ndQtYY3nkTNz3iRmLOadtxWvL8eiisQCssn1iiLD63J6MHNKERkw4QoQIEfYOFHs4L3ro2KeZ8PYS\nikVBUtq++HPwOxSkFsekvRbXw4WhS0/F0pwuUKP/nUVRjiDpF6SXjNASUhCzKdAxlNvHFhdjdyUB\nv5eEqHrVfVBoLSHQBnqETnstUSIs4t5hQZtQVBrJpMJcnC2SVodCYqCmBpJa0AdZWYhpzaPICug0\nUmVWSDwEWVkYt6Sv28oWNTwc0nBwmrBb9H6WUZ+D8ZSGxi5Dn4MuJZqn8A5BqnWA3aHLFYUU+E7h\n6SL+SFJF2ZFe0TU+OoMzXvRQh96fh7NYeqCdgk6vjisoLz5iy4b19HC40jUWTjxhI87pH8P/7VMs\nN0WINpGlnhhxs3KD9bun5FXl7ptceJ9lwjEF5tAMPKHrl8aUZhQAH0p97GaTMkWjlU+dTLBVZXHM\nVBhFnBSycCChUWWHYpYotndJgCIbVxWSka5imwWrTC1XRwlSSMr9wqLpEsqcYFwIch+OlMUdbZXa\nxJDyC+/aaum05SAVuMYXpC3BSpFlnK/Tw9sswXuqg3NdXUjp4+e14W7s4tkXdeWwjY4cUgUzhanV\nYF62Q/i0CY8KZTHZcLAjEm1ksg7PWYVkiFZLV1ILUtN9w7SLTQRDqQ8doHgT1AXue49xWig6DJMr\nMYXfgyprgTmiyfLpaaYuKQAAIABJREFUMCr3IZ5Nia/CKmF5c/7dQDfXYD45Sm807abY0ga/hxJh\nk5UOq0wNiRw+1cKh3tdLOOHr9SEC4tHzLVM031xRMG04avtZMzjohI3eafurHGgylQbrlcNXMjbB\nlrnypUrWP/8uD8WrsNA1mY/2S6h1/bDWS6ccfIW3ASOShPvH9ocvOhRKNW6WPm3CpVRZbDGDur9K\n8KXazbQ06Z12Y7aUEVYGhWDsAbr84IY1FfzEkaQs/ZoH+jEsRViHYjAoHkNJb6dDiacPeXxdppnu\nlQBwgujgv4TFJKmz/kZ6koxUvU40UChk0WJwxeDqSQR3BkXKc0WlBn0UXVbBhlmiBPWeYJU5rdq3\nJCM9QZMtw2wngA35NhLoQvTWhDHk1/+VJlvT3CEU8UEwlUCKDEoeBv2VQXFM1uakqfoYH4Dfd9Ti\nWXBsXh+UmnRcbhMxNvrdfMLXleliSvFXxw9rXVT5usDQUCS84rUu0RKsAjpkwGT197WmVkmrVDQK\njxHmtOpm4bHV0kx2lKkKNjbvst6xWSb1HI0LfXp1fAAlLWMKDs9r5nTAqFbi5S5vL9OnZrTLUlK+\nzwcxm2WGMU9UCSo8wWpbb/rr6KFD5aiVyfAw3IQSNAmPClE4+WN3yoAWa5jFJ57ElcJCr9d6c7rL\n8ZksKSfPYnQVunftPFU2TCQZ1n9xgTVO4UgpH2W03T1jx44ccwNAUGHfRw9oMDi1vmR2TlAus6xH\nL9ouKVm4eRQbzaSsjlvEVYrN0mfcOs2YJ3lZjhdx3nP0RM2jBlQTd3sEEkTAVILUzExIryBtCged\nd8AGADauqmSZ18SU2AH62iK1NpCmfNH7eG+Fwh9E5bLiKSUpHN9U6uuBbZWKlOF87VKBFIw0TMQH\nPrRdKpRNc1C+UXhcwzgm2vo0iXW3t/JYZiyvSH3CSb1MMtp3SA6yD/NCL9ygv1apNF3xOActrcQ1\nBV7G+D7rHcl7Um9ing+fyLt8GKvhHUezjhHKps63QrOGGqI5InSyFanTCD0ugebio+v6FqdVO4jw\nnqxQVPhQ5wnazCC+nJCsI02JGdUDPYeUr00/u5LwBHBYPkvDud36OWf9C2rNCkb/1woAytJx0ti0\nSZ8T8rqK2jZL0C0VR2X1s45Tpax3yrA8eNnS7RwoktQUbfqOAoQYkkAoKDALG52SvM3ku0u0ltAu\nvHBur7YTVOUdJhuhqUPGaRYeDiI8M1ACLorSsESmCKMohr2yWiQJR4gQIcLeRBSi1ieCWFDL7NIa\nilbhh6cGTMsJKq0cjzlJRhSVskz5cIyuGU2bpYzzS7Le1Bx2VJxTR29i2+Z6QNtEa5U1aOdJYHcM\nrrWNOtZuJKCckXS2+D20NmpJrtu1GRmrCO3RGy2flBLkUWGnC6V3/kDCHkz93kA6B30ygUKF0lbc\nnLiQUpL9XH3NsniehJA0K91hDX4JWRSVpiwnwMLsej5BHeOObAPgzdfqWZbIkDIqZpWywzKXu0Ig\nNQWRWw5BYXd9b6Vw2KZyPCbLONfRzxqb6eE9WcJIU6FmRQwOdV1qXYuNMlBfFTYiNLEEJzzYFMpS\n7krtDygPTBgBHEVYdzdwdHUYB2XQpyklaBJ+6Bg7NK/rCD9l/X/23jzKsqs68/ydc+69b4h4L8aM\nHCOVSqVmCY0MEoMwNgYEGAMGFR6LZZqyTUEt4y6XsV3dXZ5WVVc11S4vu6rc2FW0KbvbAzIGMRRG\nGDFrQEJCZCqVSinHyIzMyJjjDffec/qPfc69LxKhfJGKRNm1Yq8VK/NFvHvvuWfYZ5+9v/3tRUK5\n2ToRN7kB/qfbjwGQ3HYlrb//Lp9+aHJVNYmzJQK2jSxiLt8pv8gzZv7kMf4uk3l7NY5jieZl7Yya\n94DfF8Ob24YDicym3V3LrHa8st3lKc/hO+1SrnEVpnsYmjIl82MtkMngvgvjaZyM6TZ/ipnILNOR\n4kjkeENLvtTUKxxXVe5PxHJ/QrUZJ2bc6oIwv+oU0Soy+9U443UVB67fqqs/YHnBlTD4SC9lxxsU\nCsUZrzDmdZ1rty7wrrkuaeqLa+oGzio6sXxu5o6GzdnjutSs+MSORg4dOU57l0WKo+H9d4GI+1w+\nMoWPeqMKAvlUecxyT6R60CoyLFkmXaoVxEqzXETT/TFOiX8WxP2QKVX4TNeCMXU97hHO4mCqOVhR\ngik94DnAr80SXmyX+KCSwpqXRlXqTtPG4fzm97PxpUylluMP7ABgf0VxpYuK9lasEPCfjz2RKmj6\nCNpLqfKdOOMr2Wle2xHXUT3JGHSqQLKM5pDonP/AcV6LKKNtuWZWl+89aFWxcffTb+ErOaJYigoY\n/vdDVrHkbzTiNJGDg56I/pa8wkKkmPWGwd1uigk1yOvtMG/aelzeYUtG+9Qc0RVSLQRjcFYqx5yr\neU/PDhH/l6cBeGh6iX+rcyaMbFDHqgM8ls6wpzrM/kziHa9lK/fWcu5Z3gfA/1vbxkMMkqK53U/u\nr1TD+4bgooz3WoPBBZ9zgQaSWMNILn94tKLYyxJjJDR8IdlvRHUe0y2aSjbwS12FsVxxwtgyWKyk\nyEFon0E26uoF8glvuCPOkl6rBGSHDspoyComlOYZ/8c/Nqf4L9MxQypik/ZM/WTk2pT9auDz6RS/\nnm8j8ddtyRVPHRxjsSLDfqlLGLCOjj63X6w30yegGMI14qt2xQ4+qx1bckWiDCaQWjtDgimU8IBT\nLCtHzZV+RQvUXRk8600+OdccNChq/kuByDvo4gVf023KOA75SPSHqm02XbbEyHclUHKSlK0kbMkV\nXzUSDHtf7lhwCX9Wla0px3GjGyjfuw8F/GyVmQPSYMavrMGeYOQhJRvmi+I53jE8xd6jUuXjYByz\nkCc0k2qxUc5rgSoGP/eglYSTftARvZCqUM0hTP4VJfNPqgbL786onAaaKz1y5Ghk+WJ2kp/xG8JL\n7DZuGp2m2z5Ne1kUTedgxGcXJjjxUW8ZuzkiJlGG51QqKfBkEnP/vCjvr8QzNF2Vt9gRAL5lurxV\nb0VZ+PFMdtUppThsMt5eFyLx423LjkjTUG2+WvGGidPklGWvBi10TP8JOL1rVFNawgGquKTDJub4\n3eYK+6ernPTE/V9S81xDg015+eyjkWVeWfbkpdpp5o4ZI9/p+EShC0Fy7txFW/H+4rCEN2RDNmRD\nLrhsKOHVcnZkX1OC3p2C0dzxcg/03h8lxAhWOMCBqk6xJbMseX/haeN4dbyNS5NF/sYJxOqN6TLf\niAcZ9rbSiFUsGLEa+x2PkJpsUIXfseYciVNFKaNchbRbR2+9vyvVAMv++Cq1wNwqizrqeffQD/1E\n+xWrkwKK6rf+2StYrk41y1pxnxNkw1+xhTc9HnOdEZ91He2P34I5BTjAALcOz/DSZbFGTxpLxZUo\nlbUcEXstzYYVMP8Zf3QYzxU3dcDVhvkTTgEwu7LC7y1tJyUgPBwJOf8qr/LfvcXVVWIFh2Ys6tI1\ntNbja73HGm8rqfKc9iS4DKCZyBXf8ciap/JFfpat3F47I89eqTB3ps4f6yrHrJwktqoac3qJBStu\ntKZOuJQaI07zXKwPVsESrqhvN6Hr3NmtkfXMvRELe6OcRV849uv2DL9jI453pZePRRFXZG0+WjXM\nI+25jgFmtaQGg2DFO2o1QqgfN06A8IV5miOJMyd9p8cO5ueq7Eui4s679QB7Us2MH/ODUXleuU8t\nFv9/cdRg0C+IIauY7XUQr7NsWMLfR8LxIzj7QY73x7Vjt3f+XZdKMfCDkS3Kiy9o2JsoHvZK5nI1\nyNWZ4fNmmIpfplu3L/DgtOYGJ4pHOymrvhbfa+mnLt0FDsWidsVng/h6x1SVNJXDswa255pvG/k8\ngaHiBBPZqwB6j9I5/ddQc5QBvXllC3wlQFWJAt4XpVzvqz//aKdFXMkLkH7DKha0YwXH7VYSJAbz\nnCNzTVZ8PfjdmSYDVrzGj/psXejbotaZkuNgCHI9E1m+HYvL5CYj7UujUcbSNgesbLxzRrHHWr6l\nB1jwvfSiVHPalFwNJcdFf6J6fPgRPYU5kbFd1K7owwGr+LSZZ9jJ8f8tdoS33nqEv/iW8B58ysyw\nTdUZRnO9ahbPuCWrsOy11WksQ06f83itHcRKFRjkSVenbnM+5d1CN+RVHo0lOUl7TfJ6RlnodorA\n3I7U8slaxIrr8p62tHlOORZMqQi1Cxwr5bP7WQYWmZdFdqOCCes46q+uoTmQDXK97bLPB+IaTvNM\nZIsxWlA5b2xpjsQRu5W4xO5V83yVea72CTpXZhI0z/tdBGuRDXfEuSV2QoADknRwWuc85Xfao3Ro\nuxzl4F674L9veKPZzO/4FMhOd4X9dhCL4raqBDSUgjqmID0BmUC9u/r3k6BIjDdtjfvesjHBMu4g\nJdNz5XjIZ5ttRRZNuD62ikyJ4g7Ku+2tEtOj3PpZFOE74R1iFGO2JHeZMXCvXiS1lg/5QOFArct/\ntoOM+Gs2Z47pxEmUO5ULh0n5cKXNLm95bs4itFKFso85t+UUmOR6TzYpkGsY9hvorJa++8VkgXZb\nVOhX8yaPMFi81FjuMNrxN0zzSjbJfXxbgqKMEUXalzXnKHY4i/jNV4qgqaBJGr48EMAxk/H2bpNX\nbj0BwL+eMZx4ZAcHtZS8v41RyaLLy/E8HFnqzjGaehxsrPvCu4bgb9ggjYNHqrrwYVcspMax2UW8\nIV8C4HE7yFeqCTe3ZatbUZon8kUaOuEvqvLULm2ud7WCoGkkd8x7n3BRbPM52tUbyOxVjBbZUFf8\nN27p5Hy7qnl1x/KENzquzGMscGVXPv9D1XAsMkxklle/QgKZP/zwAH+YD7DieynFEJ2jTecvCrdO\n2n1qaopf/dVfZWZmBqUU73znO/m5n/u5877fRaOEoRz0iVxRd3GRAjxGwm4bcbtdYiaX4MUZHdHI\ncg52xAp5tKq5xMKurMsf5WJNXXN8hCGTFxMucqutgH4kZLA5Sgus5hRD3pIMEiOKZciz9zdUyqwx\nxdGv5XkkQpVowGNAyjatpWkCx/NtdJJye8RvWvMqZxMVbuvG5FaUxl/lQ3RJmfA10x5PLFus5rpu\nh5pHjzwQ19miFJfl8p1FXWYHQv+ZfMHFEpRTYJTzuoERq6iriKXlCg8jVtCxyFJDFaeEJafYk8PP\n55s45BXzCeOou5JJb8BJKnO/i7aoKadkLMOzak4xox1NC5/ziSmvzId4/S2Hefh+yVr7Mod5c3U3\n1zoJJAaL7bDJGe1JgDkSQcOWW/zZcLhnk9Ct4XvzxrGC5SonQa6DUU7daeHXyORZ+yuOtrI84oNw\nV3Qd/wqDyy33apn/88rypOow7BEKFSeB7GqPtdlvUFMCovK5AxyNSlfdqEqJXZVdk2cYnN4MwBGd\ns6Isu/38f1FXs1sts+AS/q/7twNwZzTHz3VTPh/LSbWryqDpugfn1tESNsbwa7/2a1x77bUsLS3x\n9re/nZe//OXs2bPnvO63UW15QzZkQ/6HFwc4q/r6OZdMTExw7bXXAjA4OMju3bs5efLkebftBbeE\nHeI7zDUFEUpA5NY9tOYfmXke6wzzmWSALX5nPWUci0ox4PeRpg8ynXIxX1x5EoCJ2uXsys0qN0Jz\njfnzIY0y7YEvaeddCQVkx5H6lNaudz/M2dgHe0JgThVpu7rn3j2n5DVxWgT+VoBMwxNRzuNWrLhr\nTJOfbOe0HcwjProXty2H4gp/4eQoaKzmF+1mBk3KZ2KxnJ6mxSuyGjWPdXs6Ft/oWtvX6+cH8Qmn\nUKRHL2B5yi0xGzV4fUcs9eusY8HGtH3vzBvNTF5hh+rweW9xvTqt0tIUaa9JrtZE4BPeI3IwgCoS\nQxYMRRJQosSyvGvHMR6+fwsfTuT4v50RRpwuXBindca4i5iwpoAq7so1RyLLkn/PIaeJXf8nnPC9\nFo7duSlOOrOR9OcJUvb5wOrrOy22jC3yzVlx1dSd5QuqyZiFWzqCbb508xxfOz3BA4n00DMmp4pm\n0JaniV7muO8nwZUz7HHBM5Gk6QflMeMSLklh3+FNnKlKp24hZsLGpH5Nn4wUS3aAeyrzfHn2CQBu\nH7ie0cEWla7MvxUdqmz3rop1kjVYwmfOnOE973lP8fmuu+7irrvuetbvHj16lL1793LDDTecd9Ne\ncCUMgdnMFUpqWtuCDBogSXKuTBfJ0gY1X7b6ZrVMrZpyfFGOs5uqLT7jmryEJX4hEuyktUKvd8S/\nZaxUQeCz1oUrmF75tKKEdjHgVa2SnwqajvenbrKWV2XL3GckUn4lFeaUo+nKDLXUv3d8nhMuKPMz\n2nKKLjfrYQBe3+4wXG/z6Wy4CEbdGc8yvFxFR8KItimzzBnFPVGdv2rJpvWq2iWcMa4IqHVxjDiF\n8u+5FmWSQdF5sYMaFOTdezJNM2nyqFtiPJYgzVGToZxiwh/tb+u2eNpUmVYRx+xpf+cqLUVBJ1nV\n/WcY9vaX6EjFKT8vHlctNpGwpHK61if2tDSXjM3z2wviEvg97fjr7AjvMhKYq/ojvqHcFOpW0XSa\neT93cxy6D/Kes2XQu1wOeffSuDOsKIci5rNGkAVfj2Iay6OkiYzWnS3F6/QcRzuD3F+Rjffo6Qle\n1pxh66z08eeqEYsqB6LSLdfn1Ot1481px4TVXNOVZ2scj8cJn1EpW5Go7pjVDOeOupP+vKnb5Tei\nM2yjwcfqNwPQqCzz8MoIU/4dRpxh0J0ft0U/4vpkjhsdHeXjH//4Ob+3vLzMBz7wAX7913+dwcHB\n827XRaGELUI+s8uW+JSO0gU5zx+0h5hUEadiyzGffDBATJpGVKsyO66xQ7yomzFNjQX/u2UsNWcK\nX26uBHAeor3Qn2LJ8ZU9XKl0G1at4sIdcIoxlbDXQ3EsCTeoDsYzWI1ljlSJF7jXR70K08barM1Q\nVWFJWV7TrfL6q4U8aO5YjcOzTfZV20XW4Z7lISbNSuEL3FdRJM5xRzvl7XXxs9+XV5jVrrDAGk5T\n6/Efpv22zfv2AmxMA7Et07yPx4rYOa5UA0WCifEK+C+zIwCMmEk0cLNZYK+ScOJxJUpvxJ+QViEc\n1qDoNEI+c9jPpRnb5hW2xrw2PGZnAPjlmTq3McRP7pAU5J9/ejOfqFaY8tt37FPMNbqwhM8Yx5BV\naD/mwWfar4T7NJ3ihHFMEVLMKxilGHeKQS2LvW4VEXDcpyT/WbXFP2o1aJLxBiUEPv89GuLwbJM9\nWwVWd8vJCR5OZD6vBQlmfTA7sO3NqYzNNmLLgDzn2PIg99pTbDOD/HhXrPCWNdR0zr+rZP7dFLvV\nMP9m8gwgJ7Y/O7ydB6IlJrzirvgN+EL5SNcTHZGmKR/4wAd485vfzI/+6I8+r3tdFEp4QzZkQzbk\nQopzYNcJHeGc4zd+4zfYvXs37373u5/3/S4KJdxRQrk44ZnvT0digQ35PTHFcULnbLURuz2OdNo4\nRmxJi/ex7DD/h5pgSiWc9Pnrm50cu0b8cfr5cB9oSr6JEP0PFnbTaZa1cO3Oe8D9zixniZh6VT6f\njErfai9XRK/PsI+YQCGpKqkhq07zyvFpspY08A/bQxyvtLmSAVZ8e+6vONrdAer++iu7GZsqLYY2\nt8gyue47yx2us5WCTH9JCx478ClETlw657I6z8bvzhhH0oMKqTvFiFUYrXjGQ5q22oiJzLElkqPz\ni7IlHtKDLHVjfOawwNNsacWleHggqwnGn016/9pRcnq43CMd/pnL2bz9OCePN7guk0SVL0aGj6dH\nedHTEu3fMzKHbQ0WrqMxK2NuHGzyA3fEWBKlinHsKOHa7Yc+VVPymGjEdXO9DRYiHDTCZRzuPa/E\n6r7KH6tqcZ17aznTLuPdbRnlPcry1WrMJV3psXGbYonIVJmC3K84Slhb1Wk6Gg4vy1gdTCIGVMJN\ntk6sxYf+qKnzRbPE6cwnskSD/PboPMuzCb+/LCebvfYUl5khLvGInapTHit/IYDC9BV060ceeugh\nPvGJT3DFFVfwlre8BYAPfvCD3HHHHed1vxdcCWdK3AYYzWHveHrUnuFKUwLgb+4aDsdwVKds7mly\n3QpECOCmZDPzbcOES4n9Mq04RVv3QKVUWfhzrRlWiVN0/cxVlETU8hxYUhKImfUbwI6hRb62PMaE\n/zyLpeL5HsJCDpC18xHXkyGX4zh8cohvzsmifYZ5blZD3NLOqVZl05pSKaDZmkl7/lOlhcMRzdUZ\nVNKnNaUYyh0LusfXzWpccn9EOUJ2HvroIG0GdETVuxGs0uRaIEmjTp49YhWfj1f4+bYs7ClgzFnu\nqSSc8sfyXXmN2R7npPb+/X531bA5pAoGneZnRiSiPXRFxoe+uYmPnXmQl4xeDsBy2uHGeIIdNVEq\n35ofYzlZKXgvZrSM52lti6CeRgK2nZ5x6dffrxy0fOe2kMonoa9DosZij7c09s9u+mfvTh1XW83n\nKoa9iSi1O/Q8D3hSdYBpnbCkUnJl1nTkt3gIpm9PcAeNGXE9rKSaU3qZJ+IaL/Mb+rWuRUsN8hqf\ncXisVeXbx2v8S55hT0X87LebcSYzXZA2rfSsr3UX1x/yoR+59dZbeeKJJ9blXnARKOEcx7zKOe1S\nTnhMa8tlvLYFf16Vxbc/rjJuNZGK2O6jRvNG8bWoxStSsWZu1Cv8bXWQN3S7WK+E55UVNjG/cILi\nXYsCDl8VELncRxf3CckHrqhB9l3PcvVEa5xrzTK7WtLFB6OIRb26TFLqN4UiMaTPSLpi9abQVpYv\nVBP2OlEYL2eI0Uzxjapm3m8CDri2Ms9yJ/GfHS+hybyyBc71kq7lRFTWoWvmsklGam2TVyHBldPe\nCk/QvL1lub8ifbFPtbnZ1ZjIxdoGuN+0OWlXqPsp+eVqxI/ly3yOmMs8kX/iRBGFzLLYSfAw7qFm\n/H795yhPGiGx5ttTgiy4Lp/hpzuW/+XGXSQj4ife/9A4ddfhWy0Jdn4xaXMN9SLoZhCs+GldspIF\nNERg2+uq1Yk437+/VkuqBP3zoJPEpKoz/HKqeEQPFNVmhiwciBzP+GSlEauZtI4Vci73AbNjDLA9\n1uReMT6cWDSCKV/LyTwgXcKmP6ss8zrnhxJZn5MtiJTmlOtwxOO+UXLd452h4ib/NZphlxrjLZkn\nkYqEEH++JwjfvFAManwP2eBFIy+4ErZAx1na5LzUR/ev7jhedsdxPv5NORrudUu8WDU4rFP2xyEw\nopmkwuW5LJoHVJNB59i+bZ7JU8J0ZRx0lSNU7FCoVQkE0D8rWIfSjWCUwNFC5laKY3Ngi1Ki5L5Z\nVbyhY/jfPcTp1Sqh6oQqMaAqCuXrnyWVBvqADCEKKOzsc0bo/8b8s0cyxRnjOEybt7ZFgVWc5UnV\n5L8lEl2/XA0ylimq2hTPOxRrFpWk2kJZbim0by1VLDrKseSV8Ks7CTe97gTp52Q8v1N1HDAZ+1ng\nMiML8jJb4Se6Ed/yyQeXZIp9bhBn2sUmejxyVFFF0kB7jYZN6O8YmQt3V8WSe2BhnBuBS1LFvodE\nMS+4mANZja/Gomg2k5A4CcQFWfIJH70BWoMqMt8U/W34DuFLKSpXODkljCk52bzPdtn96kU+9rWk\nUOpj2nBzhwKN80CS8XXV4lW2Qc1Xs7inGvHTzHNmQQyVk5Uue1yVmnMsrXFjPRtYMOg0yy2xuNu5\n4VeYYMFpDnofVNUpdqS2mDs5cL0Z5taO4QlPr3papYy7qPhOxakiu+9CZM2tlyW83vKCK+EN2ZAN\n2ZALLesZmFtvecGVcIQQzsRO8VND0/K7Ss4X7ttGw2cjXG+rGAeXkhQculd1u5zSir/3mMhru5ZB\nq/j49NaCxP3y3JAqVRzhgqzFogt+R8tqzoIFVQae6k5x1ORst4artPiym06R6JwVz6i1J3ecjPz1\n/uGBfc2cZZ331S7K5ydOM+gUVzmxnGaM44hOWbYZVY/LGdZdHolr7PYprZO54dE4ZbOLCgux6RR1\nq0s2Nr32gqihbSC4aYATkeLpfxhgVovN8y5vwk5WRnlzVTDAX1kc5x+qiqs9UcXWLOWPKy1upNHj\n03c0nS4s4CUt1VQMa2/nNqvRnpu6rSyfqqT8zpE2HXsYgBtq2xkiLoqK7swMHQWhQMZplTPiNIqy\nArPuObL39kM/EmCaIKe3HLjTu44275rhi/du5UF9nJsTgRMeJefJSs68hyC+NR3mFwa6nJjv8KWq\nXPfKtmVkxwqfPC2p10Mqo5nLKS5gwfvttpRyvm2xmjnt+K4S18MIOZfWFnFO0WzL7x6rah6qOKZ7\nUqNGXczBGJb8TN9lY0J6FkhsJZwGL4TY51lh+kLJC66EFYohF9FWtojSNy/psG+6BOJf0+3yVJxw\nZSfn/qofsCihYR03t30wQ2s+Hi2yQ9fY7MuAr+iS5hEkmLFWv5CiJPwJxyblJAtsoSfEXEfTzB0H\nPUazpgbZunWB62aEJeyE1rRUqcihPHKFf/uNMVlkovZO1l5879OqyxYX8/5qiq4LmdGftEbY5+Z5\nbS4un6qF7SpaVbxSeUxwr8EQXBKwhmw+BxUUo8E3rx13M8jTibiOPpBZZrIKK8rxhSXvooi7XJcl\n1H0yzr+Oz3CpanJl17HfH19jJNkmBHAsawtshtNoCznyT3oXknaacWO4PtnNFl8O6gCiFEzgstCi\neLd6LPsua4oyPYGYqKM8nvys2EFfbaPs566CRZUzFcs8Pj01SFsp/me7ja1t6cOndI0Vrah4hsCd\nWYf/1B1iS8Xwo12JrdSrKX91aitHfXWQUSdqdFmrNfmEhfujxMkPW5jR8JAvwEoMx32A8ApfzWOK\nNjuoFPwXkYOGlT4aVCXXRkuXmafnk9iyFuk3WeMHLS+4Eo4cDKJwKO72C/LyBxwvcpaut0LurxgO\nqBY/nWq252K9DFnLM7HihB+1irO82DXY3pXy8yCLtde6tCABgzUOdC+PKsBKyJDyg7roPy8Y5bnT\n4FXtjPZyzMGunI/7AAAgAElEQVRcfLCJGWKblcJNBdTNrW5Lv80KcKHuWTijCb+ytEl4TLV4ZHGU\nV0xOATC0orlWNQvmq7nIl/lxJcqiYzzLW68SOY/+ghJmFWRJQcOjML6sE45Xc8YcXJ2KgnhlskJu\nWnw0Ekt9mxvkWlfjSAzLvucnrKTy5oGZzvWP2OiVFMeSdiz3hMRWcDSdpGoDnFEZl9qYk/5U1XCa\nEadp+z4/owX5MGR74F6qfPfzkTBXB6wCbYpN/mCnwTWVBRY7CV9PROmO5TCWWfYnoS8S3t7usGty\nmscOi7X8d1RY0SkTXvnWPQQMtfZTVy9ELQW2Z4rt3jbelOWciJvMa8eIP8kMmSoVpzjlk0kqSnzn\nLUVxmoXVAVPrLmCixjqiI9ZbXnAlvCEbsiEb8oOQDXTEc0iMoormmJYD9pOVnFvzKm+7Vvxzr9bw\ntW9t5/NV+GYufuOrKsM0nGHQR/JDVHUqKpMoqk4qOvRugGu1mhzfS62nz/o3FCY8pnOanjBnW2OJ\n4e0t7twvXAM6F/dBW7nC4u0HxP9c7QrH3ppv44Jv0IBVjEYxf5es8MWT4g5p6JzLs4iWf2RXOQY9\nBWZIf3Ye7mXOftB5SnBzdD0eercnSE+Vo+Z9qXfX5OGLeZWGitjk4WfXZQPkCFQrkDRVndwnuF36\nQZL0SoGOUKurXOeI+6SjYNYjOja5SCpG+z4edIp2z8lqa67JlRyvAy7Y9bgi1ir+0FFI5EqOjIcq\n0O42abi8eP6lWZuqyVnJxDJu5JZvJ1U+Nb2ZlZqHrTnNpXlcLPLQX2tFHmgnczW0r+tdVqF9U5HG\nOKmfONczeVp+nEFw4B0Fsa9KA6J84p5xuNCUjhuW8HNI5ESRDPvln6B5xuT8/j6p+juvcqpV2JMb\nLndy1MpTyX4LL9DpmRTBT6jxuNznuQMGRRzmV4AgBZ9s5GA8l0rOK7Ec0X4/NQw81WTIP3wiV97n\nu34ToQiAOWlLcIu0vGraRY0xv0lp748L1zQDKY9aXTFEsT6luCSgKc9InFsFDzQohoLLw/87gCF2\npYI4HrmCs6OALamSb/b5SOTE/1jyOAdoGYz5GaWcZEg2QzDW4bk/KNrSUZKxVxADsTZCobMlTNOg\nK6phk3WKZQ1nTFTENx6sVEkpK0+fMTI7t1hD4kKykrSziB2s09QL41AJY2glaBdiFfJsyRwM7q/g\nWgklvUD6WKm1J06djzgHub3Qav785KJQwiATOGQjDfiBK8rjYGg4LZlpvh9nfcpoSEkedGLhnF39\nYr3GNyhiKEnKe9myYgwjuWOnT8E8oaSUUP2sYEC/wbd+pNhcVFCermiPIEBWP6nXok99wFI2qqAQ\nn/+G1Svl4lKrklRA/IqCqxUZdN+rwDSy0AM2tpeZDZ5fP/ZW2sgRZdpRpT88RpRYmJMdVQYEw7MN\nqiDyWXXfdRDD6qrI4bSyyfv9B63DKmj5jS4k/kCJ6W2ftWk936aF68NGGTbVivMKuGeTN0BixRcc\n5OwN9AeNGNtwR5xD9CqnfLkQQBaidlIWJ1gJFfe96cOO9VUiZ0vvrSMHIz0tzoBTpozuTnj1EhRR\neWRdfwl9F6zKGgacKUoN9T7X9lxTWS/TqA9xsIrHOXJSs64fqzb06Xr3XRGVR/kEjtVioXDfOFbX\nBiyvXX9ZvRakXUHxhfp1Lf29ffeD1jFFoFp9r3GR8+xcKOfjDlkv2YCobciGbMiGvGCiLlqImnLu\nYjXSN2RDNmRD1keWHz3AE2/8lb6+e/ORT1zg1qyWDUt4QzZkQ/7Hl43A3Gr595M//UI89vvKLx/5\nWPH/i7VtF2u7YKNta5GN8Vy79LbtfMWx4RPekA3ZkA15QeVi9btenPb5s4h6lp+LRb4fBvyFbG8/\nz3whsetnt+/stoTiqT9IebbHGf/zbOiJF3Jcn+u5L8ScO9dcvxjWrHWqr59zyYc+9CFuu+023vSm\nN61Luy5aJRwWYUHEjeScV/yP5LILWD38pEqwk2dPhguxoG3Pc3MPmleUi7bqhOik6X8GLNSd/MQ8\n+6JeT9FIn4V37yhJE0mc/LSUY1ZZFrSjo8qf3j5d7z4LY2LoTbLxz0bGLvVtmFWWWWVRlP2m4IK2\nD8oxXdCOZe0YtDBooZk7prVln+6wT3dIlWNL5hi2ZZs7fv5dCHm2+xrK8Uxc2bdhjcT+d2evpfVo\nS9Zzz14MeCCA6ijpv9A34e8t5YqfUAj1B7NpCDqin59zydve9jY+8pGPrFvLLlp3RG+ygUHSaxPn\nWPQk1i0/4QPBdyAYMT0Yy44qs6Ger/TewRX/lgccwb2uLqHTUSXpiUaYy5wq8bKpT4NdlXH1PM5M\nvemfxslzFoqEEklECANeQVFxytMvykPPxp324ozlfddHNJIt5VSJnzZI/bjA1JVpaW/Tln24qB0t\nnK/N64lg1oF5K1S47q33lyrHkNVsz2S0jkQxR2hxia/y8VPbjtO4scK37m4wbSQd2yL9Hvo4JCec\nT/N6cbeBSrV3MPKz5nWqJOFEWPFEZFMtr4ldfzUCzyUWSbQJSr2GsBOmytFVoX3ynfD8ljdWWj29\n0UR7ovzymgslvclWz1de/OIXc/To0XW620WqhDNV0k8CftrDjClZmc6QskjGjUpYt+oWprVl1Ke/\nQpkRFj6fr0Lp3enx/7euzK4KC6+lytThESu8FeHzkJVsvrbnbADIUKwoW9yn36KQzyaZ6tm0nGRb\nzRvHSa/yHbCfLqecFF4cV3UaKmKbqhTvJrXEFNZP15pX1KFFvYqhHynYsfznog8dREpOAyF9uuNr\nsxXXKNicOuaM4gkjnLlDvh7dtJJ3GsQw5HTBT7AWsarktrBAwyma1jHvGfiWlGUMzeFIUoa+EC0x\nqhLe3RD+42Qo54t3j3BvzdLxnL47XcKgpcfqW5v1Gb4aCsmGjNFAjymp0/K7wMMQUsNdTz27ZT/n\ntJMEk961pJ1seGvNout9jRTHorIkIeXcqWL8AkNaV8F4rpk28qSH3QI/4oZ48/gU/21G+I0PqS5X\nU86/JW8xx8/TGHlWcZD3GZg7c+YM73nPe4rPd911F3fdddc6N6iUi1IJb8iGbMiGrKeIJdyfEh4d\nHeXjH//4hW1Qj1w0Sri3eyK3uqaVBqYixwqWXxgVFrVKM+Onn6pwv7eMf4QGibcWgvUpfjFVHNPD\nvZ5PtYggljL3PRDjVFyZ2poifuGQ/78pcyxrRWoU21Npc1sp5kxZKUIsGNe3W+JsK6skanHMaseT\ntJj054hXtx0raoDrhoS/d3BkgU8f2c590QqJf7vrbBUDTAUOWNSqZ6yJpLzH0gQZh3CvFSVl6ges\nKipVdJS4a+r+kmeiFOKYo3Q4lov1/ocTbepbUv7P7wix0xmVMeb0mi07609a4ZqOclSUoq0U0/7d\nx5yhYeGTRkjxr6LBP910krtPbAPgnrnTqGSOV9vRnpMNRTHX0Jbg6liLhDmThhRlJf3SS2gf5lno\n44lcMWOkD0f831Z8pfElXZ42AhNdWan73BIDY5mj6vO6DiaaQ2RMesbAQQvTkRSMDe7Bgyanog1b\nPHH+XFQny6E2njJ2Sh7+OTfLZLS5IMWfV5Y6+rwrkJ9L1pM8az3lolHCwKpjca9YYEblTLsOUUX+\n2lmIqKiIUV/csqVgTuVMOF0cv4ISCRM3BPTW6kcMvAcl9aErju7yd0eKHK2Dv/JE5GhYxaL3yX65\nkjPvUlJnmapK4cVll3O9rTDiX3jJVwKpuv4ipqGfYicERoHM5ZjO6SrL67t1bhuW43M3irg7GyZf\nGAVAz8Mt8QKXtSv8m6L4ZwWDKo6ZY1ZKQy35zooRv3U/rFeWHhpIK20MJDQaRd3BtJGNFeAkXRZV\nxoCWKdl2OTmOHEdTyxjPzSiW5iscQqpLGKdQJKK0+lAqve6Rag9hUNhM50y5kd3QcdxXzbC5vOw/\n3XySg4dH+ah+BoAfSy5hW6boKpj1WrPmFLOqLG4ZoXzJnnMv/rNdXnmPe6nmFee8dkVbxzOYNTDj\n59ehOOexdIYdUZMrEXrLIVvOT/m39I324x8Nrb6q2+WWO6axLbnq8Ucn2ZudYTLaUvTbYdrEqkbb\n76ojTrOkLLnfAIac4WtqkZseneB1W08A8J25MS7rgPGtmUk0TStzo7OGTaJfWS+f8HrLRaOEc7Wa\n4CUwlQFM5DCuDU/ZLocPjcjvxpe40jQ5aKWc0BWqwriLmNelbwxWM3WFUj45Tjj0OLeV0msJBh7b\nQauoOEfFl+JpacWB2NFVUuUY4HGWmWSwaMtNacIPDc9hjGNxQabW7xHxHQ3XFaq7/4kSrDkQWsbY\nilIDOEGH97Y1Fd3h369IyfF5l2Jo8aivVj3vOvzBAJzs1rnWDPvfiSUy4Epfd6rd9/p0+2hb4CYO\n7zRrys1wzHPLGgc/YcXKfTob4NFKhT1+0K9Ry3TznI9WDMNK/LJLbcU+U4dIrqkrAz1W3bna1OsD\nHraKurfs5rX4STs4hn2bj8SKJ/M5/mUmJ4n7jwzxp8kcrzDbAZhMFcci6ZtFz0G8JYuIdVmPuaPK\n4Oa59i1HqXDaWmrABYKl2Alao+IUQ/5LByPLnMqKU8zrWoZ/NhKTpl3+KJf+elS12WZqTPpyXxmO\nBb26Jl/8fTZVRenfvWzzLNVf+lloy1rr/pOvc6I7R8VIVfMV5bje1ZntKV0fo1hWlksyefaDccoO\nVeOM0ozMSZ8etsvYSp3tNi6uCxb/ehutsgGtz00/+MEPcv/99zM7O8urXvUq3v/+9/OOd7zjvO93\n0SjhDdmQDdmQCynrZQl/+MMfXqc7iVw0SthSWioVJzytK35nXdCKAauY0DX+PhGr8V12iWvSiPus\n+OziaIiGU0zpvCAyh9W1zrRbDYnqR4LFkDgY8P9vKfh61OGElYKKsdIs5l12mkZh+b7IDXC1W6aT\nC3pjScNfLm5iXllu7Er73mNTPlrNmPEPGXRiqffriggVRDo4rNHMhKoQJFx9y3H+6ts7ebAj1Ul+\nMtq5yl9+2FT45ErCdu34WSvuiF93Ga9QI8VkPeZNpIBgGLSw0EfHSQFOVVCRdj0qZLv355wxjiM6\nw+J4LG8AkBp4Q3eFGSuuh7+vDPB6s8jPdBSPxOK+GayusNdV2O393NoplpQVuB3PfbKxwLLvrxwY\n1Ipu8J2SM+4MC9pxtTervxJ3eGc2yo4dxwF4/9GUV5vtXJPKkjkeOeZVzoQ1NL2lOWvkdBI4f9N+\njw6hjX5uFjza/l2mdE6CYluuOBTJ6Kwoy0vShNhb8ysaPrEyzpWdnDcSLPwGX0q6BZSt5k8NrudZ\n389E1wg2GmD0Rkt07R1kj38JgN2Z5sX1nezzbqFlMl7hBjmscyb8+C0pR9Xp4nRmneOtnYxHoyr1\nlqyJN0UxR5UtfOorntM5V+uPGXYo8g2f8LNL6JbeYJxCjmDBN7mixL+6nYQH3TwA7x7IuGqmxXAk\nC/S0thgUDXShRFpKjnCB7Dw8rJ+XXhUoRCZlKB80rS3DxPwiAk2yuWY6G+GEixjLRBF2tOOAqvPm\nncekfccH2N9u8nRiOOMV2WuuOkl8cLzwi27LDR2tnrNsT2hX7CigWStKXCzh+D/iNOm8NPaueCcA\nJ1VOSzm2+WrBoy7iMdXiVqt4JG8CsL/zXd5WGWUqKn2RxvtvAarOsezUOY/WkSsTCAA6BkZzReIV\nxnGd89aWZdCkdLxL579WoNGtsbcq3/l8epwvmgrvMM0i2NPOI/ZHi7wKcZ+0lEClNKZwFT2XBN+s\nxpPKey037gypknEOt9mXzfJeNcC3Dm8G4NLKCrd0DHsT74LCsTOPmNaWLYH4Hce8sgz5asILWgqn\n1s4Bjeod09BOQ+meqKKZyBVfjdrFNTflVXZlHRb8bF40mv2qzTZT4RIr38us4hm7xGYt22GMFBmQ\nqif+Wc+xaXW8P3dxnyP+2z8kf+wJAG40hq3tGh9OZC1eqhvMakfDGQ5qWRMTLqbuVFHtZqdLmNxy\nki/NbmYpk/7ZmmWcMoZNvsL10bj8/rk21TXLGuGCP0h5wZXws0lbOXIl1i/AnLYYrRhyGusXcns5\nYtlFvNiMFddV/E4ffIQDTq0CtEswrb+BDV9RSGLBkobDWrzWo87wtm4Hq0XR3RMNsNtBM7fceqkE\nHX7p+ADLtsvXjm8C4EC+wC8Aw7lURQA49MQIndgy6G1fg/jDsnNMlghJbAhVC4wWv57zL/YdVvjN\nI+NUoi6XecukimbUKs54a3nIaRo6YsvwPMtzMg1+rXINxyLHaSW22E1ZzDORZd5vGuNK940rdWo1\nztUpxVE/28acYRHFICn7jFi1D7afol7byXZvVb6Pbcyi2JZlxP6pT+kBmqpF7JVyS0HiK66ca0xD\nVW/wBQFcSZC+LYO9Uc71qeYbiYzx6+xmmoOnuXtZ2nMlAxxISlSCUmU5rYBdvyxVNLQpTkxTHrt7\nLoTE2X9SUFR1BtkMIwejxLw7FsU3t2T5bLXKX7cOAPD6ZDeX2gqfi1u8LhXD5KUjp7hqeZSJTF40\n4IcV5+6vXMGMH/d7jm9j629OMa7kFHrVbTMsfj3hFi1B3gNumUFtaDhDhxK9UekJMO9TbR48McFy\nxVLxa/gjlWW2qCrNSO4bubLW34UoztAvRO0HLReNEhaYUYD6uEJhgkSZwzGvaqTJCwuGeW2K76wo\ny4iNWFB2lTvi7CKdZV2x55YwXBpRKEvKkjpZbD/UthwwNb7rj4a3dhxbaXNfUiM9JBCmnZWMH+sM\n8EVf++t93REq5Jwyis2ZXPdHVcMmFTPqtW5viZrnbJvz7pTCchKrs+Fri+2ixrLK2WnjInhncUz3\n9E3VKfZlcxxsjZD6t42Af8ineasS6y9yjqN0GPCl6htKnxPiF6yNtGczMYh1HxTYknJ8otrln6SK\n12+T4/7NUxP8b/kSMx4JscfWmMwt01HEAd/P8yrjalsrTjqRgyZqVSD2WfvL91FRjsdCS/dUhtDy\n94Z17M/EvfULUcK9C5swRqzK67qKbyeWy3Pp40ORZIxdmSqe8Dc+Y6QYaKVnEPuFRNqeTcvhaKmy\ntNJplRNrwzHafGdZTgF74iX2pIqfqO0BYCLXPGFSvrl8mPfFUlx2eanCILrYFJbBu7vOPcks5UYw\nFeXcZzq8q+2V5eYaT5gq79sqp7z3Hx/kpq5h2ijGfULNMWO5NNfsi2VTm7NdNjnFZltlz9AMAEk7\n4Ya8DEpnSlL853oW7Hrp4oAMuRjlolHCG7IhG7IhF1I2IGp9SPDrGRS5KnfiulOcUDkVY2h4q6ya\ntLCZouW7VvlkgDplmmbgkujF8661KLkEDMUavz0VK+2Ky47z8JHtvKotz7l0aI6/6IxwSkmCAcAt\nacyBGL7rfdi3M8CXqoZXtHM6Srb6Gdvmxa5WQIHmdX9wplxBB3ry8iXZIFiak7kiVZoZ7YojcyD0\nCUbGvHY0XIIDTkW+Hh7ww2aCXW2xEb9chQ6WSbe6Xt5zSVFKXpWnjt4y9QAnsZyybb4QDfMjx8o/\nbIlrvLMtz5oyitgpnohyzngbcdhFbMsVx035TqGq73OJY/UC7Gjxo/dCybZYw+MVR+LdIVFk+bpr\ncZkPAj5Yybm3fYTDFan2HaOZti2IR5j0CQmz2jGtcyZyuUeFtVVfDnje2KeKBzhax2i2Zo4TZpmG\nLS3Hx2PLk24JgJqOuLNb5069h0Z9AYA/zAapYZnzbrP4HL7pXgmVysFbxS6n4cchP9MmVTCwR76x\n88QApzylwDZPnH6GlFdmho4/2bw8jzmlHIva0W7LGqkqw1huORLLNZJAI3223grTAblay8r/wckL\nroTDEux1G0SsxgzHriyqGVRouxPJEcMrmarTtJQriHwAGlaCSKHru2sYg159kyopu35jIkdVpR0v\nTVeY9xlDf9wdQivLVXlCrSfx4qDJ2INEgh+tGK7IFArLiUje5SrdZCCTAqZyjWPwHBolKJTeTaqL\nI0MV1Z9Pxrboz2GvQGtOMaMsc/6aCatZIWPWGCY9Sc2KMhyNFPf6XWFvPsfVZpirPaRkUZd+1OeS\n3nEEOWYv6PL316Qa4iZjuSLzi/aUq/ByZYpo+qFY+DcWVM7NmSge6/s14I2H3NqYNgoc7rNknTWt\nYp/u8ktdCVIu5W10DHsRTPIbunX++dUR1UsW/Usq/u6zE3zUneInnSjmyQwW4hInrFibMglzu+rw\nSTLy+wqKWSPGyeZE2jPXrbArNrzW+39jLAPRMr9TyVn2m+jNxrDdmuK9E7faVw/ff8PXDj+7oY6m\noWKW/YiefKTGpszytc/7Damq+Iv8CC83W7H+7Xe6hKs2TzN6ehCAE3mVI4lhSwanMmnz0XiWR5Nq\nTyhdEo7Ol/ToXLJhCZ9DcrU6OyZyFOQk89pRcWLxBTHe0TbvZEpVSYh8YC74/nIP0E96kgbWKlaJ\n8k6c47GuJD5MPDnAoE75s4qkAG+jwo48YkG7IuV3QeXc3o0ZzMNTLTGO30/mean2CSdOlM4przzr\nKOwasvnCojX+XZv+PevOUEHRzAVKBbKotjldIA06CnIs1yfzHG7JQvkP0SnmOyvcVpWEhFv0KG9L\nV9h14xkAHvjWNp5KolUb5HO2z79HqllF+LKgFU/TYqsaZNGJVdTSmlldZnld3nV8J7EMuaioeJwr\nUcDhPWMnvzvb7//9JOxvXSWwu5JtTH63P5/jWnGH87/ONxhVMcrPr5c0ZvgXB8e556HvAPBDw1fx\nH285wv2PbeV+J/PgNd2YGqsrgGeKvpAbZ8uKcoX1YJxY75tUnSyVm02OLWBmGpz0luY3Kpa3tR3a\n5LzUB6uvSCWjLwRWw/v225wQ1K4ADRXxxap8fnpljFv1Ml+JxMD4GTXH29wYW4dP8+SUPHtBGT59\nZjNtr2GaSnzxSxoGPAHTK804K5SInWVPH6r6zMpcizg20BEbsiEbsiEvqGygI/qQkKwRduDgUzTg\nd0eHhy6y0o2JnWOcEgNpe64BCvfE8yUEcQjQ/z4f6T0dddisq1hPYXhZFnHQ5FybGe73acHjLmJH\n3uHLVTlK70xhUSuuM0Ns8ZChthI/YpABT0HZT3ONK8lutBZXw4Q/2sfArLbMRhSQoVQrjtJhCkk9\n3aoH2MoA+zrVwoz87ayJUQ2ue6sgAtJD81Ru2A6RJFTs3H+GJ7sjffdbAAlEDsY9lAwkvXqAiJHc\nccRTRY7kliGrCljUH9nDvJYdbLWGed9HxhuHDVuiSZaU83jkc7txwvwKc2LelG6JroKmqjD+Q/L9\n5bszxlXChJ9f2jiWXcbvNV4MwN3uDF+5fzv/OF7hnyNJO7fqCTIsHX+Ci9z5nb5yJanxvVwXYzkc\njWP+IPbOhOUBxmoR72zLWN3UrfG0NmzRhj0+S+Sp2BIhSJjQXza06xw44d6/VVEMotnr/c/PaM0d\nSUa1K5bwM50GR2LD03MJQ1UZwMlM4RTc0JE1onFMmYS9Jmerd0fc0e7yiZou1sNTCcwpRx2ILkA9\nuA10xDnEuFL5RshxrDwOqVV5/wCxtsSZQKgArqBGhBwrw1FmwKpVFRg0a2e10k6UWqqgoUK6WIUB\nZ3hJJsf4ZSV+40OR40guSu6fj3T5v5ng6q487KuVHIsE7IKiWVKOBME/AzRzOXY+V7JGkMhRsFq1\nteIIbY6EZBK7QppbdphBXpoLmcuONOcOIpaUYDuvHzvNIzPjzBnNnkz68JrbT7N81GBnpMMe+uoW\nal/r0KjIQno0HSaNzt1/ITgXjuU155m2vNKbUimv7lYYyi3zRhpdd5auVWz2994eD3FlZtgf2QK4\nX0E6ppd1bi0EL2HuBF9t5nu5mSuWtGz0dl4U6pKL2GIb7FOi5P58eZwB1Wbcu5dui0b4/fgUd78m\nx90r75A4x4Ar3RzBMOhHehMoOgpG8tJ9cDxy1LTi8jzBeE9t4FiueqXscviIOsFL2MR+D+kbdoqq\nU4UR0vEB07WqN8EoG8Y8TrhNTqcbMeW5gp+OHDtzuKlr2JwH/mrFtsElHskFUndf3OXOtmWrjegG\n6JtJeCw7xXV6wl8jSUf6AingDXfEc4jiexvSS+cYGPsHbDmDkjiDTBAGABOuzinj0K43AOcKdEPv\ns/rxH/bihBtWYTVsDVFvF7GghUQFYFbl3JTGHIgs7/CT7tDJLlPVLnc1xHr4bKfOJVQ5YUrEwqBf\nJAEdkan+FDDIxhA2mxMqZwDDNT5yfl3XcNm2MyzOd8i9BzdDMzq6wmMnxwGYnhnk6UTzsm6br1fk\nuj/91hhH8yUmpkVx7+Uwe5JNXIdYwpUIoj5xpr0VTSxwJHIc8xmGu2zClSzTIsJ5splvVwy3dLJC\naW2Ja5wy8p6hf2JPHr7Uk3QgDGNrW12RoyAPB8EMz2nLMAkqkTYu2y4Npah65Ih28IqsxqcrMt9+\nuFvhr+0iqtpkPpMxzoyS4Jd/zqCl8Gefa0wNpQ99RTlOm3LTaFpFCoK88P7TSRszoyyLXY+rVi2u\nr47xko5mfyIPHbCKFV2eDjWldb6WzcsgVJZNLUiRU8ZxyfVHeNd+2QCWWgmjw7Mcm2nymaqskS90\nj/LSfCszsRglDSImk2UOuibDfiPrKkVsdHEarDtFw5lV6Ij1tF4vZOWO5yMXhRIO0uqxWEMFAJAK\nFBV/FF10olSs04yp7qrrtYej5d5CDFHgsNjOB/oSOxiwjmVdoi7aShRmOObdkMVY4HG3wB4lSvhz\n1Yh3tVM+6SRQsUnlXJIppo0rIE0rHuEQNo2MEnb1XCLli1zBE3vIrfBrzrHjqpMA5C3N1KEmn1UN\nprT0QtvkpPNNHlXCJfGP40uZTB0Kx2NKrL8tVJiIEoY8oqJelcSTZR84jDGYPhResDiqvrO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PkwzTynLWnASKAZF8brjbTgLbHkxUjTYT3f7hTKbTGX14x31aMDk+u6hPGVtKCXZqx0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\nYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [] + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "hpNHggv4Km_l", + "colab_type": "text" + }, + "source": [ + "# Back to PCA" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "JDa1ETEsKm_n", + "colab_type": "code", + "colab": {} + }, + "source": [ + "iris = sklearn.datasets.load_iris()\n", + "irisX = iris.data.T\n", + "irisY = iris.target" + ], + "execution_count": 0, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "BQQDnJkyKm_q", + "colab_type": "code", + "outputId": "cf2c7082-a618-40a4-c705-44a28c185800", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 351 + } + }, + "source": [ + "irisX -= irisX.mean(1).reshape([-1,1])\n", + "irisX /= irisX.std(1).reshape([-1,1])\n", + "\n", + "S = irisX.dot(irisX.T) / irisX.shape[1]\n", + "L, V = eig(S)\n", + "eigorder = L.argsort()[::-1]\n", + "L = L[eigorder]\n", + "V = V[:,eigorder]\n", + "print('L=',L,'\\nV=',V)\n", + "title('Magnitude of eigenvalues')\n", + "plot(arange(L.shape[0])+1, L, '-o')" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "stream", + "text": [ + "L= [1. 1.] \n", + "V= [[ 0.70710678 -0.70710678]\n", + " [ 0.70710678 0.70710678]]\n" + ], + "name": "stdout" + }, + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "[]" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 39 + }, + { + "output_type": "display_data", + "data": { + "image/png": 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FhYXGaY1GA4VCUWPfvXv3QqVSVVseANzd3dGvXz+T+wdERNT0RAdBz549kZeXh/z8fOj1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\nRU5ErkJggg==\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [] + } + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "exI4WZgXKm_u", + "colab_type": "code", + "colab": {} + }, + "source": [ + "#keep only 2 eigenvectors:\n", + "LK = L[:2]\n", + "VK = V[:,:2]" + ], + "execution_count": 0, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "gpLcyQ91Km_x", + "colab_type": "code", + "outputId": "323efc97-4306-4d1f-9cb1-b38a0ab13a96", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 299 + } + }, + "source": [ + "irisX = VK.T.dot(irisX)\n", + "\n", + "scatter(irisX[0,:], irisX[1,:], c=irisY, cmap=jet())\n", + "title('Projection of IRIS onto first two principal components')" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "Text(0.5, 1.0, 'Projection of IRIS onto first two principal components')" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 41 + }, + { + "output_type": "display_data", + "data": { + "image/png": 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i1xgdnVWhy3ErxSIOxZEuhUoBX1X5iGOmw2XuK0/N5csqH7Hfuod8Qx4ZplRW\nhH7PFtuGa2T99UGOyCWVgqNHc/joo+189tluCgqc6H4G5haLgY0b76NGjVA0TeeRR5bxzTf7vVwm\nZrOB11/vzbhxLa+j9ZLSyDJkMjfiY1yqy+9+ozByW15/mjlaXbKvVSHL2GPdiVC8PyCqUIlxxeJQ\nHTRwNCGuKB6rKL3qU3kga3ZKKi3ffJPIH//4I5qm43brmEwGXC7NKxrFajXQt28DatQo/iIYDCrv\nvDOQli2jefPNjRQUuAgPt/Dkk92kiN9gWHSLV1GJi3Erbn4JWUlTRwvUSzgZkk0nfEQcikf9qeZk\nAHIM2ey37mF89n2YRcWIRpIjckmFJj/fSYsWs7ySZEHxIp7q1YM5diwXm83EpEmt+Otfu2Ox+I5d\ndF1QWOgiONgka2veoCwM/5IU04kSBd0ojEzMmoLljELm7t3YqlUlomFjn+MWhc3luPkwl0rXYtSN\ndCrsQbuiToEwP2Bc0xH5U089xerVq4mKimLJkiWB6FJykyCEYN++05w6VUjbtjGEh1/e4+wvvxzH\naPQdhdntblq3juG33+49m9Gw5G+uqiqySMQNzoAzI1gSPp80Y7JfERYI9v9nDltefRWDyYTudhHZ\nrDmD/jeXoGrni090KOpMivl48aTp+cY+fbpVN8fMh284IS+JgEx23n777cyePTsQXUluItLS8klI\n+B+DBn3Jffd9R6tW7/Pmmxsvqw+TqeSPsMViwGBQ5Si7EmATNsbkTOLW/D6ouveCIoMwUnORk62v\n/RPNXoQz7wzuoiJO7dzBsnvGex1b01WHhLyBWHQrRmFCFarfbIqKUAjVwq7pNQWSgIzIO3bsyMmT\nJwPRleQm4q67FrF/fyaadt6799ZbG2nZshp9+zYoUx/du9fxuz0oyMj48dLXXdloY+8AwG/BawGB\nrug0tt9C4b8/wF3o7a4Vbjendu3gzPFjhNWp69l+i6MFTRzNyFNzMQsr30R8TrYh0yt1gAEDbezt\nr8s1BQI52SkpF44cySEx0VvEAQoL3bz//laPkO/alcF//7uNlJQ8eveux6RJrb3cIFarkU8+GcbE\niYtQlOLl+EIIJk+Oo1u32tf1miRXR5YhkxxDJlW0qlTRIks8ro29Ay3tbckznMGmB2ERVr4+9bLf\nY1WjCXt2lpeQQ3HVoXC9CgDDc+9gadg3nDae8ozQe+UNoJq74hQLkUIuKRdycuyYTCp2u+++czlR\nvvkmkT/96UccDg1dF/z+ewpz5mznp58mEhFx3pfevXsddu2awg8/HCI/38ltt9WlQYMq1+tSJFeJ\nCxdLw74hxXwCVahoik5tZ7e0xmMAACAASURBVF36nBlCtjETi7AQqVX1coEYMBJxgdjX7dOf7KSD\n6M6L8poLQWTTZqWeP0QPZWzO3ZxRc3AoDiK1qhioWLVYpZBLyoX69cMpLPSNC7ZYDAwY0BCnU+Mv\nf/npolqZbtLTC3j//a1Mn97Vq11oqIWxY5tfc7slgefXkJ9JNh1HUzTPpOMx82E+rPo2RmFEVwRh\nWjhDc8cQpvtffNXmoUdInPsljuwsNIcDFAWj1Uq3l17FaC3bBHpYBc68KFd2Snyw293s3XuKjIyC\na3aOp59e5XcSUlUVBg9uRGLiab+5TRwOjR9+SLpmdkmuLwLBPusuNNU79bBQiv3fTtWJW3GRbchk\nUfjXnpqdF2OLimLc6vXEPfwnotu2o/7AIQz5eiHNJ9x1PS6j3AnIiPzxxx/n999/Jzs7m1tvvZVH\nHnmEMWPGBKJryXVm9uxtvPzyOhRFweXS6NmzLrNmDQpoeF5+vpPFiw/6zQNeVORm8OCveOWVBNxu\n/1/aC90qkvLHrhSxOWg9hywHMAoTrYva0dIeV+baml6hgCUgFEGBmscpYzrRJfiurZFRxE9/mvjp\nT1+W/ZUBuSBI4mHFisPcf/8SL3eGxWKgV696fPLJ8ICdJyUlj06dPvRbK/Mc4eEW6tYNZ8+eU14T\nokFBRt59dxCDBjUKmD2SK8eFky8i55Cv5nkW6xiFkYb2pvTLH1qmPuaHf0aq6eQlF+mYdQsDzgyn\nrqtsEU2VEZk0S3JJ3n57k88KSYdD4+efj3omIK8Wt1vn2WdXlyriUBx98uc/d6FhwyoEB5sIDTVj\nsRh48MH2DBzYMCC2SK6eROtuCtR8rxWXbsXNQes+ctSy5Wm/Lb8fJmHGcLbghCIU/HlQNEUjxn3j\nldRzFxWx9/NPWX7/Xfz63NPkHL7+rj852SnxkJqa73e70ahy+nQhUVG2qz7H++9v5aefjlzyOF0X\n1KoVxi+/3M2uXRlkZBQQFxcbEBskgeOY+UjxJOVF6OgcthykXVG813aB4Ij5IInW3SAUmjlaUc/Z\nkInZD7DTuoVTxnSi3NU4ZN1PgVKAphYPLIzCRMeCrjdcIitn3hnm908gPyUZd2EhitHEno/n0H/O\np9Tt0/+62SGFXOKhe/faJCef8fFNq6pC/fqBmdGfPXurz6jfH1Wr2mjevCqKotC6tW/hhtTUPGbM\n2Mjq1ceIjg5i2rSO0t1SDuhofpe4A2QaMrxeCwQrQpdw2HzAk8nwmPkwTRzN6Z0/kK6Ft3mOjS/q\nxk7rVg5bDmDVbbQt6kgdV/1reCVlI9uQybrgnzlpOo5ZmIn69z7yThwvjpQBhNuF2+1i5cNTuWdP\nEqrh+oQxSteKxMPjj3cmONiM0Xj+W2mzGXnuuVsxm6/+A6lpeomj/gsJCjL6zQd+jvT04qX9n3++\nm2PHctm0KZU//GEpM2f+ftU2Si6P6q6S87pbhffTU7oxlUMXiDiAW3VxwLqHU4Z0r2PNwkKHoi6M\nzbmbYWfG3hAinq/mMTfiU46aD+FWXRQaCkj5drlHxC9Ec9jJ3p943WyTQi7xULt2GKtWTWL8+JY0\nbFiFHj1q88knw7nrrtaXbKvrgi1bUlm//oRXBZ1zCCGYOHGR3zzhvsfCrl3pJe5/990t5OU5vaJe\nCgvdvP76BvLznSW2kwSeW0pIHWvASENHU69tx81HcCu+awd0dI6bL+1uK2+2Wzd5FbcAEGEmv8fq\nmoYpOPg6WSaFXHIRwcEmrFYTDoeb1NR8Dh7MumSh4l27Mmjb9gPGjJnPpEmLaN78PZYsOeB1zKpV\nx/jll+NlsqGoqFiUS2Lt2uN+S7qZTCr792eW6RySwBCmhxNf0K14olIAAky6iSb25sS6awKQq+aQ\nbDqOIhQMfry5qlCva95vgSDTcIpMw6kS49L9kWZKQb9oPkA83AGCvcVcUVUiGjYmrG69QJhbJqSP\nXOKhoMBFv35fkJKS5xHKl176hU2bkvnggyF+25w4cYaBA7/E6fT+gE+btozmzat5lsovWLDP55jS\nSE8veTFSrVqh7Nlzyme706kRHX39RkGSYjoWdaOOqwGJlt3oikZjRzNquurgUpx8H7aQVNNJDMKA\nprjR8TMoUKCR4/rUzMwwprE07BuKlCIUil04g86MpPrZH53SiNKqkSaSvZJrifEt4Ndk1A93YzCZ\nQBTHsw/85ItreBW+SCGXeFiwYB+nThV6jXaLitwsW3aYpKQsGjXyTmSUn++kT5/P/Aq0y6Xz5Zd7\neOaZ7kBx5IuiQFlXLTRrVrXEfdOmdWTt2uNek6Zms0p8fA1q1644qUcrEzHuWGLcsV7bfgpZSqrp\nBJqioSnF75VBGBA6GC/IZTLwzEhs4tpHIzkVBwvDv8Spnvdpu3DxbfjX3JP1h0tGxMQVdSTRstvL\nPWQQRmq++RAJkzuRvmUTQdEx1OjSDUW9vs4OKeQSD7/+esJv/hODQWHbtjQfIZ8/fy8FBf590m63\nTnLyGc/rsWObs2jRfp/K9apa7BJxOM7/eJybYC2Jzp1r8vrrfXj66VW43cXl3bp3r82sWYPKdJ2S\ny8eJk0Trbk6YjxKmhdOqqB0RZ7MHFilFHDMfAqCesxFWYcWpODhiSfJxRWiKRhUtkh75fQCo5arj\n191yLThk3u/3iUCgc9Cyl1b2dqW2j9AiGZF7Bz+HLiPbkImKSlNHC27N74upjsknw+L1RAq5xEP9\n+hGYzQafEXZBgcvvJOKmTak4nSX7zy9cRNS1ay3uuqs1H3+80+NzF0Lwpz91Ii4uln/96zeOHs2h\nWbOqPP10d+LjS1/4MWZMc0aMaMqRIzlUqWKjWrWgy7lUyWVgV4r4usrHFKoFuBU3qlDZbdvG4NxR\nFKj5rApdjioUQEEoy+idN4gartolLtF3KI5yWZ1ZqBb6jXl3K24K1LLlFYp112JC9v24caFiuGSN\n0OuFFHKJh0mTWvPee1v87nvppV8YN64FNtv5iZ1GjUpPFbtjR3HkybZtacyfvw9N03nwwXa8884m\nANxuwbvvbqFVq2gWLx7rt55maZhMBpo0ibqsNpLLZ4ttAwVqvkcEdUVHR2dx+FxU1LOuk/PH/xS6\nlLuyHsSqWykweIebKkKhtqvedbT+PDVctTAIA+6L6n6ahImarsvLXW/Ef7RKeXFj/JxIbghq1gxl\n6NAmfvcJobBihXeIWPv2sX6PPYfJZOCf/1zPiBFzmTNnOx99tIO33vodt1t4Fh0VFLjYuDGZRx5Z\nRjmk/ZGUgUPW/X5HsgKBhp8JbAGHzAdIyB+AURiLl9xzPjqlc0GPa22yX6q7a1LTVRujOD9gMOpG\nYtyx1HKVn1skEMgRucSLoCD/HwlN08nN9a4C4XLpBAebKCjw9asrCvTv34B33tmE3V56tIoQsGjR\nAWrXDufZZ8vnSy4pGZNuxm+dBQW/OVGEoqMpbuo7GzE6exJbgzaSa8imhrMOcfaOBOsh19pkvygo\nDDkzmj3WHey17kAAze2taGFvW+ZMjTcqUsglXvTt24B58/b5iLOuC3r08K6P2aZNjN9UtFA8uq9X\nL6LMUSpCwH//u5VHH+1IePiNlU/jZqe1vT2rDT+iq35+kP3on4JKPWdxuoRqWgz984ZdYwvLjopK\nK3screxx5W1KQJGuFYkXvXvXp2PHGgQFnfcBBgWZmDy5LfXqnc+3sm7dcf7yl5VUqxaEyXRBCS6D\nQtWqQaxaNYmQEDOqWvaRjslkICmpbBnzJKUjEP5jtq+A5vbW1HU28Dv6VoSCKlQQxX8bhYm2hR2I\n1G6suYvK7raT+cglPrjdOt9+u58FC/Zhs5mYOLEVCQl1PblPZs78nRkzNnhCCc1mA0ajQvXqIQwe\n3Jhp0zoQGWnj1KlC2ref7XfJvj8sFgObNk2mevXyefSuDOjo/B70Kztsm3AqTqpokdya37dMuUp0\ndLbaNrLDthmHaqe6qyY98ntTTStOWvZ1xMecNmacT1krwCKs9DszlGPmwyhAE0cLqt8gqWaFEOx4\n7z9sfXsG9sxMIho2pttL/6Bu737lbdoVU1I+cinkkssiM7OItm0/8MknHhRk4pVXEhg/vqXX9iVL\nDjBt2jLPyFzTdB54II5Zs7Z6LTyyWAz07l2fjz++cR7DKyJrg1ewx7ajOCfIWYzCyMicOy+5evHn\nkGXst+4+31YUR3SMy76PCL0KTpz8GvIzidbdaGjUctbltoJ+XkWQbyQ2/etVtv3n37iLzmuN0WZj\n8BfzqdmtYs7FSCGXBIQffkji4YeXkZfnG1fet299Pv98pM/23Fw7K1YcQdcFvXvXJyrKxooVh/nz\nn1dy+nQhigIjRjTln//s7eXSkVweTsXB7Ki3PasoPQio62zAsDNjS2xbpBTyUdQ7vtEpAkzCTD1n\nQ+ILuxGplbzi9kZCczr5sGldXAW+8eGxnbow8rvl5WDV1VOSkMvJzpuY/HwnZrPhslLURkRY/fob\nVVUpcVFOeLiV0aObeW3r27cB27bVJzOziOBgk1d8uuTKyFfzUYXqFdMNgAJZxtKTiWUbsjAIo6+Q\nK+BSnCRZEjlqTmJUzkSPq+VGpijzNKKEVJvZSQevszXXHjnZeROyaVMK3bt/TJMm79KgwX946KGl\nZU7/2qlTTUJDLVycKtxiMXDvvW0vyw5FKZ4YlSIeGEK1UITiR7wEVHVXK7VtuB7hO5K/sAtF4FJc\n/Bq86mrNvC7YoqqiqP4HKJFNmvrdXpGRQn6TcORIDp9+upP//ncro0fP58CBLNxuHadTY8mSg0yc\n+G2Z+lFVhQULRlOzZpinlqbNZuSllxJo0+bGH6lVZkyYaVPUAaPu/cNowEAVLZJlod+yMegX8tU8\nn7bBeggNHE0wiFIe0hVIN6UE2uzLRiDIMpwmw5hWYmSOwWwm7tE/YQzyfko02mzEP/Xs9TDzuiJ9\n5BWczMwili49iN3upnfv+p60secQQvDcc2v4+OMdKIqC2637zeVtsxlZsWJCmZe8CyHYti2NvDwn\n7dvHEhJiDsj1SK4OgWCHdTNbgjZgV4uIdFcl35CHW3HhVtwYhAFVqIzMHe+TrVDDza/Bq9lj244b\nt98Y8XB3BHdlT71OV+NLluE0S8IWUGDIP5vf3EC/M0P95m4RQrBrzgdsfesNik5lUKXpLXR74RVq\n39arHCwPDHKysxKydGkSU6cuRdcFbreOosCdd7Zkxoy+nmNWrjzC5MlL/GY1vJCwMDPvvTeIvn2v\nfzIjyeUhECSbjnPUfAizsHCLvQVhundNVTcuQGF1yHISrXt8XC6R7mpMyJ5cYv+rg38k0bbrougX\nE7fm96GFvU3Ar6ksaGh8FPUORUqh14+MURiZkHW/zz2ojMjJzkrGmTMOHnpoqU+M9mef7aJKFQvP\nPlucBvajj3ZcUsQBHA6NW26pGBEJNzMCwfdhCzhuOoqmuFFR2Rz0G33PDKaxsxln1Fx+Cv2eFNNJ\n4Owqej9+8xxDJnbFjlVYyVWz2Rq0kXRjKlHuarQv6sytBX3QFDcHrHtRhQGh6LQr6ERz+6XL/gWK\njB3byNi2ldDatal9W2+O2474fVLQEey17qRzYcmpjys7UsgrKCtXFofz+ePddzfz6KPxhIdb2bIl\n9ZJ92WxGBg1qJIsy3OAIBMtDvuOIOckjZsU+Yp2fwpZS63Rd5kV8SpFa6KliU9rztkGonDZkMD/i\nf7gVN0IRnDZmkGRNZHjOHfTJH0z3gt4UqvmEamGYuD7uM83p5Ie77iTlt18RCFSDAUtEFVr++Cai\nqe8F6YpGvnrpot6VGSnkFRRNEyXmOVFVlbVrj1OnTjg5OXa/xwCEhJgICTEzeXJbpk3reK1MlQSI\nA5a9JFn3+fVdq0JhS/AGXIrTqxSZJ7GVcuGxKnWc9TFh5peQlbgUl2e/UARu3PwUupROhd0J16oQ\n4469pkml3HY7zrw8gqoVR9Zsf3cmyevXodmL89lrgLuoiEP3/ROxfqBPe5NuKtPK1cqMFPIKSq9e\n9Uocbem64A9/+AFFUdA0/wdVrWpj796HrqGFkkCzOeg3b5G+AB1BoVpQLMp+UIVaXCAZCNMj6JM3\nGIBU00m/Pwy5hmxWhSxHKIJIdxQjcsdhuUQptAvJSz5JxtbNBFWLoXp8J+wGO9ttmzhqOUSwFkJc\nUTzVTkWwcGg/svcnFttoMtH5ry+w97NPPCJ+DqFpZG7dQaOUqRyqcdxTbs0ojFTRomjoKE6/rLvd\nnNqxDcVgoFrrtte95Fp5IYW8ghIZaePhhzswc+Ymn32aJtC0klPHGgwKQ4Y0vpbmSa4BRWrJAQIK\nCvUdjUmy7EfDe97EJEx0LUjAIiyEaeFUd9f0jLAtupVCg5/qOGcXAgGcNmawKmQ5A/KGX9JGIQTr\nnvkLe//3MarJDAisVaviXDkGR5QVTdE4bcwg2XwCY/N3cKWe9rTVXS7WP/c0lgj/BUsUFLpl96Be\naBa7rFtxKW6aOJrRuqgdBgwkr1vL8vvvQnO6QAhMwcEM/OQLYtpX/qfNgAj52rVrefnll9F1nTFj\nxjBlypRAdCu5BH/9aw80TTBr1paztS8NFBW5S/WLmkwqoaFm/vSnTtfPUElAqOGqxSHzAd8RtIAh\nZ0aRaNnjI+IICNXDaWlv67csWZui9mwKXu8VnXIxuqJzyLIfLU/D4Dcx+XmSFs5n3xf/Q3M40BzF\nRY5dhYUw+n9oW+/zHOfedhxxgYh7nc/tQjWb0Z3ei9TC6tYjOKY6TRzVaeJo7rWv8NQpvp84Fnfh\n+R87V0E+i8eO4O4diZhD/Ed7VBau+rlD0zRefPFFZs+ezffff8+SJUtISkoKhG2SMvDcc7eyc+eD\nvPPOIObMGVpq2tgWLapy//1xrFlzF7GxlfuDXRnpUtATkzB7Ku4gQBUG+uQNwqrbOGjd6yPyCgpd\nCxJKrC3ZrqgzTe0tMQgDZt3iN1Vt8amK/12KnbPf9xJTAHQdkXgajuSc37ap5El43eUitFZtjMHB\nABisVkwhofR+94MS2xxcOM/vknyh6xxesviSdld0rnpEvnPnTurWrUvt2sU17wYPHszKlStp1KjR\nVRsnKRvVqgUxYkTxsuNbbolizx7fkU6jRlVYtequ622aJIBU0aIYl30vm4LWk2o6SbgWQYeiLtR0\n1WGb7fcSKsQL0ownqe9s6LdPFZVe+QPoXNCDHEMWW4I2cNR8GC70xQuo5q6OsQxy4czzXTUKgEGF\nCxOt3VZyabXQunUZ+9M6Di1eSOrG3whv0JBb7piArWrJ4bH2zEw0u+/Evu50Yc/KuqTdFZ2rFvL0\n9HSqV6/ueR0TE8POnTuvtlvJFfL3v9/G+PHfesWXFy+hv638jJIEjAi9Cn3zB/tstwgLKgYfMT83\nEs9TzxCqF4eXnlFz2Br0O+nGFCLdVWlX1IkorRpB7mBC88P4usonuIQTt1q8EtQgDPTKG1Am+xoO\nGc62o4c9bpVzKBYDND8vxGqTahhaxqLt9h2Z3/rPNzFarTQdeydNx95ZpvPW7H4rOz941yfboWo0\nUqNb9zL1UZGRk52VjO7d67BgwWj++c/1JCaepnHjSKZP70rnzrXK2zTJNeC46Sg7bJspUPP8jsh1\ndLYF/c62oE2EaxF0ze/J8rDv0BQ3uqJzyphOknU/w3LHUNNVh1A9nElZU9hj3VEs9Fo1Wha1JViU\nrdhHm4emcXDhPApSU3EXFaIYjRhMJhq/+1cSVSeqrqArOlXd0Qxc8Ttr736AYz/9iNB1rFUi6Tnj\nbWpdQa7wmt1vpXp8Z1I3/uZx7RiDgqjXdwDRbSpXWTd/XPUS/W3btvGf//yHOXPmAPD+++8D8OCD\nD5bYRi7Rl0iunq22jWwMXucJxVN1A7qiYxImQJwPRTznNxfFI3Qd3ceXHuGOZFJ2YIIUXIWF7J/3\nJSd+XklIrVq0vOd+qjRuggsXmcYMbHow4ddgOb3udrN/7pckfvk5itFA8wl30fj2MZUqBPGa5Vpx\nu93079+fjz/+mJiYGEaPHs0bb7xB48Ylh7dJIffP4cPZPPnkz6xbdwKz2cDYsc147rmeBAfLNK8S\nbxyKnTlR//FJPasKA83srTAKI3us23GrvlEsfgsmC4UHTz+OiWvzWdM1jeM/r+DkmtUERcfQdOw4\ngqvHXrqhxItrlmvFaDTyt7/9jfvvvx9N0xg1alSpIi7xT1ZWEQMGfElurh0hiutmfvnlHvbvz2TR\nojvK2zzJDUa6MQ2DnyISuqKRbcikpqt2qSGFF6OgXDK08ErRnE6+GzOcjJ3bcRcUYLBY2PzGPxn4\nyRcVOhPhjURAfOQ9e/akZ8+egejqhsVud/PxxzuYN28fJpPKpEmtGDeuBQZDYB7bPv98N3a7dwy4\nw6GxYUMyrVu/z4QJLZk2raNXulhdF/zyy3ESEzNp1KgKt91WN2D2SG5sbLoN3V84oIBgPZhq7upn\nJz9LXhh2IcFaaIkhiheS8tuvbPvPv8lPTqZamzhCa9XEHBZOg0FDCa1dx2+bfV/+j4zt2zy1M89N\nhP744L3cu+cQqlFO1V0t8g6WAU3TGTVqPrt3Z1BUVDzKSUw8zapVR5k9e2hAzrFzZ7rfavNCQFpa\nAf/5z2Z+/PEIP/44HoNBJTfXzrBhczlxIhenU8dsVomJCeG77+6galX/JdcklYeqWjShehjZSqaX\nq8SAgdZFHfg9aJ2viJfkRBV4lrhfjI6OS3FiFhb2f/UFa6c/jruoePl85t7dAKhmMxteeoGuL75C\nq3vv9+lj/9wvvQogn0MrspOxYzvV23e49AVLSkUO38rAypVH2bv3lEfEAQoL3axYcYRduzICco6W\nLaOxWkv+XXU4NA4fzmbFiiMAPPfcWpKSssjPd+F0auTnuzh2LJfp01cGxB7JjY2CwrDcMZjF2UU8\nZ/8LBEmWRNJMyT6+cFWoBOsh5xcUncWIidb29l7bBILfgtbwQdSbzI6ayeyQN1nz1yc8In4hutOJ\n5rCz/m9Pk3fyhM9+g8l/1kS3vYhVf3q4eOVngBG6zvGff2LNX/7Eb39/juyDBwJ+jhsJKeRl4Jdf\njlNQ4JuMSNcFGzacDMg5Jk5shcVi8KmFeSEFBS5PWtpvv93vU+nH7db54YdDfosjSyofOYZsdOVs\nBMrZ/7qis9O21W/yLF3RaexoRqyrJqowYBRGQrQwhuaO9oki+S1oDduDNuFSXeiKjv1wMpq4VF57\nweHvfVdRNp90j0/JtXPkHk5i8xv/LOMVlw2h6/xw7wSWTZ7Eno/nsP29t5nbuwf7vvwsoOe5kZBC\nXgZiY0OwWHwngkwmlejo4ICcIyrKxrJl4+nRo06JYm6zGalZs3jWuqRc5EKIUnOtSCoPSZbEs5WA\nvFFRPJkOL8QoTFTRIhmVO5H7MqcxIesB7sl6iFou71WWGho7bFu8J0ur2hDOMvjb/Xz4Go8cTb3+\nvulnoXg0v/2dt9j0xj9x+1mZeSUcWbaU5LWrcZ9dHCTcbjR7EWunP47jTG5AznGjIYW8DIwe3czv\nJKLJZKBfv8CVRmvYsArz54/m6NFHqFrV5iPoJpOB22+/BYB+/RpgNHofYDAo9OxZt9R8K5LKQ0mF\nklWheucP13TYmIxYnkTW9K/4X/uWfNu1J0ff/xLh9hVnh2L3TZcbEwIJdcFcSmSLolB/kO+ckaKq\n9HztTZQSJjWFrrP1rTdYMu72gDxNJn0732eFJ4BqNJH8y9qr7v9GRAp5GYiODubLL0cSHR1McLCJ\noCAj9eqFs3DhGGy2wMfd2mwmvvtuHC1bVsNsNmCxGGjSJJJvvx1LWJgFgJdfvo1q1YI9MeZBQSYi\nI2289lrvgNsjuTFp5mhVYv6T4bl3EKaFY/gtFbXm26h9voDBX7D7vffIO3Gc7IP72fDSc6yY6lu3\n0ypsGP38SOhfjsDcrREGqxWDpfhziKKgmkwYrFY6P/0cYXX851CxhEdQrVUbSnrc1Ox2MrZvI+33\njWW8+pIxWoP8n0cBg9Vy1f3fiMjiy5eBrgv27TuNyaTSuHEkSmkO7QCRnp6Prgu/2QqLilwsXnyQ\nPXtOccstUQwf3lQuHrrJ2GrbyIbgtShnR+FCEQzOvZ06rvrsd2xjZYu+cMZZYnuD1cqYFWuJbHqL\n1/ad1q38GrwKt3redWMURkbm3EnwUZ3CjHRUk5kTq34CFBoOGUZ4A/+Juc6RffAA3wzphzPvDMLt\nG6Glms10efYF2jw47fJuwkWkbviN7+4Y4TMxaw4L5949Sed/hCogsvhyAFBVhRYtqvndl5VVxIcf\nbmfduhPUqRPOgw+2K/HYyyEmpuQcFzabiTvuaF7ifknlp11RJ5o4mnPcdAQjRuo5G2IWFgSCtSve\nRuii1CJtimogY9sWLyHX0NAVDauwUSh0EIJodyzdCxKo7q4JtSC0VnG202qtyl6MuUrjJkzasos1\nT/yRpEULEZq3mBvMZkJr+Y9FvxxiO3eh7cN/ZNvMGSgG49kl+oJBn31doUW8NKSQB4D09AJ69fof\nZ844PIt4Fi3azwcfDKZ//9JHKRLJ1RKih9Lc4S2oTsWBMzsXHKVPUCqqQnBsDc9rgWBx+DzSjCc9\ny/uNGFFRi0X8KjGHhNLj1dc59tNynGfOXGCHiik4hLr9ypZl8VLE//kpmo2fxMk1qzAFB1O3T39M\nwYEJTLgRkT7yAPDGGxvIzrbjOPul0XVBUZGbxx9fUWJ0iURyLTEKE8pt9aCEAt0AisGANTKKWj3O\nr8pOMZ0g3ZjslaPFrbg5ZUzjhOloQGyzRlRhxKJlRDZrjmo2o5rNRMe15/YlP2IwBc41GFqzFs3G\nT6LR8NsrtYiDHJEHhJ9+Ouy3on1+vpNjx3KpXz/wmd4kNycabvZad3HAshcjRloWxdHA2dinyr0B\nA01COnBAnQ0lFOCObtuOfv/92Cs7YKox2W+OFldqFkmHfqZ6rTGYQ8Ou+jqqtmjJuDUbKMzIQDUW\n/6BIrpybVsiLF88kkOsCxgAAHrJJREFUsWLFEapVC2LChJY0aOC/6OulCA+3cvKkb2UUTROeKBOJ\n5GrR0VkY8RWnDOmeScgU40ma21vTs6Cvz/Hxjh4cMBhA8xXmsLr1GfWD7yrgYD0EozCeX1BU4EQZ\nvwh1+WEOmq0cdD1F3MN/pOOfnwrIZH9QdPRV9yG5SV0rDoeb4cPn8uijy/nqqz28994WEhL+x5Il\nV7aMd+rU9gQFef8mmkwqXbvWIirKFgiTJZWc04YMvgubz5zIt5kX8SlHzYd8jjlsPsjpC0QcwK26\n2GPbQa6a7XN8WPVaRDVp5hOKZ7DaaH7XPX7taOhoWpw86+wgXnlgKcqPh8GhoeUVoNntbH93Jgfm\nf12m63Lb7eya/T4LBvVm0cjBJC36Rq48vgbclOGHn3yyg7/9bY1X7hSAkBAT+/Y9hMVyeQ8qQgie\nf34NH364A7PZgNut06xZVT7/fKQUcsklOWVIZ36Vz4pXaZ7VXKMwcltef5o5WnmOWxnyA3ttO3za\nG3UTPQv60NzexmdfzqGDLBw2AHdREZrTiWo0Ub1DPIO/mIfB7D8HyilDOj+EfUt+4WmIft3vhGlk\ns+aMW7Oh1OvS3W4WDu1P5t7dnlBA1Wymbp/+DPz481LbSvwjww8v4Jtv9vuIOICiKGzdmkaXLpdX\nFk1RFF544TYefjie3bszqFEjlKZNpc9PUjbWB6/xEnEonmBcF/IzTR0tPOllg/QgVKEW51e5AAUF\nq+5/wBDRsDF3bd3L0R9/ID8lmZh2HYjpEF+qW6SaFsOk7Cmkpu3lO+UtND+pcItO+xb4vpgjP3xP\nVuJer3hu3enkyNLv+GZwH4YtWILRar1kP5JLc1MK+cVukHPouig1A+GlqFYtiISEelfcXnJzkmFK\n9Vu1x6W4sCtFBIniiIvm9tZsD9rkXZtTFE9s1nWWnCrCYLHQcOiIy7JJQSE2uhnm0DCKLsqBoqgq\nNctQV/P4qp/8LpUHyNi2jc0zXqPz03+7LLsk/rkpfeT33NOGoCDfMKfwcAtt2sSUg0X/3959x0dV\nZ40f/9wyk8xMGjX0DoIsgiIiEIpAAImBRURRQFF3scIP3WfdR13XR9gHF/uKvgAfWIqIFUQBQxEp\nWdFFLHSkQ2iBEEidTLv390dgJMyEJJBkMuS8/yIz9945E+DMd773fL9HVGcOo/hFX1bzt5vlsUYN\nBmYPwWpYsRpWLIaFKCOa358biVYBYzJFVek19XV0m80/z67oFixRUXR99oUSz3fE10PRg5cTGl4P\nuz6YX67xVmfVco7cNE1efHE9c+ZsQdNUVFXBalVZtGhEuazGFOJiWepZdkRuIVfNoamnBa1cbf1t\n1Xz4WB+1mp2RW4psVKWbOtc7OwatRvHh5aTlBLqpU9dbL6D0sLyd/OE//DTtLbIPHaD+rd25afxT\nxXYDulj2kcN8mNAFXzG7GlpjY/nD3sD9y0XxKqz58pUIdSK/4MiRLDZuPEqNGpHcdlszrJfb2U2I\nK3DQuo8VMUswMDAUA92wEOerwV3nxqCj80Xsx5ywHMN7odzPLJzWaF/QiV65/Susj2ZlObR6BSn3\n34vpKzrPrug6rYeNoP+7M0MUWXiSRC5EGWSp5zhqPUyEEUEzd6tidxm8HB8+ZteahkstOiLVTJ1b\n83pS2xvPVzGL8KieS57XuOvcGOp6611x/G7FxWn9FHbDQQ1fTf/jZ/ftZfdHH+DOzqLZwNtpclv/\nIguCKsKpLb+wZOigwn3B3W50ux1rTCwjVq/HEX/l77E6kkQuRCmYmHzrWMtW24/+HQVVFIZmjSTe\nW79M10rXT/B57Id41MDdB+t46tHE3Zwf7d8F3ug0FeyGnVhfHDcUdKa1q12Zpk9+tm3ie8cGVFPD\nUHzU9NYhOesujnz0Bev/PBGfxwM+H5rVSv0eCdyxcBGqVrEjf2dGBrsWzufsnj3U7dyZ60aMxBoV\nPCmJ4kkiF6IUDlsO8FXM50UW3QDYDDsPnXmyVJ3mL8jUMvi4xrzfpk0u0sDdmJbuNmy0r8enXlIK\na/JbPblhKXblZrHxx35e5DUVU6VOZiznGr0QdL6689PP0PW//1rq9yVCp7hEXi2rVoQoznbbLwFJ\nHMCLlxOWY0HPcSpOfrZtYm3UCnZFbMNLYWKu4atFlC8qoHu9bljoUHATbQquD17PfXE9uephh+0X\nctTgLcp8LhffTfobs1o3ZkbDWqy+cyTe3SeKHGMqBmf+vTloiSPAT2+/UW5t1kRoSCIX4iIXkvCl\nFAqrRS51Wktnfs0ZfG/fwHbbL6yPWsUHNWbhVJw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kdziIa96SMzu3B/TWvLAMfnjKmio3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\nIUSYk0QuhBBh7v8D+M+7qjcYr2QAAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [] + } + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "HawKXrmVKm_2", + "colab_type": "code", + "outputId": "39feb78e-5a22-489c-8fc5-68bc88fea89f", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 72 + } + }, + "source": [ + "F = sklearn.datasets.fetch_olivetti_faces().data.T\n", + "F = F-F.mean(0)\n", + "F.shape" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "stream", + "text": [ + "downloading Olivetti faces from https://ndownloader.figshare.com/files/5976027 to /root/scikit_learn_data\n" + ], + "name": "stdout" + }, + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "(4096, 400)" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 42 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "pdwB2Nd3Km_6", + "colab_type": "code", + "outputId": "fba18d49-127a-4a1c-e77c-dea27b4ae77c", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 89 + } + }, + "source": [ + "gray()\n", + "for i in range(5):\n", + " subplot(1,5,i+1)\n", + " imshow(F[:,i*10].reshape((64,64)))\n", + " axis('off')\n" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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j7ezsKJ/PazAYaG9vT3t7e1pfX9fGxoak84A5dFA2m1WtVtPy8rKuXbumXq+n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\n47fffnthWZHOuwBiNBnT6dmpGYVCQfl8XvV6XSc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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [] + } + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "pr6Y6r3FKm_-", + "colab_type": "code", + "outputId": "e256f342-c98c-4e00-d6b2-de6b670396e5", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 35 + } + }, + "source": [ + "SSmall = F.T.dot(F)/F.shape[1]\n", + "SSmall.shape" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "(400, 400)" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 44 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "2K6y3DeWKnAC", + "colab_type": "code", + "outputId": "b26689fd-4e88-487d-e0da-fba1f52f27d1", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 283 + } + }, + "source": [ + "L,U = eig(SSmall)\n", + "L=real(L); U=real(U) #discard imaginary parts that are due to numerical errors\n", + "eigorder = L.argsort()[::-1]\n", + "L = L[eigorder]\n", + "U = U[:,eigorder]\n", + "\n", + "semilogy(L)" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "[]" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 45 + }, + { + "output_type": "display_data", + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [] + } + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "tWhtae4HKnAJ", + "colab_type": "code", + "colab": {} + }, + "source": [ + "K = 50\n", + "LK = L[:K]\n", + "UK = U[:,:K]\n", + "\n", + "VK = F.dot(UK.dot(diag(1.0/sqrt(F.shape[1]*LK))))" + ], + "execution_count": 0, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "waOREz9eKnAL", + "colab_type": "code", + "outputId": "ed245bb9-e346-4046-e99d-7736af8952dd", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 287 + } + }, + "source": [ + "#check that the columns of VK are indeed orthonormal\n", + "imshow(VK.T.dot(VK), interpolation='nearest')\n", + "plt.colorbar()" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 47 + }, + { + "output_type": "display_data", + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [] + } + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "_i2q8nuGKnAQ", + "colab_type": "code", + "outputId": "8b08cfb5-3cc6-4183-af89-3146273bf4b2", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 198 + } + }, + "source": [ + "from common.plotting import plot_mat\n", + "plot_mat(VK.T.reshape(-1, 1, 64, 64))" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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f2dmxmgzZAHSMx+OxDsxIJKLT01NTpSyXSxWLRdtLZKHRaFT9ft/O/e/kdCVZ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\nevb6H3z9P++3gSG1RcjIAAAAAElFTkSuQmCC\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [] + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "JjUdHfm3KnAT", + "colab_type": "text" + }, + "source": [ + "project faces to the dim spanned by first three eigenvectors" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "qkTC7CbMKnAV", + "colab_type": "code", + "outputId": "478b0712-d5f0-425f-ffdf-2a9d5f081f54", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 265 + } + }, + "source": [ + "from mpl_toolkits.mplot3d import Axes3D\n", + "FPCA = VK[:,:3].T.dot(F)\n", + "ax=figure().add_subplot(111, projection='3d')\n", + "ax.scatter(FPCA[0,:],FPCA[1,:],FPCA[2,:], c=floor(np.arange(400.0)/10), cmap=pylab.cm.jet)" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 49 + }, + { + "output_type": "display_data", + "data": { + "image/png": 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1wSC2hVA4uXkdbqQCPZsE/FYbItmBN//oIe/xFh5H5r0/wlx7B8LNo60+H2Xb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\n7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3hFHoXihRc8RgRtbWPp7raSTt3d3bS1tdV5RR4eucnr6eZTyvHwqCfxeAhZltL36Lnn\nLmLjxv/Hddddx7p1P+e888717l+PhiSvtKOHRyOycuVKXnrpJQ4dOsS4ceO48cYbWbRoEStWrGDv\n3r1MmjSJu+++m9bW1nov1cNjEJ7R9fDw8KghXkzXw8PDo4Z4RtfDw8OjhnhG18PDw6OGeEbXw8PD\no4b8fyJjur6+e4agAAAAAElFTkSuQmCC\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [] + } + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "mM6pp7l_KnAc", + "colab_type": "code", + "colab": {} + }, + "source": [ + "" + ], + "execution_count": 0, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "_NHTOBP3KnAe", + "colab_type": "text" + }, + "source": [ + "Now lets generate data to show off Kernel PCA" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "Nc0tR9y-KnAg", + "colab_type": "code", + "outputId": "b6f7df77-7058-43a6-fbcc-b7019a548dd1", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 335 + } + }, + "source": [ + "a = np.random.rand(20)*2*pi\n", + "X=[]\n", + "for r in [1,2,3]:\n", + " a=np.random.rand(20)*2*pi\n", + " X.append(np.array([np.cos(a), np.sin(a)])*r)\n", + " \n", + "X=np.hstack(X)\n", + "\n", + "Xcolors = (X**2).sum(0)\n", + "Xcolors = (Xcolors-min(Xcolors))/(max(Xcolors) - min(Xcolors))\n", + "Xcolors = pylab.cm.jet(Xcolors)\n", + "\n", + "xmin,xmax = floor(X.min(1)), ceil(X.max(1))\n", + "xg,yg=meshgrid(arange(xmin[0],xmax[0]+1,0.5), arange(xmin[1], xmax[1]+1, 0.5))\n", + "mxg = hstack((hstack((xg, zeros((xg.shape[0],1))+nan)).ravel(), hstack((xg.T, zeros((xg.shape[1],1))+nan)).ravel()))\n", + "myg = hstack((hstack((yg, zeros((yg.shape[0],1))+nan)).ravel(), hstack((yg.T, zeros((yg.shape[1],1))+nan)).ravel()))\n", + "G = vstack((mxg,myg))\n", + "\n", + "plot(G[0,:], G[1,:], color='gray', alpha=0.5)\n", + "scatter(X[0,:], X[1,:], color=Xcolors)\n", + "axis('equal')" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "(-3.3768485279316645,\n", + " 3.8274689775205557,\n", + " -3.423235905986818,\n", + " 3.8296779002850867)" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 50 + }, + { + "output_type": "display_data", + "data": { + "image/png": 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65MIJFzY1t5v2oy+PSwyivKgk8rvvvptevXpxySWXROPlRIK5ye/mxMuaXguuCLjwJNjq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\nclFt7jp1aDV4CJrHc8rn6n4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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [] + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "3uKUmqWSKnAo", + "colab_type": "text" + }, + "source": [ + "PCA will not transform this data significantly:" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "C3xllvzvKnAq", + "colab_type": "code", + "outputId": "e5129d84-052d-4dc1-b171-af513a811ccd", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 299 + } + }, + "source": [ + "S = 1.0/X.shape[1] * X.dot(X.T)\n", + "L,V = eig(S)\n", + "eigorder = L.argsort()[::-1]\n", + "L = L[eigorder]\n", + "V = V[:,eigorder]\n", + "XPCA = V.T.dot(X)\n", + "GPCA = V.T.dot(G)\n", + "VPCA = V.T.dot(V) #this will be the identity matrix!!\n", + "subplot(121)\n", + "title('Data space')\n", + "plot(G[0,:], G[1,:], color='gray', alpha=0.5)\n", + "scatter(X[0,:], X[1,:], color=Xcolors)\n", + "plot([0,V[0,0]], [0, V[1,0]], 'r')\n", + "plot([0,V[0,1]], [0, V[1,1]], 'g')\n", + "axis('equal')\n", + "subplot(122)\n", + "title('PCA space')\n", + "plot(GPCA[0,:], GPCA[1,:], color='gray', alpha=0.5)\n", + "scatter(XPCA[0,:], XPCA[1,:], color=Xcolors)\n", + "plot([0,VPCA[0,0]], [0, VPCA[1,0]], 'r')\n", + "plot([0,VPCA[0,1]], [0, VPCA[1,1]], 'g')\n", + "axis('equal')" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "(-4.8021444637865764, 4.174413161330814, -4.651031241048406, 4.325526384068985)" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 51 + }, + { + "output_type": "display_data", + "data": { + "image/png": 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czm0f8t6bqxjzyhtoCywORiJy8c/UqTPQ6XT4/XLGSleXbM6l0+lIZ2sZ+nsC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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [] + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "J665bG1RKnA5", + "colab_type": "text" + }, + "source": [ + "Let's try to use a polynomial kernel!" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "AuwDDggVKnA6", + "colab_type": "code", + "outputId": "5489e781-f5c5-4246-9074-82319e3cbd85", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 333 + } + }, + "source": [ + "def kern(X,Y):\n", + " return (X.T.dot(Y)+1.0)**2\n", + "\n", + "K = kern(X,X)\n", + "L,U = eig(K)\n", + "L=real(L); U=real(U) #discard imaginary parts that are due to numerical errors\n", + "eigorder = L.argsort()[::-1]\n", + "L = L[eigorder]\n", + "U = U[:,eigorder]\n", + "\n", + "print(L[:8])\n", + "plot(L, 'x-')\n", + "title('Magnitude of eigenvalues')" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "stream", + "text": [ + "[1.05873487e+03 5.52373780e+02 4.16501350e+02 2.94883600e+02\n", + " 2.38588182e+02 1.89182141e+01 6.42606759e-14 4.73855108e-14]\n" + ], + "name": "stdout" + }, + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "Text(0.5, 1.0, 'Magnitude of eigenvalues')" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 52 + }, + { + "output_type": "display_data", + "data": { + "image/png": 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33ktGRgabNm0iPj6e1atXAzB16lR2795NUlISISEhLF++3D096EXxkUEAlFXX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\nTkSuQmCC\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [] + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "x5OufgS3KnBA", + "colab_type": "text" + }, + "source": [ + "Let's keep only the 2 most important eigenvalues" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "AtJ3Ot6vKnBA", + "colab_type": "code", + "colab": {} + }, + "source": [ + "U2 = U[:,:2]\n", + "L2 = L[:2]\n", + "XKPCA = diag(1.0/sqrt(X.shape[1]*L2)).dot(U2.T).dot(K)\n", + "GKPCA = diag(1.0/sqrt(X.shape[1]*L2)).dot(U2.T).dot(kern(X,G))" + ], + "execution_count": 0, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "TUTLu-xDKnBF", + "colab_type": "code", + "outputId": "b00b312d-0fe0-49c5-c88f-2ea2f9c84f35", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 351 + } + }, + "source": [ + "subplot(121)\n", + "title('Data space')\n", + "plot(G[0,:], G[1,:], color='gray', alpha=0.5)\n", + "scatter(X[0,:], X[1,:], color=Xcolors)\n", + "axis('equal')\n", + "subplot(122)\n", + "title('KPCA space')\n", + "plot(GKPCA[0,:], GKPCA[1,:], color='gray', alpha=0.5)\n", + "scatter(XKPCA[0,:], XKPCA[1,:], color=Xcolors)\n", + "axis('equal')" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "(-0.10396200030282303,\n", + " 2.7280931499993404,\n", + " -2.2038155302767164,\n", + " 1.0191270953671026)" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 54 + }, + { + "output_type": "display_data", + "data": { + "image/png": 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WlkZEUSRnYsH0UOKFG9oTAoaOJUBnatbCuEdN1VH5mOt0OtLSHKSlOVCUMrze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\nM+NEqfok2LRpE5s2bRpx3G63s3Pnzsi/p0v1arYxmUyRtrOx6OhoJzs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