{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from utils import *\n",
    "from ipywidgets import interact, widgets\n",
    "from scipy import stats\n",
    "np.set_printoptions(precision=3)\n",
    "from mpl_toolkits.mplot3d import Axes3D"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 0. The curse of dimensionality"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What percentage of points in a square of side length 2 are contained in a circle of radius 1?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "78.55% of points are within a radius 1 of the origin\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(0)\n",
    "num_points = 2000\n",
    "dim_points = 2\n",
    "points = np.random.uniform(-1, 1, [num_points, 2])\n",
    "points_within_sphere = np.sum((points[:, 0]**2 + points[:, 1]**2) <= 1)\n",
    "print(f\"{100.0 * float(points_within_sphere) / num_points}% of points are within a radius 1 of the origin\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Let's visualize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.patches.Circle at 0x106a76400>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(6, 6))\n",
    "plt.xlim(-1, 1)\n",
    "plt.ylim(-1, 1)\n",
    "circle = plt.Circle((0, 0), 1.0, fill=False, color='r', lw=4)\n",
    "plt.scatter(points[:, 0], points[:, 1])\n",
    "ax.add_artist(circle)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What happens when we go to higher dimensions?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'Fraction of points within a sphere of radius 1')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_points = 100000 # 100 thousand\n",
    "max_dim = 20\n",
    "percents_within_sphere = []\n",
    "for dim_points in range(1, max_dim, 1):\n",
    "    points = np.random.uniform(-1, 1, [num_points, dim_points])\n",
    "    points_within_sphere = np.sum(np.linalg.norm(points, axis=-1) <= 1)\n",
    "    percents_within_sphere.append(float(points_within_sphere) / num_points)\n",
    "\n",
    "plt.figure(figsize=(6, 6))\n",
    "plt.plot(np.arange(1, max_dim, 1), percents_within_sphere)\n",
    "plt.semilogy()\n",
    "plt.xlabel(\"Dimensionality\")\n",
    "plt.ylabel(\"Fraction of points within a sphere of radius 1\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. PCA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Intuition: Find redundant dimensions of your data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x102b107b8>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.random.uniform(-1, 1, 50)\n",
    "y = 0.5* x + 2\n",
    "plt.figure(figsize=(6, 6))\n",
    "plt.scatter(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x102adf9e8>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.random.uniform(-1, 1, 100)\n",
    "y = 0.5* x + 2\n",
    "plt.figure(figsize=(6, 6))\n",
    "plt.scatter(x, y + 0.05 * np.random.randn(*y.shape))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<mpl_toolkits.mplot3d.art3d.Path3DCollection at 0x102b7a518>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xy = np.random.uniform(-1, 1, (1000, 2))\n",
    "x, y = xy[:, 0], xy[:, 1]\n",
    "z = 0.5 * x + 1.0 * y + 4\n",
    "fig = plt.figure(figsize=(6, 6))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "ax.scatter(x, y, z + 0.5 * np.random.randn(*z.shape))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Let's find the principal components of a simple dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate a simple dataset\n",
    "x = np.random.uniform(-1, 1, 100)\n",
    "y = 0.5* x + 2 + 0.05 * np.random.randn(100)\n",
    "xy_raw = np.column_stack([x, y])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Now center the data\n",
    "def center(X):\n",
    "    return X - np.mean(X, axis=0)\n",
    "xy = center(xy_raw)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1073adba8>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compare the datasets\n",
    "plt.figure(figsize=(8, 4))\n",
    "plt.subplot(121)\n",
    "plt.title(\"Raw data\")\n",
    "plt.scatter(xy_raw[:, 0], xy_raw[:, 1])\n",
    "plt.subplot(122)\n",
    "plt.title(\"Centered data\")\n",
    "plt.scatter(xy[:, 0], xy[:, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2, 2)\n"
     ]
    }
   ],
   "source": [
    "# Let's look at the eigenvalues and eigenvectors of the centered data's covariance matrix\n",
    "def cov(X):\n",
    "    return (1 / X.shape[0]) * X.T.dot(X)\n",
    "\n",
    "cov_x = cov(xy)\n",
    "print(cov_x.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvalues:  [0.382 0.002]\n",
      "Eigenvectors:  [[ 0.896 -0.443]\n",
      " [ 0.443  0.896]]\n"
     ]
    }
   ],
   "source": [
    "# Now we'll compute the eigenvalues and eigenvectors\n",
    "eig, eigv = np.linalg.eig(cov_x)\n",
    "print(\"Eigenvalues: \", eig)\n",
    "print(\"Eigenvectors: \", eigv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.12 , -0.506, -0.279,  1.183, -0.381, -0.087, -0.288, -0.666,\n",
       "        0.797, -0.731,  0.566, -0.52 , -0.624, -0.062, -0.86 , -0.315,\n",
       "       -0.402, -0.011, -0.068,  0.176,  1.11 ,  0.817,  0.376, -0.15 ,\n",
       "       -0.182,  0.936,  0.282,  0.39 ,  0.373,  0.469, -0.894,  0.574,\n",
       "       -0.931, -0.323,  0.212,  0.173, -0.882,  0.618,  0.15 ,  1.19 ,\n",
       "        0.143,  0.367,  0.577, -0.705,  1.092, -0.263, -0.229, -0.609,\n",
       "        0.934, -0.956,  0.231,  0.137,  0.945, -0.287, -0.978, -0.885,\n",
       "        0.526,  0.982, -0.049, -0.53 , -0.676, -0.722, -0.448,  0.086,\n",
       "        0.126,  0.676, -0.962,  0.516, -0.17 ,  0.826,  0.945, -0.333,\n",
       "        0.872, -0.214, -0.692,  0.091,  0.567, -0.57 , -0.872,  1.026,\n",
       "        0.826,  0.124, -0.816, -0.419, -0.405,  0.441, -0.76 , -0.806,\n",
       "       -0.054, -0.866, -0.902, -0.289,  0.832,  0.603,  0.087,  0.468,\n",
       "       -0.682,  0.671,  0.444, -0.12 ])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's project the data on the first eigenvector\n",
    "xy_proj = xy.dot(eigv[:, 0])\n",
    "xy_proj"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Now let's make this more interpretable by reprojecting back into our original space\n",
    "xy_reproj = xy_proj[:, None].dot(eigv[None, :, 0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1074a2fd0>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6, 6))\n",
    "plt.scatter(xy[:, 0], xy[:, 1])\n",
    "plt.scatter(xy_reproj[:, 0], xy_reproj[:, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fun with PCA - more complicated datasets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "import tensorflow as tf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:From <ipython-input-17-8bf8ae5a5303>:2: read_data_sets (from tensorflow.contrib.learn.python.learn.datasets.mnist) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Please use alternatives such as official/mnist/dataset.py from tensorflow/models.\n",
      "WARNING:tensorflow:From /Users/josh/.pyenv/versions/3.6.5/envs/cs189-su18/lib/python3.6/site-packages/tensorflow/contrib/learn/python/learn/datasets/mnist.py:260: maybe_download (from tensorflow.contrib.learn.python.learn.datasets.base) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Please write your own downloading logic.\n",
      "WARNING:tensorflow:From /Users/josh/.pyenv/versions/3.6.5/envs/cs189-su18/lib/python3.6/site-packages/tensorflow/contrib/learn/python/learn/datasets/mnist.py:262: extract_images (from tensorflow.contrib.learn.python.learn.datasets.mnist) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Please use tf.data to implement this functionality.\n",
      "Extracting MNIST_data/train-images-idx3-ubyte.gz\n",
      "WARNING:tensorflow:From /Users/josh/.pyenv/versions/3.6.5/envs/cs189-su18/lib/python3.6/site-packages/tensorflow/contrib/learn/python/learn/datasets/mnist.py:267: extract_labels (from tensorflow.contrib.learn.python.learn.datasets.mnist) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Please use tf.data to implement this functionality.\n",
      "Extracting MNIST_data/train-labels-idx1-ubyte.gz\n",
      "WARNING:tensorflow:From /Users/josh/.pyenv/versions/3.6.5/envs/cs189-su18/lib/python3.6/site-packages/tensorflow/contrib/learn/python/learn/datasets/mnist.py:110: dense_to_one_hot (from tensorflow.contrib.learn.python.learn.datasets.mnist) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Please use tf.one_hot on tensors.\n",
      "Extracting MNIST_data/t10k-images-idx3-ubyte.gz\n",
      "Extracting MNIST_data/t10k-labels-idx1-ubyte.gz\n",
      "WARNING:tensorflow:From /Users/josh/.pyenv/versions/3.6.5/envs/cs189-su18/lib/python3.6/site-packages/tensorflow/contrib/learn/python/learn/datasets/mnist.py:290: DataSet.__init__ (from tensorflow.contrib.learn.python.learn.datasets.mnist) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Please use alternatives such as official/mnist/dataset.py from tensorflow/models.\n"
     ]
    }
   ],
   "source": [
    "from tensorflow.examples.tutorials.mnist import input_data\n",
    "mnist = input_data.read_data_sets(\"MNIST_data/\", one_hot=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "images_raw = mnist.train.images"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_mnist(vec):\n",
    "    assert len(vec) == 28 * 28\n",
    "    plt.imshow(vec.reshape([28, 28]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 1. Center. We will subtact the mean.\n",
    "mnist_mean = np.mean(images_raw, axis=0, keepdims=True)\n",
    "images = images_raw - mnist_mean\n",
    "# 2. Eigenvalues and eigenvectors\n",
    "cov = (1 / images.shape[0]) * images.T.dot(images)\n",
    "eig, eigv = np.linalg.eig(cov)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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MP5FTDD+RUww/kVMMP5FTDD+RUww/kVPTps+flAb6vgWJb9yGptNncoFe+Sv2zvtfvNCs//do/PXtF+bsZbBD/erQvPdCg10fmRX/I1a0Vw8P15NcW99BHz+ER34ipxh+IqcYfiKnGH4ipxh+IqcYfiKnGH4ip4J9fhFZCmArgDYACqBDVR8WkQcAfA3A8eiu96vqjkoNNKngfH+7FW/+mgz1ozUbuEZ8YPt8k12XYvzjB7+ugNA5DMG6cX5E6NCTdN9Jrq0/Hfr4IaWc5JMH8G1V3SUiswC8JiLPR7WHVPWfKjc8IqqUYPhVtRdAb/TxWRHZD2BxpQdGRJX1if7mF5FlAD4H4DfRTfeKyB4R6RSRuTHbbBKRLhHpKgyeSzRYIiqfksMvIjMBPAPgW6r6IYAfArgYwGqMvTL43kTbqWqHqraranu2uaUMQyaicigp/CJSj7HgP6mqPwUAVT2mqgVVLQJ4BMCayg2TiMotGH4REQCPAtivqg+Ou33RuLt9BcAb5R8eEVVKKe/2XwXgLgB7RWR3dNv9ADaIyGqMtf8OAfh6RUZYJYlagaHpn8F2WGDfgVah/eCT33Rs54GHT9ISSzitNgkPrbyQUt7tfxkTfxtqtqdPRGE8w4/IKYafyCmGn8gphp/IKYafyCmGn8gpXrq7RBXtZ4f2nWTXSfv8FcRee7p45CdyiuEncorhJ3KK4SdyiuEncorhJ3KK4SdySlSr1wgWkeMADo+7aT6AE1UbwCdTq2Or1XEBHNtklXNsn1bVBaXcsarh/9jORbpUtT21ARhqdWy1Oi6AY5ustMbGl/1ETjH8RE6lHf6OlPdvqdWx1eq4AI5tslIZW6p/8xNRetI+8hNRSlIJv4isFZG3ROSAiNyXxhjiiMghEdkrIrtFpCvlsXSKSJ+IvDHutlYReV5E3on+n3CZtJTG9oCI9ETP3W4RuSWlsS0VkRdFZJ+IvCkifxHdnupzZ4wrleet6i/7RSQL4G0ANwLoBvAqgA2quq+qA4khIocAtKtq6j1hEbkWwACAraq6KrrtHwCcUtXN0S/Ouar6NzUytgcADKS9cnO0oMyi8StLA7gdwJ8ixefOGNcdSOF5S+PIvwbAAVV9V1VHAfwEwPoUxlHzVPUlAKfOu3k9gC3Rx1sw9sNTdTFjqwmq2ququ6KPzwL4aGXpVJ87Y1ypSCP8iwEcGfd5N2pryW8F8JyIvCYim9IezATaomXTAeAogLY0BzOB4MrN1XTeytI189xNZsXrcuMbfh93tap+HsA6AN+IXt7WJB37m62W2jUlrdxcLROsLP1baT53k13xutzSCH8PgKXjPl8S3VYTVLUn+r8PwLOovdWHj320SGr0f1/K4/mtWlq5eaKVpVEDz10trXidRvhfBbBCRC4SkQYAdwLYnsI4PkZEWqI3YiAiLQBuQu2tPrwdwMbo440AtqU4lt9RKys3x60sjZSfu5pb8VpVq/4PwC0Ye8f/IIC/TWMMMeNaDuB/o39vpj02AE9h7GVgDmPvjdwDYB6AnQDeAfALAK01NLbHAewFsAdjQVuU0tiuxthL+j0Adkf/bkn7uTPGlcrzxjP8iJziG35ETjH8RE4x/EROMfxETjH8RE4x/EROMfxETjH8RE79PwIKsPQ93R8OAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot some centered mnist digits\n",
    "for i in range(10):\n",
    "    plt.figure()\n",
    "    plot_mnist(images[i])\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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XAuemiv2CkKoRt2JIvkT3SsAzP5FTLH4ip1j8RE6x+ImcYvETOcXiJ3KKxU/k1Mrq81uSzsvfZTd2rSWbK/32tnMjgX1n7eS1x+615wbj5wNYNWivGTDSba8JkM3Y+y5X7YHxs6X4AzdftCfmL87b62TXFuyXr/WshPr4Wrv1rwPgmZ/IKRY/kVMsfiKnWPxETrH4iZxi8RM5xeIncirY5xeRrQCeB7ARi63TA6r6jIg8BeCbAG4uLv+kqr7aqkQTSzhPunWdQGiuALXGtAOQ3ooZ7+krm/HV/fOxsf4uu4+fE7uPP1+xe+2FQK/e6uWXivbLr1YKLbaQYDx/oE9/K/TxQ+q5yKcC4Duq+raIDAI4KiKvR7EfqOp3W5ceEbVKsPhVdQLARHR7RkTeBbC51YkRUWt9ps/8IrINwC4Ab0Z3PSYix0XkoIgMxWyzX0TGRGSsWggsO0VEbVN38YvIAICXADyuqjcA/BDA7QB2YvGdwfeW205VD6jqqKqOZgfsNeuIqH3qKn4RyWOx8H+sqj8FAFW9pKpVVa0BeBbA7talSUTNFix+EREAzwF4V1W/v+T+pWPVvgbgZPPTI6JWqeev/fcC+AaAEyJyLLrvSQB7RWQnFpsm4wC+1ZIMVwK7W2a3nADovP00LASmsLaGvmZCbciEQ1s1yfTaoWGzgeOGwKzh1rrtHlp5IfX8tf8XWL5L3rk9fSIK4hV+RE6x+ImcYvETOcXiJ3KKxU/kFIufyKlbZ+ruFjP7wkY/GUD4OoByoJdebPx3dGDXiRvewZHSoWNjPTZ78S3FMz+RUyx+IqdY/EROsfiJnGLxEznF4idyisVP5JRoaEB3M3cmchnA2SV3rQNwpW0JfDadmlun5gUwt0Y1M7cvqOr6er6xrcX/qZ2LjKnqaGoJGDo1t07NC2BujUorN77tJ3KKxU/kVNrFfyDl/Vs6NbdOzQtgbo1KJbdUP/MTUXrSPvMTUUpSKX4ReVBE/k9EPhCRJ9LIIY6IjIvICRE5JiJjKedyUEQmReTkkvuGReR1ETkd/b/sMmkp5faUiFyIjt0xEXkopdy2ish/isg7InJKRP4quj/VY2fklcpxa/vbfhHJAngfwAMAzgN4C8BeVX2nrYnEEJFxAKOqmnpPWET+BEABwPOqeld03z8AmFLVp6NfnEOq+rcdkttTAAppr9wcLSgzsnRlaQAPA/gLpHjsjLweQQrHLY0z/24AH6jqGVUtAXgRwJ4U8uh4qvoGgKlP3L0HwKHo9iEsvnjaLia3jqCqE6r6dnR7BsDNlaVTPXZGXqlIo/g3Azi35Ovz6KwlvxXAayJyVET2p53MMjZGy6YDwEUAG9NMZhnBlZvb6RMrS3fMsWtkxetm4x/8Pu0+Vb0bwFcAfDt6e9uRdPEzWye1a+paubldlllZ+tfSPHaNrnjdbGkU/wUAW5d8vSW6ryOo6oXo/0kAL6PzVh++dHOR1Oj/yZTz+bVOWrl5uZWl0QHHrpNWvE6j+N8CsF1EbhORLgBfB3A4hTw+RUT6oz/EQET6AXwZnbf68GEA+6Lb+wC8kmIuv6FTVm6OW1kaKR+7jlvxWlXb/g/AQ1j8i/+HAP4ujRxi8voigP+N/p1KOzcAL2DxbWAZi38beRTAWgBHAJwG8HMAwx2U278AOAHgOBYLbSSl3O7D4lv64wCORf8eSvvYGXmlctx4hR+RU/yDH5FTLH4ip1j8RE6x+ImcYvETOcXiJ3KKxU/kFIufyKn/Bwy/8KEOUwdHAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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RUyx+IqfWVp/fEmvLNiPnAVTsQ3G9GX6drFbtcefFot0r10jutYp9/7mL4X73+lP26/uG43UzPvbri2ZcL18x4/mpzcFY6057LoGr99rrZJe32I+tNhE+sM3hSJ//FliCO4bv/EROsfiJnGLxEznF4idyisVP5BSLn8gpFj+RU7dOnz+m2/MAquHXyWbT7sO3ipH1nCM9ZW3Yr9HW6uGx+emvTdm/Ao3RcJ8eAKRpxxvG3PnVCfuYV2+z442SfdysXv6tsMR2t/jOT+QUi5/IKRY/kVMsfiKnWPxETrH4iZxi8RM5Fe3zi8hWAM8CmMJyt3yfqj4tIk8C+BqAC8lNn1DVl3qVaNd62be1p+WHRs4hiKUmebuf3RoPzxdQmba3rU3Yr//5yHoHsfMjrAfXKkQeVyQem1u/Zf12OxivH9POST4NAN9W1TdEZB2A10Xk5ST2fVX9h96lR0S9Ei1+VT0L4GxyeVFEjgHY0uvEiKi3PtDf/CKyDcAnAbyWXPWYiBwRkf0isiGwzV4RmRWR2Wa53FWyRJSetotfREoAfgbgW6q6AOAHAO4FsAPLnwy+u9p2qrpPVWdUdSZfKqWQMhGloa3iF5Eilgv/x6r6cwBQ1fOq2lTVFoAfAtjZuzSJKG3R4hcRAfAMgGOq+r0V10+vuNmXARxNPz0i6pV2vu3/DICvAnhLRA4n1z0BYLeI7MBy++8kgK/3JMNBYXWGIsuDox4ZLmzPnh1n5RZJrRWbwtoerRyfd9zYvzUUObbt8vZdtOsctPJi2vm2/1WsfqgGt6dPRFE8w4/IKRY/kVMsfiKnWPxETrH4iZxi8RM5xam72yRmw7q7++5aF33+2LDYWBu/K+y1Z4rv/EROsfiJnGLxEznF4idyisVP5BSLn8gpFj+RU6I9beTetDORCwB+t+Kq2wFc7FsCH8yg5jaoeQHMrVNp5naXqm5q54Z9Lf737VxkVlVnMkvAMKi5DWpeAHPrVFa58WM/kVMsfiKnsi7+fRnv3zKouQ1qXgBz61QmuWX6Nz8RZSfrd34iykgmxS8iD4rIr0XkHRF5PIscQkTkpIi8JSKHRWQ241z2i8iciBxdcd2kiLwsIseT/1ddJi2j3J4UkTPJsTssIg9llNtWEflPEfmViLwtIt9Mrs/02Bl5ZXLc+v6xX0TyAP4XwOcBnAZwCMBuVf1VXxMJEJGTAGZUNfOesIj8OYAygGdV9f7kur8HcFlVn0peODeo6ncGJLcnAZSzXrk5WVBmeuXK0gAeBvDXyPDYGXk9ggyOWxbv/DsBvKOqJ1S1BuAnAHZlkMfAU9VXAFy+6epdAA4klw9g+Zen7wK5DQRVPauqbySXFwHcWFk602Nn5JWJLIp/C4BTK34+jcFa8lsB/EJEXheRvVkns4qpZNl0ADgHYCrLZFYRXbm5n25aWXpgjl0nK16njV/4vd8DqvqnAL4I4BvJx9uBpMt/sw1Su6atlZv7ZZWVpf8gy2PX6YrXacui+M8A2Lri5zuS6waCqp5J/p8D8DwGb/Xh8zcWSU3+n8s4nz8YpJWbV1tZGgNw7AZpxessiv8QgO0icreIDAH4CoAXM8jjfURkPPkiBiIyDuALGLzVh18EsCe5vAfACxnm8h6DsnJzaGVpZHzsBm7Fa1Xt+z8AD2H5G//fAPibLHII5HUPgDeTf29nnRuA57D8MbCO5e9GHgWwEcBBAMcB/BLA5ADl9s8A3gJwBMuFNp1Rbg9g+SP9EQCHk38PZX3sjLwyOW48w4/IKX7hR+QUi5/IKRY/kVMsfiKnWPxETrH4iZxi8RM5xeIncur/ACK0AHz965n/AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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wKw17YvqHK7eY7S/M2zsZnb11j9m+f2zdzZIAAJWCPYDhvaVdZvuZi5Nm+/IHxt7lAEZm069boWb/ozW9d6c7nz+9zV1XP2sdn3V+IhpUDD9RUAw/UVAMP1FQDD9RUAw/UVAMP1FQbp1fRPYBeBbAbrSq6cdU9WkReQLANwBcSZ76uKq+1KuOZpZ1HMBKeluhbhd1i8t20bgxm762PQC89b4zDqByh9lukVW776Ulu3140fnajeumBWft/IrZ7NbSzfUAvGM3QR3f084gnzqA76jq6yIyDuA1EXk5afueqv5D77pHRL3ihl9VZwDMJB/Pi8jbAPb2umNE1Fuf6md+EbkTwL0AfpU89KiIvCEix0Vk3X2dROSoiEyLyHSjmr7cFBH1V9vhF5ExAD8F8G1VnQPwfQCfAXAAre8Mvrvecap6TFWnVHWqOGL/7EpE/dNW+EWkjFbwn1PVnwGAql5S1YaqNgH8AIC9YyMRDRQ3/CIiAJ4B8LaqPrXm8bXTvb4KwF5ilogGSju/7f88gK8DOCMip5PHHgdwWEQOoFVEOwfgmz3pYb94pUCrsWEfa5W7AL9U6JXbzOmnTklKnL577c6MYfO6elN2vW3TMy2PvQlKdVm189v+X2D9SzW4NX0icnGEH1FQDD9RUAw/UVAMP1FQDD9RUAw/UVCbZ+nuXrO2B884XdgbJzDQnK/dlHVaLWXCOz9RUAw/UVAMP1FQDD9RUAw/UVAMP1FQDD9RUKKapVD7KU8mcgXAb9Y8tAvA1b514NMZ1L4Nar8A9q1T3ezbHapq7wmf6Gv4P3FykWlVncqtA4ZB7dug9gtg3zqVV9/4bT9RUAw/UVB5h/9Yzue3DGrfBrVfAPvWqVz6luvP/ESUn7zv/ESUk1zCLyIPiMj/isi7IvJYHn1IIyLnROSMiJwWkemc+3JcRC6LyNk1j02IyMsi8k7y97rbpOXUtydE5EJy7U6LyIM59W2fiPyniLwlIm+KyF8lj+d67Yx+5XLd+v5tv4gUAfwfgC8BOA/gVQCHVfWtvnYkhYicAzClqrnXhEXkTwEsAHhWVe9JHvt7ALOq+mTyH+cOVf2bAenbEwAW8t65OdlQZnLtztIAHgLwl8jx2hn9ehg5XLc87vwHAbyrqu+p6iqAHwE4lEM/Bp6qvgJg9mMPHwJwIvn4BFpvnr5L6dtAUNUZVX09+XgewM2dpXO9dka/cpFH+PcC+GDN5+cxWFt+K4Cfi8hrInI0786sY3eybToAXASwO8/OrMPdubmfPraz9MBcu052vO42/sLvk+5T1T8G8GUA30q+vR1I2vqZbZDKNW3t3Nwv6+ws/Vt5XrtOd7zutjzCfwHAvjWf3548NhBU9ULy92UAL2Dwdh++dHOT1OTvyzn357cGaefm9XaWxgBcu0Ha8TqP8L8KYL+I3CUiQwC+BuBkDv34BBHZkvwiBiKyBcD9GLzdh08COJJ8fATAizn25XcMys7NaTtLI+drN3A7Xqtq3/8AeBCt3/j/GsDf5tGHlH79HoD/Tv68mXffADyP1reBNbR+N/IIgJ0ATgF4B8C/A5gYoL79M4AzAN5AK2iTOfXtPrS+pX8DwOnkz4N5XzujX7lcN47wIwqKv/AjCorhJwqK4ScKiuEnCorhJwqK4ScKiuEnCorhJwrq/wGUp+Hs/gp2FAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Let's plot some of the eigenvectors\n",
    "for i in range(10):\n",
    "    plt.figure()\n",
    "    plot_mnist(eigv[:, i])\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## How to choose the number of dimensions for our projection?\n",
    "\n",
    "Explained variance: proportion of the total variance of the dataset explained by our projected data\n",
    "\n",
    "How to compute?\n",
    "\n",
    "k = our chosen subset dimensionality\n",
    "\n",
    "\n",
    "    sum(eig[:k]) / sum(eig)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "explained_variance = [np.sum(eig[:k]) / np.sum(eig) for k in range(0, len(eig) +1)] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.LineCollection at 0x10b28bfd0>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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BY4M0JWLMaihr8Y+ISNWrinA/GKyUMbOwSxERmRaqI9xP6ANMIiKFqiLcDx0fYuFshbuISF7kwz2dyXJ0IEl7sy6tJyKSF/lwPzqQxB3aWurCLkVEZNqIfLgfPpkEoK1Z4S4ikhf5cD9yahhQuIuIFIp8uB/uz4e75txFRPKiH+75aRnNuYuIjIh+uPcPk4jV0FKnT6eKiORFPtx7+4dpa07o06kiIgUiH+6H+5OakhERKRL5cD/SP6yVMiIiRSIf7oeDaRkRETkt0uGezTpH+pPM08hdROQMkQ73k8Np0llnXpNG7iIihSId7n2DKQBmNcRDrkREZHqJdLifCMJ9tsJdROQMkQ73kZF7vcJdRKRQtMN9SCN3EZHRRDrcT4zMuevUAyIihSId7n2DaUAjdxGRYpEO9xODKWoMmnXSMBGRM0Q63PuGUsxqiOukYSIiRcoKdzNbb2a7zKzLzO4Zo98vmZmbWUflSiztxGBKUzIiIqMYN9zNLAY8ANwMrAY2mtnqUfq1AL8NvFDpIks5MZjSMkgRkVGUM3K/Fuhy993ungQeBW4dpd+XgC8DQxWsb0x9GrmLiIyqnHBfDOwv2D8QtI0ws7XAUnf/xwrWNi5Ny4iIjO6831A1sxrgq8DvltH3LjPrNLPO3t7e8z00fUNprXEXERlFOeHeDSwt2F8StOW1AFcAz5rZXuB6YPNob6q6+yZ373D3jvb29olXHTgxmNJJw0RERlFOuG8FVpnZSjNLALcDm/MPuvsJd29z9xXuvgJ4HrjF3TsnpeLAUCpDMp3VG6oiIqMYN9zdPQ3cDTwN7AQec/ftZna/md0y2QWW0qczQoqIlFTWhLW7bwG2FLXdV6Lvjedf1vjyJw3TtIyIyNki+wnVU8MZAJrrYiFXIiIy/UQ23AeSuXBviGu1jIhIsciG+2Aqd0bIhoRG7iIixSIb7vmRe6PCXUTkLJEN98GRaRmFu4hIseiGeyoId43cRUTOEtlw17SMiEhpkQ/3+lqFu4hIsciG+1AqQ328hpoaXYVJRKRYZMN9IJmmMaE17iIio4lwuGe0UkZEpITIhvtgMqOVMiIiJUQ33FMZrZQRESkhsuGuaRkRkdIiG+6DSY3cRURKiW64pzTnLiJSSnTDPZnR6X5FREqIbLgPJNM0JCJbvojIpIpsOg6lsnpDVUSkhEiGu7szlM5Qr3AXERlVJMM9lXHcoa42kuWLiEy6SKbjUDo4I6RG7iIio4pkuA+nsoBG7iIipUQyHYeCqzDVaeQuIjKqSIb7cFojdxGRsUQyHfMjd825i4iMLpLhrpG7iMjYIpmOwxq5i4iMKZrhrpG7iMiYIpmOmnMXERlbJMNdI3cRkbGVlY5mtt7MdplZl5ndM8rjnzezHWb2mpn90MyWV77U0zRyFxEZ27jhbmYx4AHgZmA1sNHMVhd1exnocPcrgceBP610oYXyI3eFu4jI6MoZuV8LdLn7bndPAo8CtxZ2cPdn3H0g2H0eWFLZMs808glVTcuIiIyqnHRcDOwv2D8QtJVyJ/DUaA+Y2V1m1mlmnb29veVXWWRI55YRERlTRdPRzD4DdABfGe1xd9/k7h3u3tHe3j7h4wynM9TWGLUxhbuIyGjKuQhpN7C0YH9J0HYGM1sH3At8zN2HK1Pe6IZSWc23i4iMoZyh71ZglZmtNLMEcDuwubCDma0B/hK4xd17Kl/mmYbTGU3JiIiMYdyEdPc0cDfwNLATeMzdt5vZ/WZ2S9DtK0Az8Ldm9oqZbS7xdBWhkbuIyNjKmZbB3bcAW4ra7ivYXlfhusakkbuIyNgimZBDqSwJhbuISEmRTMhUJqurMImIjCGy4R6vsbDLEBGZtqIb7lrjLiJSUiQTMplx4ppzFxEpKZIJmc5kScQ0LSMiUkokw13TMiIiY4tkQqYyrnAXERlDJBMymdbIXURkLJFMyFQmS6JWc+4iIqVENtxrayJZuojIlIhkQmrOXURkbJFMyGQmS1zTMiIiJUUy3HPr3CNZuojIlIhcQmayTtbRtIyIyBgil5CpTO7i2Ap3EZHSIpeQyZFw15y7iEgpkQv3VDoX7rpYh4hIaZFLyFTGAbTOXURkDJFLyJSmZURExhW5cM/PuWtaRkSktMglZDqYltFqGRGR0iKXkFoKKSIyvsglpJZCioiML3LhPrIUUiN3EZGSIpeQ+aWQukC2iEhpkUvI/Jx7bY2mZURESolcuCf1hqqIyLgil5D5pZBa5y4iUlrkElJLIUVExldWQprZejPbZWZdZnbPKI/Xmdm3g8dfMLMVlS40T0shRUTGN264m1kMeAC4GVgNbDSz1UXd7gSOufvFwH8HvlzpQvPyI3cthRQRKa2chLwW6HL33e6eBB4Fbi3qcyvwzWD7ceATZjYpQ+v8OndNy4iIlFZOQi4G9hfsHwjaRu3j7mngBDCvEgUWGznlr6ZlRERKmtLhr5ndZWadZtbZ29s7oedY0dbEhvdfoNUyIiJjqC2jTzewtGB/SdA2Wp8DZlYLzAaOFD+Ru28CNgF0dHT4RAq+afUCblq9YCJfKiIyY5Qz/N0KrDKzlWaWAG4HNhf12Qz8arB9G/Ajd59QeIuIyPkbd+Tu7mkzuxt4GogBD7r7djO7H+h0983AXwMPmVkXcJTcLwAREQlJOdMyuPsWYEtR230F20PAv6tsaSIiMlF6V1JEpAop3EVEqpDCXUSkCincRUSqkMJdRKQKWVjL0c2sF9g3wS9vAw5XsJxKUV3nRnWdu+lam+o6N+dT13J3bx+vU2jhfj7MrNPdO8Kuo5jqOjeq69xN19pU17mZiro0LSMiUoUU7iIiVSiq4b4p7AJKUF3nRnWdu+lam+o6N5NeVyTn3EVEZGxRHbmLiMgYIhfu412se5KP/aCZ9ZjZtoK2uWb2fTN7K7ifE7SbmX0tqPM1M1s7iXUtNbNnzGyHmW03s9+eDrWZWb2Z/dzMXg3q+qOgfWVwIfWu4MLqiaB9yi60HhwvZmYvm9mT06UuM9trZq+b2Stm1hm0TYfXWKuZPW5mb5jZTjP7YNh1mdmlwfcpf+szs8+FXVdwrN8JXvPbzOyR4P/C1L6+3D0yN3KnHH4buBBIAK8Cq6fw+B8F1gLbCtr+FLgn2L4H+HKwvQF4CjDgeuCFSaxrIbA22G4B3iR3MfNQawuevznYjgMvBMd7DLg9aP868BvB9m8CXw+2bwe+Pck/z88D3wKeDPZDrwvYC7QVtU2H19g3gf8UbCeA1ulQV0F9MeBdYHnYdZG77OgeoKHgdXXHVL++JvUbPgnftA8CTxfsfxH44hTXsIIzw30XsDDYXgjsCrb/Etg4Wr8pqPEfgJumU21AI/AScB25D2/UFv9MyV0z4IPBdm3QzyapniXAD4GPA08G/+GnQ117OTvcQ/05kruy2p7if3PYdRXV8gvAT6dDXZy+pvTc4PXyJPDJqX59RW1appyLdU+1Be5+KNh+F8hfAzCUWoM/6daQGyWHXlsw9fEK0AN8n9xfXsc9dyH14mNP2YXWgT8Hfg/IBvvzpkldDnzPzF40s7uCtrB/jiuBXuD/BtNYf2VmTdOgrkK3A48E26HW5e7dwJ8B7wCHyL1eXmSKX19RC/dpzXO/ekNbfmRmzcDfAZ9z977Cx8Kqzd0z7n4VuZHytcBlU11DMTP7FNDj7i+GXcsoPuzua4Gbgc+a2UcLHwzp51hLbjryL9x9DXCK3HRH2HUBEMxd3wL8bfFjYdQVzPHfSu6X4iKgCVg/lTVA9MK9nIt1T7X3zGwhQHDfE7RPaa1mFicX7A+7+99Pp9oA3P048Ay5P0dbLXch9eJjj9RlY1xovQJuAG4xs73Ao+SmZv7HNKgrP+rD3XuA75D7hRj2z/EAcMDdXwj2HycX9mHXlXcz8JK7vxfsh13XOmCPu/e6ewr4e3KvuSl9fUUt3Mu5WPdUK7w4+K+Sm+/Ot/+H4B3664ETBX8qVpSZGbnr2O50969Ol9rMrN3MWoPtBnLvA+wkF/K3lahr0i+07u5fdPcl7r6C3GvoR+7+K2HXZWZNZtaS3yY3j7yNkH+O7v4usN/MLg2aPgHsCLuuAhs5PSWTP36Ydb0DXG9mjcH/zfz3a2pfX5P5Jsdk3Mi94/0mubnbe6f42I+Qm0NLkRvN3ElubuyHwFvAD4C5QV8DHgjqfB3omMS6PkzuT8/XgFeC24awawOuBF4O6toG3Be0Xwj8HOgi96d0XdBeH+x3BY9fOAU/0xs5vVom1LqC478a3LbnX99h/xyDY10FdAY/yyeAOdOkriZyo9zZBW3Toa4/At4IXvcPAXVT/frSJ1RFRKpQ1KZlRESkDAp3EZEqpHAXEalCCncRkSqkcBcRqUIKdxGRKqRwFxGpQgp3EZEq9P8BXiX00NKk/g8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(explained_variance)\n",
    "plt.hlines(0.8, 0, 800, color='orange')\n",
    "plt.hlines(0.9, 0, 800, color='red')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What do the reconstructions look like?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x1296 with 35 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_dims = [1, 10, 50, 100, 200, 500, 28*28]\n",
    "mnist_mean = np.mean(images_raw, axis=0, keepdims=True)\n",
    "n_imgs = 5\n",
    "plt.figure(figsize=(10, 18))\n",
    "for i, dim in enumerate(n_dims):\n",
    "    # Compute the projection matrix\n",
    "    proj_mat = eigv[:, :dim]\n",
    "    # Compute the projection\n",
    "    proj = images.dot(proj_mat)\n",
    "    # Compute the reprojection\n",
    "    reproj = proj.dot(proj_mat.T)\n",
    "    # Recenter so it looks like the original images\n",
    "    reconstr = reproj + mnist_mean\n",
    "    for j in range(n_imgs):\n",
    "        plt.subplot(len(n_dims), n_imgs, i * n_imgs + j + 1)\n",
    "        plot_mnist(reconstr[j])\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
