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kiwamizamurai/pca_bpca_01.ipynb

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pca_bpca_01.ipynb
{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"kernelspec": {
"display_name": "Python [conda env:anaconda]",
"language": "python",
"name": "conda-env-anaconda-py"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.14"
},
"colab": {
"name": "PCA_BPCA_01.ipynb",
"version": "0.3.2",
"provenance": [],
"include_colab_link": true
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/kiwamizamurai/860d5b3f34dfcc7745dfd22275999f30/pca_bpca_01.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "a9liB6eYZOCr",
"colab_type": "text"
},
"source": [
"# IINTRODUCTION\n",
"This notebook is about Bayesian PCA. \n",
"The content is based on [This paper](https://papers.nips.cc/paper/1549-bayesian-pca.pdf)"
]
},
{
"cell_type": "code",
"metadata": {
"id": "dtcO3muHZOCt",
"colab_type": "code",
"colab": {}
},
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "8ZaWRK3vZOCx",
"colab_type": "text"
},
"source": [
"# Hinton diagrams\n",
"From\n",
"- https://qiita.com/ctgk/items/89c11192affe7f236852"
]
},
{
"cell_type": "code",
"metadata": {
"id": "m6grsCKsZOCy",
"colab_type": "code",
"colab": {}
},
"source": [
"def hinton(matrix, max_weight=None, ax=None):\n",
" \"\"\"Draw Hinton diagram for visualizing a weight matrix.\"\"\"\n",
" ax = ax if ax is not None else plt.gca()\n",
"\n",
" if not max_weight:\n",
" max_weight = 2 ** np.ceil(np.log(np.abs(matrix).max()) / np.log(2))\n",
"\n",
" ax.patch.set_facecolor('gray')\n",
" ax.set_aspect('equal', 'box')\n",
" ax.xaxis.set_major_locator(plt.NullLocator())\n",
" ax.yaxis.set_major_locator(plt.NullLocator())\n",
"\n",
" for (x, y), w in np.ndenumerate(matrix):\n",
" color = 'white' if w > 0 else 'black'\n",
" size = np.sqrt(np.abs(w) / max_weight)\n",
" rect = plt.Rectangle([y - size / 2, x - size / 2], size, size,\n",
" facecolor=color, edgecolor=color)\n",
" ax.add_patch(rect)\n",
"\n",
" ax.autoscale_view()\n",
" ax.invert_yaxis()\n",
" plt.xlim(-0.5, np.size(matrix, 1) - 0.5)\n",
" plt.ylim(-0.5, len(matrix) - 0.5)\n",
" plt.show()"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "5AjZwnLZZOC0",
"colab_type": "code",
"outputId": "51f06018-eb52-4d25-c0b6-28b91e6b7ff3",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 255
}
},
"source": [
"testmatrix = np.array([[-1, 2],\n",
" [10, -4]])\n",
"hinton(testmatrix)"
],
"execution_count": 3,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAO4AAADuCAYAAAA+7jsiAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nC0HChaB/AG5FUbe8NhUfAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "-g69k98TZOC3",
"colab_type": "text"
},
"source": [
"# MAKE A DATASET\n",
"Make a data set consisting of 300 points in 10 dimensions, \n",
"in which the data is drawn from a Gaussian distribution having standard deviation 1.0 in 3 directions \n",
"and standard deviation 0.5 in remaining 7 directions."
]
},
{
"cell_type": "code",
"metadata": {
"id": "TZXxrXW6ZOC4",
"colab_type": "code",
"outputId": "132c5815-c038-4dd6-d3a8-19c32d47f72a",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 34
}
},
"source": [
"import random\n",
"\n",
"random.seed(3)\n",
"\n",
"intrinsic = np.random.normal(5., 1., (300, 3))\n",
"noise = np.random.normal(0, 0.25, (300, 7))\n",
"sample = np.concatenate((intrinsic, noise), axis=1)\n",
"sample.shape"
],
"execution_count": 52,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"(300, 10)"
]
},
"metadata": {
"tags": []
},
"execution_count": 52
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "2fW-PVLdZOC7",
"colab_type": "code",
"colab": {}
},
"source": [
"class BayesianPCA(object):\n",
" \n",
" def __init__(self, X):\n",
" self.x = X\n",
" self.ndim = np.size(X, 1)\n",
" self.num = np.size(X, 0)\n",
" self.n_component = self.ndim - 1\n",
" \n",
" # INITIALIZE PARAMETERS #########################################################\n",
" def MLpca(self):\n",
" cov = np.cov(self.x, rowvar = 0)\n",
" \n",
" la, v = np.linalg.eigh(cov)\n",
" index = self.ndim - self.n_component\n",
"\n",
" # mu_ML #################################################################\n",
" self.mean = np.mean(self.x, axis = 0)\n",
" self.mu_ml = mean_vector = self.mean\n",
" \n",
" # var_ML ###############################################################\n",
" self.var_ml = np.mean(la[0])\n",
" \n",
" # W_ML #################################################################\n",
" Uq = v[:, 1:10]\n",
" Lambdaq = np.diag(la[::-1][:9])\n",
" Iq = np.eye(self.n_component)\n",
" self.W_ml = Uq.dot(np.sqrt(Lambdaq - self.var_ml * Iq))\n",
" \n",
" # alpha ################################################################\n",
" self.alpha = np.var(self.W_ml, axis = 0)\n",
" for i in range(self.n_component):\n",
" gamma = self.ndim\n",
" self.alpha[i] = gamma/(np.linalg.norm(self.W_ml[:,i])**2)\n",
" \n",
" \n",
" def e_step(self):\n",
" M = self.W_ml.T.dot(self.W_ml) + self.var_ml * np.eye(self.n_component)\n",
" Minv = np.linalg.inv(M)\n",
" self.xx = np.zeros((self.num, self.n_component))\n",
" for i in range(self.num):\n",
" self.xx[i] = np.dot(np.dot(Minv, self.W_ml.T), self.x[i] - self.mean)\n",
" \n",
" \n",
" self.xxt = np.zeros((self.num, np.size(Minv,0), np.size(Minv,0)))\n",
" for i in range(self.num):\n",
" self.xxt[i] = self.var_ml * M + np.dot(self.xx[i][:,np.newaxis], self.xx[i][:,np.newaxis].T)\n",
" \n",
" \n",
" def m_step(self):\n",
" # UPDATE W_ML ###########################################################\n",
" left = np.zeros((self.ndim, self.n_component))\n",
" right = np.zeros((self.n_component, self.n_component))\n",
" for i in range(self.num):\n",
" #from IPython.core.debugger import Pdb; Pdb().set_trace()\n",
" left = np.dot((self.x[i] - self.mean)[:,np.newaxis], self.xx[i][:,np.newaxis].T)\n",
" right = right + self.xxt[i] + self.var_ml * np.diag(self.alpha)\n",
" #from IPython.core.debugger import Pdb; Pdb().set_trace()\n",
" self.W_ml = np.dot(left, np.linalg.inv(right))\n",
" \n",
" # UPDATE var_ML ##########################################################\n",
" kakkonai = 0\n",
" for i in range(self.num):\n",
" first = np.linalg.norm(self.x[i] - self.mean)**2\n",
" second = np.dot(np.dot(self.xx[i].T, self.W_ml.T), (self.x[i] - self.mean))\n",
" last = np.sum(np.diag(np.dot(np.dot(self.xxt[i], self.W_ml.T), self.W_ml)))\n",
" kakkonai + first + second + last\n",
" self.var_ml = kakkonai/(self.ndim * self.num)\n",
" \n",
" # UPDATE alpha ###########################################################\n",
" for i in range(self.n_component):\n",
" gamma = self.ndim\n",
" self.alpha[i] = gamma/(np.linalg.norm(self.W_ml[:,i])**2)\n",
" \n",
" \n",
" def fit(self, n_iter = 10):\n",
" \n",
" # INITIALIZE PARAMETERS ##########################################################\n",
" self.MLpca()\n",
" \n",
" for i in range(n_iter):\n",
" # E-step ##########################################################\n",
" self.e_step()\n",
" \n",
" # M-step ##########################################################\n",
" self.m_step()\n",
" \n",
" \n",
" # MAXIMUM LIKELIHOOD METHOD FROM PRML #######################################\n",
" def mpca(self, component):\n",
" cov = np.cov(self.x, rowvar = 0)\n",
"\n",
" values, vectors = np.linalg.eigh(cov)\n",
" index = np.size(self.x, 1) - component\n",
" var = None\n",
"\n",
" # PRML (12.46) best sigma^2\n",
" if index == 0:\n",
" var = 0\n",
" else:\n",
" var = np.mean(values[:index])\n",
"\n",
" # PRML (12.45) best W\n",
" W = vectors[:, index:].dot(np.sqrt(np.diag(values[index:]) - var * np.eye(component)))\n",
" return W"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "92a_y09kZOC9",
"colab_type": "code",
"outputId": "c2ebe79f-2e14-4ebb-e7b3-90c295bc0294",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 255
}
},
"source": [
"bpca = BayesianPCA(sample)\n",
"bpca.fit(n_iter = 10)\n",
"hinton(bpca.W_ml)"
],
"execution_count": 60,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAANkAAADuCAYAAAC0waJjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIEzIIEzIIEzIIOy/GX+xXP56YSsAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "code",
"metadata": {
"scrolled": false,
"id": "z7W2-sT_ZODA",
"colab_type": "code",
"outputId": "47fad512-d2b9-4754-e005-7931e2a9ce9b",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 1000
}
},
"source": [
"for i in range(20):\n",
" bpca.fit(n_iter = i+1)\n",
" hinton(bpca.W_ml)"
],
"execution_count": 61,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAANkAAADuCAYAAAC0waJjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAANkAAADuCAYAAAC0waJjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n+xf7VpMcsrF1dAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAANkAAADuCAYAAAC0waJjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4zLCBo\ndHRwOi8vbWF0cGxvdGxpYi5vcmcvnQurowAACVJJREFUeJzt3T1y20gYhOFPWxtZDpQ4UbKX2Jyl\n0+gALOfMUT4TSwfwIRw52A3lGBtYs0KBIImfbmo+4H0iW4ZRKNb0YABz2ndt2wYAnz8++gKAtSNk\ngBkhA8wIGWBGyAAzQgaYETLAjJABZoQMMPtzysGfPn1qHx4eXNcCpPHz589/27b9MubYSSF7eHiI\n5+fneVcFrMjhcPgx9liWi4AZIQPMCBlgNumZDLe13+/j8+fPo459fX2Nb9++ma8IcxAykaZp4tev\nX1ePu7+/j69fv44659iATT0Wt1V1yK4N3CkDtu/cXWLuHWFMwKYch/WQhmxo4C5ZxlwbkEsG7LmZ\nf2t3hKGJbMnkhVPSkA0N0K0N2myGJirF3bY/4aqeGfuTQoYJgbeLsOhPrqrJtj8BKJffTdNE0zSy\n8xWEDDCr+sUH0Hd/f3+yXFRxLTulIXt9fR188YF69Qdt+dlS/bGgGge1P38NkYYs0z+GDk0I5edb\n4hq0mcaCW9XLxaFZtv/nc6kHwbVr7R6Hbak6ZJmWBo5rPXe3PXcs6lR1yLaOJdc68AofMCNkgBkh\nA8wIGWBGyAAzQgaYETLAjJABZoQMMCNkgBkhA8wIGWBGyACzNN/C77YUKRuKSquSsoHXfa0RNAZn\nYgnZfr+PCO1Wje6GSGVDURm0yuo697X2f71UmRTU9WqOCSwi/m+UUu/hc52X5SJgZrmTOZYx3e39\nyi38Zfexcmex+1rLr1Wy9Xy4rtd13ru2bUcf/Pj42PI/bQIRh8Phe9u2f485luUiYEbIADNCBpgR\nMsCMkAFmhAwwI2SAGSEDzAgZYEbIADNCBpgRMsCMkAFmhAwwI2SAWZqOj63r9nt00fVRvxQh6xbT\nROjKafoDVzFg+9caobnec50eyq4PeMhD5mhU6g9aVTlNf4AqBuzQtSnLdBwyNYFF+Ip/XOTPZK5G\nJfhkagKLeL9G9eR1PB7jeDxKzxmRZLmInBwlRRHvRUXKkqKIiKenJ+n5CnnIHI1K3fan8nuF7rWW\n32+Rq10rW1uVizxkjg82U2VZf0IoP1uqPyF0f75UtkGbDctFsUwTAm6Df4wGzAgZYEbIADNCBpgR\nMsCMkAFmhAwwI2SAGSEDzAgZYEbIADNCBpgRMsCMkAFmhAwwI2SAmWXT5n6/jwjtRkNXQ1GmRiVH\nE1jRNE1EsEvawRIyR0uVq6EoU6OSswms9tq6rtIopS6+cZ3XEjJHIY2roShTo5KjpKhQf65OrlYp\n13nv2rYdffDj42P7/PxsuRAgk8Ph8L1t27/HHMuLD8CMkAFmhAwwI2SAGSEDzAgZYEbIADNCBpgR\nMsCMkAFmhAwwI2SAGSEDzAgZYEbIADP+z+gESpXBEHUdA/RShKzbbVGoOy5Uhq41Ytn1XqoGyFQb\nsFXykHVnXdUsOzRoFR0X/TuE4nrPXZej90TFVdDjKj/KRh6y7qCtfZbtX1/t1+viKuhxlR+5GsZc\nePGBdFwNY7vdLna7nfScEYY7WWlpKr9G/VwtWNkaxl5eXqTnK+Qhc6y9u4Og+7OluhNC+f0WuZZc\nruewDEvErhRvFzMNgqEJofx8rv5k0P8z1C1FyDJxTAhbfjO3Brz4AMwIGWBGyAAzQgaYETLAjJAB\nZoQMMCNkgBkhA8wIGWDG16oqdW6H9SVZ9ldtTbUhu9Rr0VXDrtux11qMueY5e6Vq3n29ZdWGbOyg\nnbPr9tpdYuodYeo1bHUH9lbJQnZp4Na2jLk242/ljkAL1m3IQnZpYG5l0GbjbMHqT7qqidZRfuTG\n20VY9CdW1USbsfyIkAFvmqaJpmnk5yVkgFm1bxeBW3M923Eng0W/OEhV39YvDspQJCS7k51raSp/\nhvo4W7AyNYy5yUKm/lAvDYD+cVNdmhDKn29BxgGbUbXPZM4B8FETQvd4bEe1IcvkliWp1/4O6kPI\nKlXT19CwDG8XATNCBpgRMsCMkAFmhAwwI2SAGSEDzAgZYEbIADO+8ZEAhTe5pQjZUBNWbQ1YEb7G\nLmfhDfzkIevOuqpZdmjgKopZ1M1HGRu7XK1SeCcPWXfQ1j7LZmw+UnO1SkW8T2LqJW2ZGLJMCLz4\ngE2ZtNSTV5kI1KuD3W4Xu91Oes6IJM9kQFfZa6feP/fy8iI9XyEPWXeXcO07gPs7mmu/Xof+5lDl\nwC2fr/pzzbBE7JKH7Fa7hBWDgVff3gHL5/tbiuVilpnL1djlbJWCX4qQZUENGobwdhEwI2SAGSED\nzAgZYEbIADNCBpgRMsCMkAFmhAwwI2SAGSEDzAgZYMYXhBNwFfTgNlKEbKgSrcYqNFd1W8aCHryT\nh6w766pm2aGBq+iNUDc1ZaxuUzd24ZQ8ZN1BW/ss62xqysLZ2OVqlXK1YLnw4gM2rlYpVwvW8XiM\n4/EoPWdEkmcy5ORqlXIV9Dw9PUnPV8hD1u25UH+4as6mpiycjV3UMfwmD5njgx0qklEMBvW1Ziy8\nyTZgM0qxXMwyEFzX6WrBwm2kCNnW8Y/NufF2ETAjZIAZIQPMCBlgRsgAM94uVuLSdpa52AZTB+5k\nlXB8OXmLX3iuEXeymS7tHZsiyzfJMV91IVsyeG85YFXfAK91nxl0qgvZkkF37e9Ofe7hmQYKi0M2\nZeB+9KCd+ozCMw0UFodsykBk0NZh7JKc50WN6paL8Bu7JJ+zdL+2spm7mnGVFN0Cr/AhdW21Mnc1\nk7GkqCBkgBkhA940TRNN08jPS8gAM158AG9cL0+4kwFmhAxS14p95hb/XGr7qrUJrGC5CCm6Fk8t\nvpNNmZmoL6vD2Jm/9jtEFovvZJm+QHupv/Dc8WuU+a6QUXXLxUstvGP+7iWZJgSsR3UhY5bF2vB2\ncSbV8wrPPetX3Z0sC/Udd+rz4thz4uNxJwPMCFklaKtaL5aLM9FWhbGqCxltVVib6kJGWxXWRhKy\nsYP3owctbVX4CJKQjR2MDNo60FZ1W9UtF+FHW9Vt8QofUrRVnSJkgBkhA97QVgUkxYsP4A1tVUBS\nhAxStFWdkiwXx+6FYn9THcZWPMwZvLRVnZKEjO/35ZJ5wGa0qeXi1Dspd14oVPd2kbYqrE11Icuy\nlFkyGfTPg3WrLmRZUKSDse7ath1/8N3dPxHxw3c5QBp/tW37ZcyBk0IGYLpNvV0EPgIhA8wIGWBG\nyAAzQgaYETLAjJABZoQMMCNkgNl/cFmbs1sCQEQAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "display_data",
"data": {
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"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAANkAAADuCAYAAAC0waJjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nkEkwQybBDJkE+xfks6jPBiRAuwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAANkAAADuCAYAAAC0waJjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAANkAAADuCAYAAAC0waJjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nVZWhIytsAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAANkAAADuCAYAAAC0waJjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRsgAsf8BGnF8bHxRcjsAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAANkAAADuCAYAAAC0waJjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\neLDZwuASugAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "display_data",
"data": {
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"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAANkAAADuCAYAAAC0waJjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\npmeHAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAANkAAADuCAYAAAC0waJjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nmQQzZBLsb/dui7+S14U4AAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "display_data",
"data": {
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"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAANkAAADuCAYAAAC0waJjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAANkAAADuCAYAAAC0waJjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "display_data",
"data": {
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"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAANkAAADuCAYAAAC0waJjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n5IrX23GgAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAANkAAADuCAYAAAC0waJjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ncOSKYl/ARgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "display_data",
"data": {
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"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAANkAAADuCAYAAAC0waJjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "OiJnVJqmZODC",
"colab_type": "code",
"outputId": "cf620c82-d14f-4f70-e491-fd646a8968bb",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 255
}
},
"source": [
"hinton(bpca.mpca(9))"
],
"execution_count": 62,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAANkAAADuCAYAAAC0waJjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nsP8DpJpFM8+HPCMAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "Zwj5ViP3ZODD",
"colab_type": "code",
"colab": {}
},
"source": [
""
],
"execution_count": 0,
"outputs": []
}
]
}
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