svd.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sklearn.datasets import load_digits\n",
    "from matplotlib import pyplot as plt\n",
    "from sklearn.decomposition import TruncatedSVD\n",
    "float_formatter = lambda x: \"%.2f\" % x\n",
    "np.set_printoptions(formatter={'float_kind':float_formatter})\n",
    "from sklearn.ensemble import RandomForestClassifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, y = load_digits(return_X_y=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 64)"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, ..., 8, 9, 8])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "image = X[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00, 0.00, 5.00, 13.00, 9.00, 1.00, 0.00, 0.00, 0.00, 0.00, 13.00,\n",
       "       15.00, 10.00, 15.00, 5.00, 0.00, 0.00, 3.00, 15.00, 2.00, 0.00,\n",
       "       11.00, 8.00, 0.00, 0.00, 4.00, 12.00, 0.00, 0.00, 8.00, 8.00, 0.00,\n",
       "       0.00, 5.00, 8.00, 0.00, 0.00, 9.00, 8.00, 0.00, 0.00, 4.00, 11.00,\n",
       "       0.00, 1.00, 12.00, 7.00, 0.00, 0.00, 2.00, 14.00, 5.00, 10.00,\n",
       "       12.00, 0.00, 0.00, 0.00, 0.00, 6.00, 13.00, 10.00, 0.00, 0.00,\n",
       "       0.00])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "image = image.reshape((8, 8))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1a189780f0>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.matshow(image, cmap = 'gray')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.00 -1.10 4.74 12.16 9.52 2.44 -1.33 0.00]\n",
      " [0.00 1.81 15.31 13.79 11.23 12.27 4.48 0.00]\n",
      " [0.00 3.86 13.36 1.19 1.49 12.59 7.65 0.00]\n",
      " [0.00 3.39 10.76 -0.35 0.20 10.36 6.61 0.00]\n",
      " [0.00 3.11 9.52 -0.85 -0.24 9.26 6.04 0.00]\n",
      " [0.00 3.61 11.79 0.12 0.60 11.27 7.07 0.00]\n",
      " [0.00 2.08 12.63 8.58 7.13 10.60 4.66 0.00]\n",
      " [0.00 -1.18 4.88 12.71 9.96 2.47 -1.44 0.00]]\n"
     ]
    }
   ],
   "source": [
    "U, s, V = np.linalg.svd(image)\n",
    "\n",
    "S = np.zeros((image.shape[0], image.shape[1]))\n",
    "\n",
    "S[:image.shape[0], :image.shape[0]] = np.diag(s)\n",
    "\n",
    "n_components = 2\n",
    "\n",
    "S = S[:, :n_components]\n",
    "VT = VT[:n_components, :]\n",
    "\n",
    "A = U.dot(Sigma.dot(VT))\n",
    "\n",
    "print(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1a1b46a080>"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.matshow(A, cmap = 'gray')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[10.97, -12.23],\n",
       "       [26.04, -6.82],\n",
       "       [18.73, 7.95],\n",
       "       [14.60, 8.08],\n",
       "       [12.72, 7.84],\n",
       "       [16.19, 8.21],\n",
       "       [20.45, -2.05],\n",
       "       [11.36, -12.85]])"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "U.dot(S)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "rf_original = RandomForestClassifier(oob_score=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/cmaklin/anaconda3/lib/python3.7/site-packages/sklearn/ensemble/forest.py:246: FutureWarning: The default value of n_estimators will change from 10 in version 0.20 to 100 in 0.22.\n",
      "  \"10 in version 0.20 to 100 in 0.22.\", FutureWarning)\n",
      "/Users/cmaklin/anaconda3/lib/python3.7/site-packages/sklearn/ensemble/forest.py:458: UserWarning: Some inputs do not have OOB scores. This probably means too few trees were used to compute any reliable oob estimates.\n",
      "  warn(\"Some inputs do not have OOB scores. \"\n",
      "/Users/cmaklin/anaconda3/lib/python3.7/site-packages/sklearn/ensemble/forest.py:463: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  predictions[k].sum(axis=1)[:, np.newaxis])\n",
      "/Users/cmaklin/anaconda3/lib/python3.7/site-packages/sklearn/ensemble/forest.py:463: RuntimeWarning: invalid value encountered in true_divide\n",
      "  predictions[k].sum(axis=1)[:, np.newaxis])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "RandomForestClassifier(bootstrap=True, class_weight=None, criterion='gini',\n",
       "            max_depth=None, max_features='auto', max_leaf_nodes=None,\n",
       "            min_impurity_decrease=0.0, min_impurity_split=None,\n",
       "            min_samples_leaf=1, min_samples_split=2,\n",
       "            min_weight_fraction_leaf=0.0, n_estimators=10, n_jobs=None,\n",
       "            oob_score=True, random_state=None, verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rf_original.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8603227601558152"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rf_original.oob_score_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "svd = TruncatedSVD(n_components=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_reduced = svd.fit_transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([45.86, -1.19])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_reduced[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "image_reduced = svd.inverse_transform(X_reduced[0].reshape(1,-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "image_reduced = image_reduced.reshape((8,8))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1a1866b198>"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.matshow(image_reduced, cmap = 'gray')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "rf_reduced = RandomForestClassifier(oob_score=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/cmaklin/anaconda3/lib/python3.7/site-packages/sklearn/ensemble/forest.py:246: FutureWarning: The default value of n_estimators will change from 10 in version 0.20 to 100 in 0.22.\n",
      "  \"10 in version 0.20 to 100 in 0.22.\", FutureWarning)\n",
      "/Users/cmaklin/anaconda3/lib/python3.7/site-packages/sklearn/ensemble/forest.py:458: UserWarning: Some inputs do not have OOB scores. This probably means too few trees were used to compute any reliable oob estimates.\n",
      "  warn(\"Some inputs do not have OOB scores. \"\n",
      "/Users/cmaklin/anaconda3/lib/python3.7/site-packages/sklearn/ensemble/forest.py:463: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  predictions[k].sum(axis=1)[:, np.newaxis])\n",
      "/Users/cmaklin/anaconda3/lib/python3.7/site-packages/sklearn/ensemble/forest.py:463: RuntimeWarning: invalid value encountered in true_divide\n",
      "  predictions[k].sum(axis=1)[:, np.newaxis])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "RandomForestClassifier(bootstrap=True, class_weight=None, criterion='gini',\n",
       "            max_depth=None, max_features='auto', max_leaf_nodes=None,\n",
       "            min_impurity_decrease=0.0, min_impurity_split=None,\n",
       "            min_samples_leaf=1, min_samples_split=2,\n",
       "            min_weight_fraction_leaf=0.0, n_estimators=10, n_jobs=None,\n",
       "            oob_score=True, random_state=None, verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rf_reduced.fit(X_reduced, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.36672231496939345"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rf_reduced.oob_score_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.17760900862040058"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "svd.explained_variance_ratio_.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8479578256047824"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "svd = TruncatedSVD(n_components=16)\n",
    "\n",
    "X_reduced = svd.fit_transform(X)\n",
    "\n",
    "svd.explained_variance_ratio_.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/cmaklin/anaconda3/lib/python3.7/site-packages/sklearn/ensemble/forest.py:246: FutureWarning: The default value of n_estimators will change from 10 in version 0.20 to 100 in 0.22.\n",
      "  \"10 in version 0.20 to 100 in 0.22.\", FutureWarning)\n",
      "/Users/cmaklin/anaconda3/lib/python3.7/site-packages/sklearn/ensemble/forest.py:458: UserWarning: Some inputs do not have OOB scores. This probably means too few trees were used to compute any reliable oob estimates.\n",
      "  warn(\"Some inputs do not have OOB scores. \"\n",
      "/Users/cmaklin/anaconda3/lib/python3.7/site-packages/sklearn/ensemble/forest.py:463: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  predictions[k].sum(axis=1)[:, np.newaxis])\n",
      "/Users/cmaklin/anaconda3/lib/python3.7/site-packages/sklearn/ensemble/forest.py:463: RuntimeWarning: invalid value encountered in true_divide\n",
      "  predictions[k].sum(axis=1)[:, np.newaxis])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.8647746243739566"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rf_reduced = RandomForestClassifier(oob_score=True)\n",
    "\n",
    "rf_reduced.fit(X_reduced, y)\n",
    "\n",
    "rf_reduced.oob_score_"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
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