{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# PCA on artificial data: Lecture " ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from mpl_toolkits.mplot3d import Axes3D\n", "from scipy.cluster.vq import vq, kmeans, whiten\n", "\n", "# seed the pseudo random number generator with 0 \n", "# so that the results are consistent in all discussion sections\n", "np.random.seed(0)\n", "\n", "# Matplotlib produces annoying warnings (see https://github.com/matplotlib/matplotlib/issues/5209)\n", "# ignore warnings for now\n", "import warnings\n", "warnings.filterwarnings('ignore')\n", "\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this example we'll generate two clusters of data points on a plane, combine them into a single dataset, randomly embed it in a higher dimensional space, add quite a lot of noise, and then try to use PCA to separate the data into the two original clusters." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generating 2D data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For each cluster we'll draw random points drawn from a Gaussian distribution centered around its mean, with a predefined standard deviation.\n", "\n", "[You will learn more about probability, the gaussian distribution, mean and standard deviation in CS70. For now it is enough to know that the points of each clustered are centered around the mean and at least 95% are within twice the standard deviation from the mean.]" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def cluster(mean, stddev, size):\n", " return np.random.multivariate_normal(mean, np.eye(mean.shape[0])*stddev**2, size).T" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We'll create four clusters of 500 points each, centered around (5,5) and (-5, -5) and (0,10) with standard deviation of 1." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "N = 500\n", "\n", "#mean1 = np.array([5, 3])\n", "#mean2 = np.array([-7, -5])\n", "#mean3 = np.array([-5, 2])\n", "#mean4 = np.array([1,-4])\n", "mean1 = np.array([5, 5])\n", "mean2 = np.array([-5, -5])\n", "mean3 = np.array([-5, 5])\n", "mean4 = np.array([5,-5])\n", "stddev = 1\n", "\n", "cluster1 = cluster(mean1, stddev, N)\n", "cluster2 = cluster(mean2, stddev, N)\n", "cluster3 = cluster(mean3, stddev, N)\n", "cluster4 = cluster(mean4, stddev, N)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We'll combine all clusters into a single dataset and shuffle it for good measure" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "dataset_2d = np.c_[cluster1, cluster2, cluster3, cluster4]\n", "np.random.shuffle(dataset_2d)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 5.40015721, 7.2408932 , 4.02272212, ..., -5.50388989,\n", " -5.03057244, -5.8128021 ],\n", " [ 6.76405235, 5.97873798, 6.86755799, ..., 5.39494819,\n", " 6.77955908, 6.57708821]])" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dataset_2d" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The dataset looks pretty much like we expected." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(*dataset_2d, alpha=0.1)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Embedding the 2D data into a 25D space" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have a 2D dataset, we'll embed it into a 25 dimensional space by multiplying it with a random 25x2 matrix." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To understand how this works, we'll first embed it in a three dimensional space in two ways." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "def embed_and_plot(M):\n", " \n", " dataset_3d = M.dot(dataset_2d)\n", "\n", " ax = plt.subplot(projection='3d')\n", " ax.scatter(*dataset_3d, alpha=0.1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, embed the our points in the X-Y plane:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "embed_and_plot(np.array([[1, 0],[0, 1], [0, 0]]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, embed it as a different plane. From our point of view, it is now harder to separate the clusters." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "embed_and_plot(np.array([[1, 0],[1, -1], [1, 0]]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now return to our 25-dimensional space. We'll generate a random 25x2 matrix and multiply the matrix by each point.\n", "\n", "[Note that this matrix has to be of rank 2, otherwise the data will become one dimensional - but the probability of a random 25x2 matrix to be of rank less than 2 is negligible]" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The rank of M is 2\n" ] } ], "source": [ "D = 25\n", "M = np.random.rand(D, 2)\n", "print(\"The rank of M is\", np.linalg.matrix_rank(M))\n", "\n", "dataset_Dd = M.dot(dataset_2d)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "How does this data look like? Let's pick two random axes and view the data projected over these axis." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "axes = np.random.randint(0, D, 2)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([20, 12])" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "axes" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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aoxmEAWkS0gsVZWvYGiZsjVKSUNEcdQ95PvA9z/uGdiYFh0WDc11pJ0sUpQ74k1/tcmGYMsokt/Zz7s0KBmlIpS3L2mD084d9APRi6KURgXBsjTKMA4nAOsmy1ijteP/6kLc2BwySkDiQNNrSaPPK75B9UXzge5733KrWcPuwYJiGhIFEW8f2pOLO4RIlJGmouHNYkkSK1jo+m5QkUlC1Lcv2+Y4lgUEC72yMaKwlDSXGdT39UkAoFY0x/N6NdX776pDNQcK9WUXRGOJAfqVF9Dzzge953nM7WNb04oBGW6ZlS6Mti7Llo3sLhknAh3dnTJYNi6pld17RaEsdwLJ+9mMoutk3/ajbPLU5ikiigNZY5qVmnAZUjWW1H3FpJeUH10ZYB0pKrq5mflX/GD7wPc97brW2DNOAn9+aUuhusuWt/YLP95aM0pDaWMqqZVq2lK3FOghO9FkGPL6sE9N16khgNRWkccCVlR5pKAmVYhCH9GLJYdQSKsEoC1nNEt69MEQKgcP5Es7X8IHved5XPG1cQhxIbu0vOSy6CZj35zUSQRoF3XiEQDKvNHljCJUgixRFrZG2664RgHBwXN0ZBdBPAwIlKeoW7RyDfsRbqwPe2uzTGMvGIOGN9T5Fo7kw1CAFq72It9Z7zCvNvGx9v/1T+MD3PO8hzzIuoRcH/PLunHnVktcGax1Fq3HWUreavHIsKo1SMEwDQqkw1gEG445m3EQhVaOx1tFPI9b6IUkYEKqMq+OM999cZVZo9pcl71zoI4RktRcxzgLW+gmNsaSBBCG4NA5f+0mXL4IPfM/zgC9X9V8cFigp2BwmCCG/Mi4B4DBvsA5u7uW0xiKl4LBsKBsNOMJA0ssClBMYBxhLHAVoYwglCBGQhJIoiIgUrA9SLg5SLI4bGz2ujBOurfWJNiVZrJgVLUXdnUAGUXdrwat9v5J/Xj7wPc9jWjQPNlBNlw0r/YjbBzlRKBEIIiWIA8XllaMOnYOcXqIYxIpl0917dl62aGtQAnQQkkYSbUAbRxpLlHQIYiIFFwYJhm5yZaxgkEQM4oDvXx3x9uaQWAkGaUSoBK1xqJ7gt6+MfcD/hnzge945V7WGj3ZmBFKSRoq8MuxMSwSCfhJwaZxSNoaiaZgWDb+8O+ezvSV7yxprHbf2C6ZlgzYWa0FLiKUjDUImbcM4C0njEAG8dzEjUpJxFpHFklmhiQLJ5XGKEILfvb7GpXEKdK8ofGvli+UD3/POuYNljXOQRgohBGuDiLuzEiUgixXaOByOYRry89sT9hYVm4OkG2dcaqyzpKGitIIwEQghGaSK1V5EHCjG/YitQUIcKa6MU5ZVy96y4dLqgPV+QhQo3ljvsdaPeXOj/+Bx+U6bF88HvuedY8flmcOiYVFr1gcxcaDoxYrtSUFrHYESXF/rUdSaadEwSmOkhI1BTBRJokASBiFKaRSCQAm0sczLlqsrGf004ruXR4SqG2+gpGS1n/D9y2McDuMcq1n0YGXvnR4/YMLzzqnjbpwgkKz1Ixpt2Z4U7C1Kbu3nVK3jwjAmUpKP7y34cGfOomyJFNybV+znNStpQKAEaRByY7XHOIvQTpAoxTCLWR/EDNKAURKxkoWUtSZvWn5wbYS23UlhLYt8yeZb4lf4nndOHd+85HgUwcYwZndW8dPPDhkkXZtjYxz3dheMsghtLXGk+HhvycYgoWwCpJQkKmStHxEGAocgiyPe28q4sjpgmISM0gDjIG901zffG9CPI9Z6X+3v906XD3zPO6eOb14ihGRrlDAtGpQQjNOIH91YoTGWD7ZnLEpNoQ2racwkb1iW3caqS+OUg0XDD64q9vKGSdHSiyRXxymDXsxbG71u1IESvLXRpzVf7oL1If9y+MD3vHPq5M1LklCxNUpZ1poo7IahzQpNFiqGScAXByVtZFnvx2Sh4t6spp9EvLHRY1a2jHsxQgikFERK8uZmn3cuDFmULbOq8d02Z4QPfM87p9b6MduTAuBBv7sALo1TPtsvCFR3Irg3q0giycYwoag1m8OUC6OUrVFCpQ3bhyW9OGCtH3F3WnYnEdWNJhYCfuuS758/K0498IUQnwMLwADaOff+aR/T87ynS0LF5ZXsoX73710aHU3CVFhrEVKQN5p3L/RJQ0XVGoqmZWuUUrUGYxzrvZAkDrEOLoxSnLVUrUEK/Ir+jPm2Vvj/hnNu/1s6lud5R04OQcM5EN2YhJMD0R7td09CxbRsqFrLW/2EC4OYvDbktWaQBFxf6zErWox1xJFkI0kYpuGD72+0fRD23tniSzqe95o6OQRNCrgzrQDHlZUM6/jKQLRjSaj4rUvjB987zkLuTMoH36ukRPXEg0DfnhQ02j4oC/nxxGfXt9GH74D/Swjx50KIH38Lx/M8jy/bLqNAMitbenFALwqZFi1RIIkCxcET7khyvPKXAqyDS6OES+PuRHGyVHPy64rGl3HOum9jhf+vOed2hBCbwD8RQvzSOfenx588Ogn8GODatWvfwsPxvPPhuO3y+O30KITL1gDdhdqiMU/8/seVe36Tr/NevlNf4Tvndo7+3QX+IfD7j3z+j51z7zvn3t/Y2Djth+N558Zx2+Xx29o69FEHDUBrHHHwam62Py5X3dxbsj0pqNonn7i8L53qsy2E6AkhBsdvA38H+OA0j+l5XmetH9NoQ6MtozQkPxprMM5CGm1ptGGtH7/sh/ncjsPeOsgi9eB6hA/9pzvtks4F4B+KrjMgAP4H59z/ccrH9DyPh9su26M6PEJgXXebwVe11r4zLTnMGxwQKclKL3pwPcKXlr7eqQa+c+4m8IPTPIbneU/2OtTXH2otpbvZyno/Jgwk2jjuzUouDBNa95If6CvAt2V6nncmVa1hZ1Lwyd4SbS2DKGDRaIrKMMxCnIG9Rc3evObDnTnvXhxwaZy+kq9avi0+8D3PO3OO6/T3ZhWzoqE1jvuzGuscvUjx8f0FdWu7cc2hRODYm9f873+5zSgNWe1HvLUxYJxFL/tXOVN84Hued+Yc7yHYndcsSk2lDbNSc5jXhBIqbVnJIhwgW0EAtGbJOI1ZyUKMgZ/dOuRH11d96J/gA9/zvFN1sgZ/cqTD16mPxjN8vr/kMK+O5uwrnOvKOK129JKANAgYpgGzomVRtaz0YloLWdxF26d7C373+tq38Wu+El7NJlzP814J37SFcl42/LOPdvlsb8ntSck0b/l8t0AbQxQoSm04mDeUjQYhEBIkgrI1REd7C5JQsqz0t/FrvjL8Ct/zvFNzcrwDQBSIBx9f68ePXflPi4YPd+ZUbYtSMM9r5mVLGiqUilhUDVEoyWKFAL44yNFHo53HvZjR0SC3qrX0Ex9xJ/m/hud5L9xxGeeT3QVJKGm1Y3a02h4mAXVrCZSgFwdsDGKsg5u7C5Io4Bd3pt3F2ECRRSHDfozWjlZrisaw0k9w1tJPQuZFDUKRBJIoVEjpsNZS1I68bvnR9dWX/Jc4W3zge6+lb1I39l6Mk1M6BfDzWzP2lhWDNCBRiknR0k8CfvfGCsY6PtiekUWKw2VDEAjuTAruTXIEAXGseGMtY5q33Js5SmNYESFxHHQdO3HE1ijm4jhlmIYsK8MXhyXX1zN/wfYxfOB7r52TgZNFita4J44C9l684zKOdY79ZcNhUTMrW4ragHDEoWI5bfjgjgQBed1yuGxQStJPQqwxHOSaSV4icIx7If04JFSC1V7IxiCmlwRobdkcxDQWhmnEOxcGxIGkaAxvbvRf9p/hTPKB7712vq5u/KrvOn0VHE/pvD+vu0CvWprWcK8oWVQaax2DNOCzgxxnu6md2sHFUcLhoqGfKBa1IQlAW8Gs0hzmLb/3xpj1fopDcGGUsChaytawNYx558KAJFQ0R6/ovMfzge+9dk6OBT72tFHA3otzPKWz1pay0SxqQ2Us1oIxlt15xZ1DQ21grR/RjxRlY9hf1ggccaB45+KQ+5MK7Sxbw5iyMRgLwyxivR+jjaMMNHmueX99lTiQDwbC+ZP6k/nA9147x4FzvLKHV3sU8Fl0fI1kXmmKpiULg+7vKwS1tkzzGgMUtUHg+GJSoI1lf1ExLx0WsICZNSxCSJOAREJeGw7ziiiQbI1SVnoRcSCZ5g0Xxz1+9/oq06Kh1pZBGvC9rSHDLHpwT15ftvt6PvC9185aP2Z7UgD42+6dgpO99bOiRgrJ9rLk/qIir1o2hsmDi7Cf7i85WNbMljWNsSxLh+bL4Gkc6AYaq2m1w1iHlI5KG4pK852LQySw1osxziGF6AalnXhOfcA/Ox/43mvn5Fhgv/J78Y7HE29PSuZVyyyv+WB7jjaWNzZ7tNYwKTQHy4Yv9pdMqhbrHEKAodvt6QBB974FrIZRBkI7kAFFrWlSS1lrRlnEKAl5Y+PLWyn65/Sb8YHvvZZeh7HAZ9G0aPiLW4cI4OZ+TtNqbh0W1K0hkLA9Lfnnn+zjXHd3LedAG0PeGKztwr59zM91AE6yNU4JBCghCaXAWMvVlYzraxnjLPLP6W/IB77nec+kag0f7cwIhOTOJOfWfs5B0aAEzMqGotbd3ocaogikhKaFJAZtoDVfhr2iC3l74v04koRKEAeSMJD86PoK726N+O6l0St7d66zxge+53nP5GBZs79s+PXejF/uLChrw/YsZ162aA1OgLNdqNcNRHSBXhegjq6fK7oyznFpJwGEgjgEe1Sjz+KQtzcGjNIIIQXyFb4711njA9/zPKAr13y6t2BZacJAspJFxIGibg2784o/++yAn92aULaastXszhua1mIsSAX5I3PKqhNv60fuRiWBWEEaCpJAEQaCjSxhbRCThoo3N3p87/KIFV/GeaF84Huex7Ro+Jef7pO3hmnesL+sySLFD6+t8NlBzjSvuXWwZG9Rsp/XFEdp7oAG4BmGUh6HjQM2BpJIdbtns0gRSYETgrV+zFtrPX7n+ipC4Ms4L5gPfO9c8TN2Hu+XOzOmZUtrHNp2G9f2Fw3/659/waVxSq0tH+8W7MxqtIb6GxxDAEet+jgDcSIYxCGDOODqasqNjQFbo4Q4UKSR8s/NKfCB751JpxHMfsbOk+3MKpxzVK3mL25NuD+ruouuxmKcozWOO4c5xn6zsIfuRUBPQZoookDRjyP6iSKOQtI45L2tIVujlDTyHVanxQe+d+acVjD7GTtfPZH24oC81tyflXx+kHN3VrG3qBA4qtawt2i4Ny2wSGr9Zf+8e9qBTojpVvWtA+tgsxezMUjoJSF5Y7i+mvHv/eAiK73Ed+OcMh/43pnzvMH8rK8GzvuMnZMnUings/2c2wc5a70Ig+XX9+ZM8u7vmDcGQddWuWgdgu59+7SDPOK4/bKXdCeKi+Mel1d7XF1J2RimpJHk6jijn0S+G+db4APfO3O+Lpgft0I9PkE87dXAeZ+xc3Js8f15xTRvaYzhTz/eo2o1B3nN/ryltRCIbuzB8anQ8Xyr+mOZ6loyA6G4Ms74d36wxfcujolDRaQk4yzEOvw442+JD3zvzHlSMANfKfV8tDNjfZA806uB8z5jZ1621NqwPenq9XfnJcuqZXtSsLesKOsWKcHYrvzym8okrAwCsijuLsqu9/jb711kcHQLQoBGW0LxNT/Ee6F84Hsv1ePKMU8KZgFfKfU4B8uqZXgiRJ5UpjkPM3Ye9wrocFlzcy/nzz8/xDjH4bJkd9EwK1vypmVZaQTQWqj185dtHhUAm8OALFKESvHWRo93NnoMshghjkL+HJ5wzwIf+N5L83UXZx8XzDvTklA9vBzMYkX+SLh/XZnmdZ6x8+jfc1lpPrgzpdJdfX57kvPpXje90jgIhGNW2m6omYPqOZJe8tUTQ0DXdrnaD1jtRVwaZSAEf/PdTeal5tJK+tqfcM86H/jeS/O0i7OPBvPjSj39OKRojF818tW/Z950N/2+fZBzWDTszEruLxuKyiAF6KOh9DXPX5+3dKF/fFFWA+MYtlYy1gfd+OLWWC6PU4raUGnND6+uvNYn3FeBD3zvW/G40s1xTbk5WpGPswjnHNuzilpbcK7r54OHLtDCl6UeIeB7l0bktT73q8ZHL3Z33Taaxlhu7RXcPsyZ55aWLqifYXPsVwR0F3KP2zOjAJQE6bpNa5RqAAAgAElEQVSLvONexI21jEBJPtvLu3q9cPzdf+UyW6P0Rfya3m/AB753qqrWsDMtuX2Q00sChnHAQV7zi+0Zi0ozzkKEEOw1hk93c7KoOxm02vDh3QXaGLaGCVJ2AX9hECOEoDU8FO7jLHrZv+pLNS0aPtiecmdSYC30k4BF1fLp7oI7hyW/vjtneaI+/03CHr7swT9e3ceBIFCSWAmMdQzjkCgMGKYB//71VX54dcXvmD1DfOB7p+a4pnyYNwyTkMZafrGz4NJKQt1a9pYlH92bcXmccWmUsF+17M81l1cyPt5dkoYKEwhu7ues9mLWBxHL1hAdlQV8iHSO5+DMy5ai6lpX/+LzQ+JQsjMp2Murh8L+mwiASEIUwqK7NzlSgnOOfhwgpWSzH/PdSyP+6Lcv+Z76M8oHvndqjmvKdWtY1JrP9nJqa5gfdYfsLWpwjo/uzfl8f0EWhaz1Qr44LBBOkISS/WVLIBVZHFA0hkEiiQJ1rnbHPs2newu0hdZYKq35YGd+1A1jSOOQapb/RmEf0l2ITUOBdSCFpjaOLIQkCOglAf044ofXR1wep2R+Ds6Z5QPfOzW1tkgBe8uaadEA0AskN/cX5FXLsjaMs+6iayhDdpc1UgoO8ynvXRygraRqLWmkUAIWtWG9H5+r3bHHvm438fLoRuK39nNaY3HOUjeW7VlJIAV1882PGwAbw4BxFjEvNaESXF/r0YtDDvOatSzmylrKH7y5zjAN+dH11XNfXjvLfOB739jjQgi6lf28bLl1mLOsNHmju4t8Aqal5v68Iq9bIiXZnrTMa41uDVkUEonujkcf3pmxNkwQwEoWUh2dPMZZdK52x0L3d765uyBvDdY6pBTMioZLKxl5rZmXLb/YmTFvNPcmJXdn3SaqZeMwpvu7P8/8GwHEorspySCJ2BonvLfZ5/a0om01b14YsDFIWO/H9JMAYxxX1jLe2hj4sD/jfOB738jjeug/3VsinMMBv7q7YH9Zc3NvyTjtVoiTsuXevGSyrMlbTasdrXUoCVhHUzTcmpS8eyFDC5BKEEnJ5wcLQhXw3YtDWt31jb/u5ZyTJ9N785KqMWRHg86KxrAoW/76zpSrq72jUcY1s9KwPclZVC1VA5GCynTdM88a9iEwiGHcj1npxaz3Y66vZFgBb6wrysYgkFwcJfzW5TGpv57ySjn1wBdC/BHwX9Nd1P9vnXN//7SP6X1zx0EzL1uKVpNFIcMk+EpN9rg+X7aaX97LyWvNJG9IAsV+XnNYNIzTkEEs2Ssa9vOuBTNQEmsdB4sGJbu7HTkHQgoiqchCgZKSK+OMURZhjGWY9tkaxmgHu4uK710avdYB8+jJdG9eo41lUWv6cUisJH+9v2Bv0TCrWrS1DJKQ7WnJvGoJpYKw67UfhpJZYXlSVSek67gByCLI4pA3L/RJI8UgDLix2edvvbfJJ3cXLFqDMZbWOlayiCwKuDROX+vn4nVzqoEvhFDAfwP828Ad4CdCiH/knPvwNI/rfTPHQeMczMoWKQSzoiaQguqRgWS1trTG8JObh0xLTWM02wc5xgnSqGuTbFpHEoeUs5rdeQUCrq5kVMbSGI1tYVm39OKA1TRGSEdjLPNKU7WaK0nGai9CW8f1tR7QbcvPa/1alw4eHnJWc7DsbhA+7oeM04idacX9WU0SdSfLvXnDF5MCYyxJGJAqyUFpcc6RBJJebAna7paCs/bLHnxJV+7pJwCSS+OEi+OMN9f7gGClH/KdzSHGwI2NAWEgaU1XWlvtxUiBD/tXzGmv8H8f+MQ5dxNACPE/AX8P8IF/RpwsHUyKmlESkTeaOFSEStIeBexaP/5KZ8yf/GqXz/cK+knAsmo5LAx7y5JxGrLaCxFSMilqhmnI7qzAIrhzWGKcox9HNE1L2Tr00bEHaYRzgjRQzEqNPCo8R+rLev15uGB7fLH7/rwmCiRb45gP7lQ0M8tmP+H2YUEcSgZJyEHe4JwjEjCvWualZuJAHP3nnEYJGGUCR8h63BLJ7pVZq2GYhQzTkDQM2BjEDJOAQAouraa8sdFnFIdMypZBHNAaS6MtW6PkXDwPr6PTDvzLwBcn3r8D/I2TXyCE+DHwY4Br166d8sPxTnp0Pvqdw5JbtkDIbiUeKkmgBHuLit1FyWHe8s6FPmu9mA+3Z/yTD+5TaY21oK1jrR+C6+bhNNqCkvRCydYwYdxLiAPJQdEgm25j0NRCL3DgHGmsGKUh/aNgubaWUbWWItBcXe09eMzn4YJtHEh2ZiVRIAmV5MIwZadXsWxa9pYVTWtY6cVMiwYpBI2x3J2XVK1hnAbMSk1j6MYnGOj3AnpxSBoFOBOyqFpaJbkyTtga93DCcXGQ8PbWkFBJroxT4rBrrbw0TvnFzpRlpeklAVujhCRUNEcX6r1Xy2kH/uMGnz50/cg598fAHwO8//77L2Aoq/esHtThG82v7y/ZX9aUTddjvb9ouDCMKRvD9mHBxjAibwz/4pOSTw8K4kCyaFrKqqFsHRZHpTUSx7RsUVLQOkcaSGZFy/ogxgE7s4KmtqhAEKuuXq+tQ0rJGxt93t0adaWJQNKPA1Z6MVII3NFt9l73OTlV2+1T+MnNA3pJwOYgYSWLeGM9Y1q2NK0liyWf7+WUrWOUSLanFdOiRQhBEChGPWhai7GWLAl5Y63Hai8hVI55aVhpY8ZJwNo4ZhCFrA8T3t7oI6Vga9TV5J1zFI0hCRW/dWn8YGEQKkGj7Wv/PLyuTjvw7wBXT7x/Bdg55WN6z+i4dPDx7gLrunLJwjrqSrPXaKZlQwioQPBXd2as92MmZcuH2zNmeUUchsxrTaO7sbqLokFJCMOuNq+UgkAyq1pCKSlqjdHdPVIzqUhChVKCQRrx9maf9y529zQdJgFNa7m+3ntQSjoPc3KO2y8Pi5arqxmzoptVXzWa37oy5oK2/OrugiQMGUQS6yxFa2mtJY0k1kIcKLSBcRIRBYpxGjLux2wNI5RU/O4bKRv9hGEakNeGWhvSQBEoyeYwefC3PflK6jyMlT4vTjvwfwK8I4R4A9gG/iPgPznlY3rPyjk+vLfg3qzCHm2RH2cxB8sK00Cdt+StBmtZVJpf3+16wQ8WJWUDaVBTWqjNlxMThe3ecMYyyBSLpgELedjtkI0DQRh0b4/7IW3jyCLJO5t93lzv04uDrvVP8KAz6LysJA+WNXlr6MUBaaQIVN3NqTeGD3dm7C3qB8/Tu5fG7C0rbu7lhEqwkiYcVDUORy8JCUQ3SiGJupEHN9b77C9rrq/0uLSSoqR8aJW+PSm+9pXUeXoeXmenGvjOOS2E+M+B/5OuOeAfOOd+cZrH9J5N1RpKbcmrll6o2F3W5JXGOkccBNye5xhjmRUNB3nDomoxztG0UBwFfNV+9ec6wBgIo6MbV2uBs5q9ecM4C1jrp4zSbndtFiqMtGyNUn50fZVWW+ZVi4DXvvXycWptsdZRaM3OtGRatCzrhsNFTRaFrA9jAinIa03VWq6s9Km1I4sD7k4r4kahrcMax9wYrowzLq+k3FjPuLqa8a+/u4mxjvroLlMnV+l+BX8+nHofvnPuHwP/+LSPc9496428j+1MCopGE6qu1NJoy7Ju0cbxq7sLSm1YSUM0gr1Fgz7awPMsOzYN0Bi66wHaEQi4OO6mYi5qzYVhyqVxj8urKYui4Y2NPitZRK0tm8/w2F83x8/d/VnJ9rTk/rxirRczSBR3Jpq9ZcPWSLIz7TZgXVnp0dqu3OPoyi8bg5h+JNlfNoSB5L31PtfXh7y5mvHdy+On9sv7Ffz54Hfavga+7s5Rj/s/edUaPtlbYq1DG8u0qrE4bu8vuT0pscYipECbo5n0QPUMl9MFkMqjlb2BRjuOD6+UREmJs46DvGZzFFM0mgvDmLcuDM5t2FSt4dO9JUWt0dZxcz/vunCysKuxt4aqMVSt5c2NHtvTko/vz7mxmnF3XjGtmgdjifuDhLc3h0gpeHdryOWVlLV+7G8Q7j3gA/818LQ7R0EXLL+8O+Mv70y5tZ8zKVrWehGLWlPVhu3JkruzgtZCLwpZ1pqyrsliiaOrx31d13V49HkBpJFgGCqs7UboJoFiEIdo5xinEVIJtoYJl8c9rq9nrLzGm6ieZmdaMslrelHIOFOMYsVSwN1pSdE68qqhHyuMdcRhwJWVDGtz5m3L6iDCOkeWBEzylkhAbQw3xn0uraRcXc18r7z3EB/4r4FH73QED29QqlrDz29P+H9v7iEs3JmW1LXhg+0JiVJoo9mZ1zgLcSTRrtsMVbaQt91g3a8brxsBgYLQQZxAHHQ3sK60Za0XsTlKqRvNKAj4/rUhV1Z6/MGb6w8uDh4PXTuP7s9KpBBMioa8bo+6ngzGCt7c6FG1msNFze685t60Iosl64OY1V7Mai/iQzejl4RdSay1VNpQNZpIyXOxZ8F7Pj7wXwOP3uu1ag27i4qi0uzOSnZmFT//YoK1MEgC+pEir1oWRcvUNggBdd2t0LW2LGVDbb4M+cdtpjgWAmkEoYQoCNkchOStIQ4VG4OUUMIoixiMYgZxxDsbQ66t9/zFwSONcUyLmlApFpVhtRfzV7cm9NKAqjEsKw0C1oYRtw6WpJHirY0e1lk+uDNFIKi0IRASRNfBUzSaXhz4XnnvK3zgvwbW+jHbkwIAYy13JiXLqmVWNEyKlmXdcn9WEgeK7WlJXrd8vrtkWhqUhCTqwr0FWgfSPLyif7R8LzlxT1MFcdiVbK6uZVhrEbVhaxRzcZyRBpKysUgJF1dS/sZb66/1HJznFQYCawUL3RIGgigIWR/FBAJmtWazHzKvJP00JOwJ0ljy8e6Sv/O9i1gLk2WL1paNcczQBkyLhvVR4m9C4j2WD/zXwMmNMduzCoCiMWjnGKQh+0XN9qwgCwN2FxXWCqal6SYoWghMV2s/TvnHlW8Cuj77EIiDbsu+djDKFFdWB9xYT5kVBiVgmMGN9T7GOlQgWYkC/s33LjDOIh/2j1hJI7R2fHaQE0qBUoLLKxkrSUQSKw6WDf0k4P6somoMTat5Y61PHCkujjOcKCnKllnZ8J2tEdfWetxYy/zK3nssH/iviePQn1eaLw5yDouGedGwaLoZ6Xlp+ORegelG3Dxk2T691VLTXbi1HE1YjCEMJEEQECse7NTdGMas9yMa47i6mrGaRhRtt0X/PNfqn2SYhoRK0hhLfXR3r62hYFm13YwiY+lHAfFaxuYw4ee3JwzTgEZbNgYxdWvphZJp0bLSC+mFiks+7L0n8IH/CnpSz33VGj7ZnfMvP93vLvLNKwSCRdUwLWuqo6V7ax9+4p91gJGjW+EnoSAOQy6vZCyqGmsBJ9gcxMSBJA1DshD6YcC0bLi62jv3tfonOS7H3Vjrsb+skUJgnWVtvcf+omZRKSpt2BolSCGIlEQiiQJJHCiurKbcnUEWBlwapb6M430tH/ivmJM99602/NUXU3ZmJVuDGI3lJzcPuXNQUbQN92Ylk9zi+GqZ5llaLU86jpA0hjBU3FjvM0wCUgWNhYvjhDfW+izqbkfutdWMYRqRxQFvbfR9CPHkE/VxOW6UhhStZhB1Y4rf3hxQtYaPdmZHQ9ME37s85Jd354QyxlqLMY5eqPjR2/5est7T+cB/xRwsa5yDW/tLfvbFhLIxxIHg072Wn35+iHWW1jh2ZhUHuX1iO+XzdGeHwDjuRiqs9UJW+ylZKClqyyCL2RzE/Ktvr7M1TLuNWqLr63mWHb/nxdM2x11eybi88tXvS0LFj66vPnSiuDzO2J4WTIquvu9vHO49Kx/4r5Cq7YZofXJ/wa39nLo1BKFilIVIJEWruTctkIGiqMzX9s4/znH3zXGJJ6Y7MUQBREnAhSRCBRJrHGEgeG+rRxAEvHdhyO9cW/XB/jWeZXPckzxu7MHWKD2dB+q91nzgvyKOt+D/enfO3rxhUmmWVcUoSxBCYKxlXjQcFg6Hfu6wPyaO/pPAMFUIHEmsCJXijY0+415EGkrSqJuseXmU8Ptvrfmwf4qnbY7zvG+DD/xXxMGyZpI3TJctpdaApWgcRd0N0NpdVBwu9HOVah4Viq6DRx79G0eScRYSB4phGnFxnPLW5pAslLy9NXzszc29x3t0cxycj7t3eWeLD/wzrmoNn+0u+Oef7vPp/QUHRcvFccoodXy8u2CWNxjjHvTFP6+ErmyTRZBFCmMMVggujjIujFIGcUAaBUjR7Zi9MIz54bUVXzN+Tic3x4VKnIu7d3lnjw/8M2haNHy6t+AwbzmYV5TGkoYKDThr+Pj+AmMcWEHZOJqjnbHfpIxj6HrqlRLEgWLQj7m21qOXhmRHA9C0sbx7ccT711d4Y3PgV/TfgL9rlHcW+MA/Y6ZFw89uHdKLQ4Rz3FtWlJVhkAV8cVhwMC+ptKO2mkh2t7OTdBujnkUAxCG0bTdKIQlgbZAQSsWFYcqbGylb44xACFYGEaGUDJOQ33/T1+l/U37mvPey+cA/Y355d07eGJa14YvDnHuzkrqx3Nw3hEIQRorDvOxKAs+5pk+AlZ7CAGEikAqSIGCjn/DbV8aEShKHgvVBzPcvjxilEc3RfW992Hveq88H/hlStYbP9nMGseLevObWQc4v7y5pdIsSktV+wkoaMctbTNVSthCFj7/V4DEJpKq7sbhC0ktD5NHos3EvZmMQsdFP+M7WgGESEh6VGgZJt33f15k97/XhA/8lO7n7cndWMilq/uRXE27u5ZStoW5bmsYRhpLGGNKwu4i6LFus68L+cddqj3tBEtX10a9lCUrBII1REtIo4EI/4s0LA/7mdzb57sURVWvYmZbcn5UcLLtRCb7O7HmvDx/4L9HJ3ZdSwK/uzbl5f8GHd2fkZUukFDhBg6NtLLgaMeii3Ipu3IGGB8PLGttduJV0n+uFkCaKLAr5zoUBWaTYHKfkpSYLJVfWenzv8vj/b+/eYyRLz/qOf59zr1OXrurqy1x7ZmftXbw2vmwWB4fcCA6QBIGIFIlIQShIsYIAkShRAliRIiGkiBAISqIoDjj/xBFCBAIiJAEriERRbGLAYO8u9u56d2dnemf6Vl23cz/nzR+ne7Zndnp6bj3Vl+fzx8x0VU/VUz09v3r7Pe/7vDy10LqtlqcWW7dWkSilTg4N/Cfkbn1UVgcRW1FGmpdc3454ZW3MxiQjL+qWCOOsJC+g4QICUWHwkxzXtghdi6mpbp0hawyE1KFvCXQChzBwcUV4/lKPVuAQei7nug0Eod/yuNhv3jrcejfsH2YnqFLqeNDAfwLuHMmvbse8eH3I1iSl1XB4Y2PK29sJV7ciojQnTuuRtW3XfeeTYmfUbkFRgWUZFloNgrQAMWAgKytavsuZtodlWzQ8F9+1ONdtcGm+SWkqPvb04r4HWutOUKVOPg38J2C3j0qcF3zxzQE3xglb45S0rMjLiovzIYsdn9XtmI1JSmkgL6A078zPOzYstVwW2g2GcU6SlzQ8oTQWncCBChqBS9MTLvdbIMJc6HK+G2JZQst3ONfdv/+K7gRV6uTTwH/M7jZ1k+4sbfziGwNe3ZjgiBDnBavbMcYI3dBjuR3QDhySvLo1RWPt/F4CeQmIEHo24ywnKysalsNi6JMUBf1OA8cB3xJsx8KUhiQt8FyLucDlfefm7nnxVXeCKnXyaeA/Rvu1wBUR1scp1wYxYPBcm9B3sSVDLMPbw4T5sO5v3m95rA5jWgGIWCRFRZaDY0GcVUyykqWWzzQtMWI4022QlyW+47DU8jEWPHd2jijL2RpnZHnF+67MHdgKQXeCKnXyaeA/Rvu1wM2LkmlaMIwzmp6DEfAdm7mmQ7xzTmluKnzP4evPz5HkFb5r0fRdNkYJ69OM0BUanmBLvSKn2/S50m/wsfcsM4hS3tiY4toW8y2Ppu/guzbzTR/ftZmmxX31vtGdoEqdbDpB+xilRYVry223ubaACCvzIa3AJsoLTAn9lseFXkhZVriOjWdBy7PxXZe/8OwSC82ArCgpMJzpeCy1QxbaDQLXotfw6Ddd3nNmjqKqp4Asuz6IfLHtU1SGrKgIPYfQtUmLh22WrJQ6SXSE/xjd68Jnv+XzoYvzvHxziIvUh5dYFs9fXsDGsDwXcGYuZBDV3S/XRwlC/YYx36pPklps+1SVIc1Lek2Pj1zsMkoLfMfi6cUWr61NiNOSTmjRC936sPHA1QuvSilAA/+xuteFz8C1+eiVPkZgdRBjjGG+6bOyENJteLi2RWUMr9wcsz5JONMLEStiXnwMcGE+RDBM04pOw+UbLs3jOjbnApf++bon/eWFFi+tDjHUbz6twMWSui6llBJjHqKJ+iF54YUXzBe+8IVZl/FI9juo+l73A1zf2YRliyAIkyQjq2B9HDOYZFRUjOOS+abHBy/2+PBK764XVA96fqXUySMiv2+MeeGgz9MR/mO2e+FzN3hXt+Pbgne/C6PneyFro4TKqvvSryzUG6Ravg1mQst3aQfObbtj7/X8Sil1Jw38Q3Dn8sxxUvDmm1v0Qo9Ow73rqDtwbVb6TSrDrVU+AOe6IRd6oYa4UuqR6dW8Q7B3eWZaVGxNUxzLIi1KKlNP3yT5u1sW9Fs+WVGSFRXGmFvtiXUOXin1OGjgH4K9yzMH0wzPtml4Nllp8BwLz7HZnKTv+nu70zGWQJSVWMIT3fy0+5PJ19Yn+74pKaWOr0Ob0hGRfwr8HWB956YfN8b85mE931Gyd3lmtnsebfVOX5p7NSWb1Rz8dpTx8uqw7rrp27R8l+uDSHfbKnWCHPYc/s8aY376kJ9jJu61Gua25ZmWEGclBjgzFwBHrylZkpe8tDrEsSwaXv3mtDnN6Dc9bY+s1AlydFLnGNmd+qgMhJ79rnn5vVMzgedQVhX9pofvWEdyXn5zkmKAhmcjIri2hedYTNJcd+kqdYIcduD/kIj8sYh8WkR6h/xcT8zei7Iictd5+d3Qf9/ZDh+5NE/Ds2cyL38/0qIidG2K8p09GY4lRGl5pH4SUUo9mkea0hGRzwJn7nLXJ4F/C/wEdUv3nwD+BfD9d3mMTwCfAFhZWXmUcp6YBz0s5Kivjd/dlbs1rd+wHLuehhLdpavUifJIgW+M+fj9fJ6I/HvgN/Z5jE8Bn4J6p+2j1POknLTDQvotn2QQMd/0mSQ5G+OUUVpwqd9kc5Lqbl2lTohDSygRObvnw+8GvnxYz/WknbT18rs/gYSeTeA5IEK/6ZPmJavbMa+tT3SJplInwGEOSX9KRL4kIn8MfDPw9w/xuZ6oWa+XPwy7r8l3LFxbaHoOoefgWBaDad0iQil1vB3askxjzPce1mM/Tg/bbOyoz8vf6c7X2fQdpmnxrtd9cxgTug7u7p4BRwiNw81hvO8B6Eqp4+FU99LZ70jCozhaf5QumHe+zklS8NUbIy7MN2kHzm2vW0RAIC1KhnFOVlQIhsA5Wl8PpdSDO9WBv9+RhEdts9GjvjHd+TqnWYFtW7yxOWGu4eHZFnFe8PnXN9gcZ8R5ydluwNm5EFtgklT4jk2Sl0fujVApdf9OdeA/6PLKWdnvjWl1EOHvHGG436g/yUuubk6xdtou95oe4yRnHGdkucEWi9XtiD+6vs3FboNnltv84ZvbvPjWCMey6DcDFtoeZ+YaR+6NUCn1YE514B+X5ZW7b0xJXrIdZaQ7q4OuDyICzybNSyyxaDgWF/vNWy2Yod4B7DgWtghJXvIHr2/y5lZElpd4nsMzvs3NYULoOkRZhW3ZXOyH+F7C62sT5i55+I6Da4vuulXqmDvVgX+vIwmPEt+xmCQFm9MMz7FouDYvrw555eaYZ892yIqK64MJVSXYttAK5rg+iBARKgNVZfjKzTFvD2OSrGBjnDLJSpqeQ1kZ1icJvdAj8CxGcY5tWzgWOLbFxfmQojRcG0Sc6x6tr4tS6sGc6sDfXWmzOUmJsrqNwFG5YLv3Ii3Ata2I0K/78qyNM750fUg7cFgdxjQcm/mmzzjJ+N2vrDFKC2wjbEwSsrJiFOesDmImaUFWVZRG8C0oTMlr62OMMfQaPq3AJa8qMJDm0Ap3vj1k55cjdBymUurBnerAh6OxvPJuSyZ35+13V9WsjhIcDOOsZKkdMBe6FHnJ2jAjySsGUc4wznAs4fJCk17o8r9f2wRjcG1hGOVkpSF0LTxbwLJwLZuWZ5MWJevTlF7LxbZgGOX4rsWzyx3ivH4jvNBrUGneK3WsnfrAn7XtKOOl1SEGCF2bVuDy5uaUpXaA51gMo4yv3hyTZAWjNKcbeGxOM1xbWB2kjJOCYZxRlYZBlGGA33rxBp2Gy83thH7LpTJCw3XYThLiNGel32SxE3BzlBB6Nt2Wx5lWgONYJHlF6Ns8f6nH+V7zVp1ZUeHKvi9DKXUMaODPUJKXvLw6pKgMeVExmGYIMY5jEXo5FYbfefkGq8OEUZRxdRDRDTzagUtlDKvDCEss8qpinBRkRUVRVVwdxMggous5DGKDb9v0Qo+ma3NzmDLNCtpFRdt3WWwHtBsOZzoNPv7+MwSufWsZaLZzctdRvbahlHowGvgztDlJiYuKJCsAIS1KJnE9Yp/2mqyPE37/zW3iLOftYczmOMV2hOVOQMf32ZxkbExSbBscgTgD24LQh7ysiGyh5VjkZcUkLbCoL06LCNO0YLHpcK7rs9RpcLnfvHXt4ihf21BKPTwN/BkaxTlrw5jBNGVrmhHlJXFash1n/J9XN0CEtWHE1jQjK8C1wRSGNzdimkGKqQxxDm4JlUs9x15BkpYErkVaGCpT0A4cojSnqAxPL7VZ6YVkQMt3iXNDL3Q5d8fo/Shc21BKPV4a+Idsv5YISV4yiDLK0nB1ELM+ThlOc0LPYpTk5FXF2ihma2qoqA8VyCpu/TmfVjQ8sKkXzyQpuM7OfRVYVUUgFpWp8Gy7bo/gCc9fmifwHJbaAbZV7zvwXP02UOo00P/ph+huLRFeW5/QcDvHDNAAABKPSURBVCzeGsSsj2K+/PaQNzcisqIgr2B7lFEWhswUbE8NBfU/UgHs3f9rDMR5HfAYyAApIfQFRyDwHULPpiih1/RouBa90CMrK86GHk8ttsjLCkugE7i6i1apU0AD/xDd2RIhznNeuTGiqCre3o6J8pJRkpOWBWujlLIyFJWhLAsmSR3iUIf9nUrAqcCyAAOuARHwHHBsB9+xKSvDxV7Is8sd8qqk6Tvc2I5ZbAfkZUVWVJyZC45kOwml1OOngX+I9vbqSfKSV26MQeD1jYjX1saAYFkGRyySPKcyUFaGJIf03g+NASyBqqrfGByg4YJgMddwWW4HxEVFu+FiW4bQd5kLPIZJzijJsQTOzAUErk22M92klDrZNPAP2VtbEWle8vrmlKtbU+K05Np2TJFXbCcZwyhjGOcUBcRVfSLN/Yy1XaA0deg37Xpu3/dsznWbnO82WGoHjNOchmfT8BwqY7Bs+DNX+gzjgvmmj2vLrdO6dDpHqZNPA/+QbEcZb21OubYdE6UF6+OEYZSxMU15dW1MkpVQVpTANHsn5A8Ke6G+UAvgudDyHRbbPhhIqpLz3YClts+ZbsAZE7AxzYizgufOd+k1PYrScKHXvHValy65VOr00MB/jLajjD95e8QbGxOuDxIu9nyavsP6OGVjnLI+SXllfYwYQ1VW5Aay/P5G9LscwLWgrOrwtwSyomSu6REaB9cSljo+7cBlqe3TjzKqCuabHpYldHyHpxZbGvBKnUIa+I/JdpTxv766zvooJs4KtuOUtUlCVpTcHCZsjlPWJjFRUod0/JB9aTwb2g2LKK8IbPBdm8B1MBV0Gi6uUy+5fP5yn8C1GcU5oySjF/oPfFKWUupk0cB/RLvr7D/32gavrk0IPZvtKGcwzdmKMt7anLAd54iBUb7zlx4i7HdH9q4Dcw2PwK1oBS6X5puUpgIsHBH6oUs39PAdi6yol12+/1xXQ14ppYH/KJK85GtrY6Z5yZevD1jdTmg3PIypiPOCa1tTNic5ZXnwqps7CfUFXBvwbQgbDrYI7cCiqKDbcLnQbxJ6Do4lnO82cB2LS/0WndDV+Xml1Lto4D+gvTtnr21OuTlOsSzh+iglSktG8ZQ4r1gbp0zijKSsV9DcLwtwBXpNm7nQI8sr5psu862ArWlKWRocx+L5S/OcmQu4uhXTDRwW2j6ebdMJHB3RK6XuSgP/AHceRJJkBZ5jszlN+N2vrjFOcranOS+/vc0wLrCsegPUMHmwoId6VO9Z0AqEp/otljoNhknGc2c7ZGXFcidgmhbMhx5zgUtRGM516iMILbHoNT3ed25Ow14pdVca+PtI8pLVQcTVrYjmztLH9XHdf96xhVGcM0xy3tyYcnOUEqUFeQlJ/lBT9AB41JunAsfBdoTFOZ+L/YCVfos4K9mcZFzqhyx3QvKqIkoLWoFPVRk+stLjnE7fKKXuQQP/LrajjJdXh6xNUgLHJnANN0cJeVGRlxV5BZvTlK1JyjDJGScpZQVF9fBh37Tr1sYLnYCVboOlbggGLi+2iZKSK4stznUr2oFDK3AxxhDnJWfnGliCbpxSSh1IA/8OSV7y0uoQx7IQU4f/1c2IwLWI85LBNGUU5axNMm5sJxR5RZxA8gjPOeeC59atDRZbAVgWvmOz3PbpNVwcqXvYX+qHDKKMvKgwGGRnDb6GvVLqfmjg32F1ELE+TsmLklfWxtiWRVEafEfYmmZcGyTkZYlrCTfHEdP00cLeBRwH2jvB3mt6XO436TRc4rLi+nbClcUmYBgmOcudgPVxyjQtWJkPdRpHKXXfNPD3SPKSV9cmDKYpb2xFWAKb44xuaPPWVsbNcco0KRjEKYIhLSB50Cuze7hAv2UTBi62GC71myBClJd0/HrXrDFgKsPSXMDWJKMycK7b0A1USqkHpoG/x+ogYpqV1D0nwbNsojxhsp2xOogYpTmebWFZ9WlVUX7QI77D3fm92PPnlg/NwGGxFRA4Ng3HAYQ532GYlSy1fZ5ZbhG4DqO4YKXf1OkbpdRDO1WBv9/pU7vWxinzTYerGxPSvOTaVsR2nLE1SUmKijQrqHyHsoToAeZxLKDftuvDyvOKfsenF3i0Qx/PFkLXohk45CWcmfNZ6bcQgbPdBk3PIS8rpmlBv+U//i+KUurUODWBn+Qlr61PiNKCytQHjbxyY8TyXKPuBS/CG5tTkqyg4TkUlaEoDZO0wBgoqpJpatiKczypT5w6iC/1yhvXgV6j7mjZbjj4rs2HL/TAEkZJzvY0Yy70Wek2+NDFLq2GR2UM21FGnJeIwMq8ztUrpR7NqQn81e36sPCm51KaimtbUwZxwdokxXVs5nwby1S8PUy5MYjYmKZsTVOyoiLKS7LcgAU+kFbvdLjcOXDqtj72HnWTMyPQbbn0Aw/fc8irivcst3j+Ut3YbJIW2EM4Oxdwodvg8mKLSoRxnNFueCx3AvLSkBXluw4ZV0qpB3VqAv/mMCZ0HVzH4tr6lOvDFFNVrI0S3n9+jpvjjFdujBklBZtxyiTJ2ZykGOqRvm3Z2JSUvLud8W7fm9AG1wXXtnAdC6mE0HNoN1x8x+KDFxd49myHhbbPYsvnpdURtsClfpPlucat06d2z5rVfjhKqcfp1AS+iIBAWtRTO7YlRFnF6xtTbo5ipnFBlJW0Q4etSX1QSW4qihzSAkpKLG5vl+ACjtQnTxmBTtPhfLeJ69iYqsC2LBzH5uuW65D/xqf7IELDsagM9EKX5851aHjv/DO4tpCXupFKKfX4nZrAX2r7rA4TpmmBqeq5+O0ox7WFSVywHWVkRcVWlLI2isFAnEGyM1e/O4rfnboPZOcDgW5DKA10Gh5/9plFxklOkpW8d7nNJC240AtZ6Yd0Q++2C8X+TvDvlZdGz5dVSh2KR0oWEfkbIvKiiFQi8sId9/2YiLwqIl8RkW97tDIf3bleSOjb9Vx+lHFzGCPURwQmhWGcFsR5QZRXJDnkFWR7wngn23F3fm/4cLbn02na+J5Dq+GyEPo4lkW34dJrujQ8m+cvzfOtHzjLh1fm3zU102/5ZEVJVlQYY26dL6urcZRSh+FRR/hfBv468O/23igizwHfA7wfOAd8VkSeMcY8yGl+j02Sl7y+PuGrqyNubEcMpvXB4WvDneOnKgOmboQzSVMcGxzLws4rhPqLVAKODWKACkLfZaEdEGc5aWFYaHu8cKXHXOgQJyXn50Peu9zh6XscJxi4Nud7IZuTVOfrlVKH7pEC3xjzMuzMj9/uu4BfNMakwOsi8irwUeD/PsrzPYzd5Ziv3BhRYZjmJZOkwAB5VbE2ygg9i7w09ZRNCVUFJRW2DXm506PeglZgAxW+43ChFxJlJY5t0Qxs/tTKPB843yUtDYst4T3Lbc51GweG927oK6XUYTusOfzzwOf2fHxt57ZDca8NVZuTdGftPby5OSV0HNqhy8b6hOuDKcaAhQsYxkmBvZPPvabP5jSlKkEsCH1wRHAdlzOdBh+51MdzoOHazDV8PnRhDt9z9NxYpdSRdWDgi8hngTN3ueuTxphf2++v3eW2u25VEpFPAJ8AWFlZOaicd9l7zGBVGSxLGEYZV5baAFzdnHJjFLM+SRklBZ5j1RupSoNj21RlSVoU2GLj+4JrOYgtmAoCR2j7FiB4tkW36TPf9HjhqR7feGWRKK03Rb3v3Bzd0Hvg2pVS6kk6MPCNMR9/iMe9Blzc8/EFYHWfx/8U8CmAF1544YHbya8OIrainKbv4DhCURm2ohxZn+A5Fo5jEXoOtuSM4pym5zJNSwwG17YwtuBaNpYlWOLgexZnWg0cx2J1a4Lj2DxzpsOFXkjTd4izgk7Do9PwWGzraF4pdXwc1pTOrwP/SUR+hvqi7XuB3zuMJ1obp4SejWvXC45cWwg9m1dvjvnwpXmW2gHxzlz7csfn7WHMJM4oqopq50KttXMx1mDohx5Xltu0PJuFpke36bEy38RzLaK0xJiK5852ubLYOoyXo5RSh+aRAl9Evhv4V8Ai8F9F5IvGmG8zxrwoIr8EvETdIPIHD2uFjjHm3ZNFBqZZyeYkISsNgWtxpuPzxsYE37ZphQ55ZTBGcF0LU1Q4jpAboe27XJoPabgWYsEzyx3GSc5gWrdgeP5Sn8W2LptUSh0/j7pK51eBX93nvp8EfvJRHv9+LM81WN2OEBEcWyhKwyDOcGwhKwwNz2aaFURZxZ9+qs8rayMQ+NLVba4sttiOMkZJjjHw3EITx7Jo+Q5LcwHvWW4TZSWdhkvo2rQCF0vQdfJKqWPp2O+0PddtEOclUVqQlQZLBBt4arHJ29sJYoSoKLAQKmP4wPkuIAjCta2I9y61MAJpYbjYa/DMmQ6XF1q3HR14r5bKSil1XBz7wA9cm6cXW7eF8vpYSPKKhbbPNCm4Mc7xbKHXbNJveVQGPvb0Al/rTJhreKRFSVXBXFhvpto9FHw32HWdvFLqJDj2gQ/v3rx0YxRjiRD6Di3fRSxhmhSUlaHh2ryyNibPK0LPphU4+IWl58MqpU68E9mlK/RcKlOR7/SoCV2brCgoTcXWNGMu8HBsIfRdLODDKz2uLLU17JVSJ9qJGOHv2t1xuz1NqQxkZUleCYFr8+zZOa4NIkpjaAUOF/vhrf7z07TQjVNKqRPvxAR+kpdcH0R4js3ZboNrg4i8hAu9ANuyyIqSS/NNek3vtt4/ri1E2Ux6uiml1BN1YqZ0NicpnmPjORYNz+HifBPfsbgxTG5dhO00XPLy9kX72n9eKXVanJikS4sK135n5B64NhfnQ5Y6wa0VN9p/Xil1mp2YwPcd68DR++5qnt3zYu9cfqmUUifZiZnD77d8rg8iYPdcWHPb5qld2n9eKXVanZgRvo7elVLq3k7MCB909K6UUvdyYkb4Siml7k0DXymlTgkNfKWUOiU08JVS6pTQwFdKqVNCjHngc8MPjYisA2/O6OkXgI0ZPffDOG71wvGrWes9XMetXji6NV8yxiwe9ElHKvBnSUS+YIx5YdZ13K/jVi8cv5q13sN13OqF41nzXjqlo5RSp4QGvlJKnRIa+O/41KwLeEDHrV44fjVrvYfruNULx7PmW3QOXymlTgkd4Sul1CmhgX8HEflhEfmKiLwoIj8163ruh4j8QxExIrIw61ruRUT+uYj8iYj8sYj8qoh0Z13T3YjIt+98D7wqIj8663oOIiIXReR3ROTlne/bH5l1TfdDRGwR+UMR+Y1Z13IQEemKyC/vfP++LCIfm3VND0MDfw8R+Wbgu4APGmPeD/z0jEs6kIhcBP4ycHXWtdyH3wY+YIz5IPBV4MdmXM+7iIgN/BvgrwDPAX9TRJ6bbVUHKoB/YIx5H/CNwA8eg5oBfgR4edZF3KefA/67MebrgA9xfOq+jQb+7X4A+GfGmBTAGLM243rux88C/wg48hdjjDG/ZYwpdj78HHBhlvXs46PAq8aYrxljMuAXqQcBR5Yx5m1jzB/s/HlMHUbnZ1vVvYnIBeCvAT8/61oOIiId4M8DvwBgjMmMMduzrerhaODf7hngz4nI50Xkd0XkG2Zd0L2IyHcC140xfzTrWh7C9wP/bdZF3MV54K09H1/jiIfnXiJyGfgI8PnZVnKgf0k9UKlmXch9uAKsA/9hZwrq50WkOeuiHsaJOgDlfojIZ4Ezd7nrk9Rfjx71j8XfAPySiFwxM1zKdEC9Pw5865Ot6N7uVa8x5td2PueT1NMQn3mStd0nucttR/6nJwARaQH/Gfh7xpjRrOvZj4h8B7BmjPl9EfmLs67nPjjA88APG2M+LyI/B/wo8E9mW9aDO3WBb4z5+H73icgPAL+yE/C/JyIVde+M9SdV3532q1dEvh54CvgjEYF6euQPROSjxpgbT7DE29zr6wsgIt8HfAfwLbN8I72Ha8DFPR9fAFZnVMt9ExGXOuw/Y4z5lVnXc4BvAr5TRP4qEAAdEfmPxpi/NeO69nMNuGaM2f2p6ZepA//Y0Smd2/0X4C8BiMgzgMfRbJSEMeZLxpglY8xlY8xl6m/K52cZ9gcRkW8H/jHwncaYaNb17OP/Ae8VkadExAO+B/j1Gdd0T1K/4/8C8LIx5mdmXc9BjDE/Zoy5sPN9+z3A/zzCYc/O/6m3ROTZnZu+BXhphiU9tFM3wj/Ap4FPi8iXgQz4viM6Cj2u/jXgA7+981PJ54wxf3e2Jd3OGFOIyA8B/wOwgU8bY16ccVkH+Sbge4EvicgXd277cWPMb86wppPmh4HP7AwCvgb87RnX81B0p61SSp0SOqWjlFKnhAa+UkqdEhr4Sil1SmjgK6XUKaGBr5RSp4QGvlJKnRIa+EopdUpo4Cul1Cnx/wE21E3fZpGCzwAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(dataset_Dd[axes[0]], dataset_Dd[axes[1]], alpha=0.1)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Not too bad, even though we picked random axes, the clusters are clearly distinguishable." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Adding some noise" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But what happens if we add random noise? let's add quite a lot of noise:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "noise_stddev = 5\n", "noise = np.random.multivariate_normal(np.zeros(D), np.eye(D)*noise_stddev**2, dataset_Dd.shape[1]).T\n", "\n", "noisy_dataset = dataset_Dd + noise" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's draw it again over the same axes:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(noisy_dataset[axes[0]], noisy_dataset[axes[1]], alpha=0.1)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The separate clusters are pretty much gone now, as the clusters are overshadowed by the noise." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## PCA" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Can we use PCA to recover the clusters from the noise?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In PCA, we perform SVD and project over the columns of U that correspond to the singular values with the highest magnitude. These vectors are called the **principal components**." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "U, S, Vt = np.linalg.svd(noisy_dataset.T)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this case, we'll pick the first two principal components. Why two? we started with two dimensional data, so it makes sense to pick two principal components. We'll revisit this decision later." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "PC = Vt.T[::,:2]" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[-0.22319463, 0.20562393],\n", " [-0.13608718, 0.2125757 ],\n", " [-0.2864234 , 0.03172776],\n", " [-0.16524457, -0.16279052],\n", " [-0.17645201, 0.18754551],\n", " [-0.29001766, 0.02234059],\n", " [-0.21143687, -0.10076984],\n", " [-0.30245918, 0.01389629],\n", " [-0.2343862 , 0.23015472],\n", " [-0.16809925, -0.12431053],\n", " [-0.21253381, -0.22645792],\n", " [-0.18938012, 0.21203984],\n", " [-0.26118411, -0.12058781],\n", " [-0.18011733, 0.22916835],\n", " [-0.16045106, -0.3594636 ],\n", " [-0.13647443, 0.14203625],\n", " [-0.15788609, 0.11681608],\n", " [-0.14953455, -0.32921663],\n", " [-0.20071877, -0.03621849],\n", " [-0.25834198, -0.06901349],\n", " [-0.15491399, -0.29385544],\n", " [-0.16626447, 0.34353028],\n", " [-0.08733157, 0.10986641],\n", " [-0.13992965, -0.33506743],\n", " [-0.16870746, 0.03282469]])" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "PC" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We'll project the data into the first two principal components:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "projected_cleandataset = PC.T.dot(dataset_Dd)\n", "projected_noisydataset = PC.T.dot(noisy_dataset)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then plot the result:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(*projected_noisydataset, alpha=0.1)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(*projected_cleandataset, alpha=0.1)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Even though we added a lot of noise, we still get distinguishable clusters, but they are blurring together on the boundaries. That's from the noise. Notice that we have gone from a square to a diamond shape. " ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "NextPC = Vt.T[::,2:4]\n", "nextnoisyprojections = NextPC.T.dot(noisy_dataset)\n", "nextcleanprojections = NextPC.T.dot(dataset_Dd)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(*nextnoisyprojections, alpha=0.1)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(*nextcleanprojections, alpha=0.1)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that even in the next pair of dimensions, there is no visible trace of the signal in noise, and very little (look at the scales) signal present even without noise. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Principal components:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us go back to the signular values and plot them:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.bar(np.arange(S.shape[0]), S)\n", "plt.show()" ] } ], "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": "3.6.5" } }, "nbformat": 4, "nbformat_minor": 1 }