tutorial-mnist-simple.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from PIL import Image\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import os\n",
    "import urllib\n",
    "from urllib.request import urlretrieve\n",
    "dataset = 'mnist.pkl.gz'\n",
    "def reporthook(a,b,c):\n",
    "    print(\"\\rdownloading: %5.1f%%\"%(a*b*100.0/c), end=\"\")\n",
    "    \n",
    "if not os.path.isfile(dataset):\n",
    "        origin = \"https://github.com/mnielsen/neural-networks-and-deep-learning/raw/master/data/mnist.pkl.gz\"\n",
    "        print('Downloading data from %s' % origin)\n",
    "        urlretrieve(origin, dataset, reporthook=reporthook)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import gzip\n",
    "import pickle\n",
    "with gzip.open(dataset, 'rb') as f:\n",
    "    train_set, valid_set, test_set = pickle.load(f, encoding='latin1')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "train_set (50000, 784) (50000,)\n",
      "valid_set (10000, 784) (10000,)\n",
      "test_set (10000, 784) (10000,)\n"
     ]
    }
   ],
   "source": [
    "print(\"train_set\", train_set[0].shape, train_set[1].shape)\n",
    "print(\"valid_set\", valid_set[0].shape, valid_set[1].shape)\n",
    "print(\"test_set\", test_set[0].shape, test_set[1].shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 0, 4, 1, 9, 2, 1, 3, 1, 4, 3, 5, 3, 6, 1, 7, 2, 8, 6, 9])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 訓練資料， Y 的前 20 筆\n",
    "train_set[1][:20]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjAAAAAcCAAAAABaa9rXAAANMElEQVR4nO1aaXRUVRKugRAWEzAE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\n0wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<PIL.Image.Image image mode=L size=560x28 at 0x7FC6F47CB2B0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 訓練資料， X 的前 20 筆\n",
    "int_X = (train_set[0][:20]*255).clip(0,255).astype('uint8')\n",
    "int_X_reshape = int_X.reshape(-1,28,28).swapaxes(0,1).reshape(28,-1)\n",
    "Image.fromarray(int_X_reshape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# 資料正規化\n",
    "train_X  = train_set[0]\n",
    "train_X  = train_X / np.linalg.norm(train_X, axis=1, keepdims=True)\n",
    "test_X  = test_set[0]\n",
    "test_X  = test_X / np.linalg.norm(test_X, axis=1, keepdims=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 矩陣乘法\n",
    "A = test_X @ train_X.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([44566, 28882, 15224, ...,  3261,  1311, 22424])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.argmax(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_predict = train_set[1][A.argmax(axis=1)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<PIL.Image.Image image mode=L size=560x28 at 0x7FC6F40674E0>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 測試資料， X 的前 20 筆\n",
    "int_X = (test_set[0][:20]*255).clip(0,255).astype('uint8')\n",
    "int_X_reshape = int_X.reshape(-1,28,28).swapaxes(0,1).reshape(28,-1)\n",
    "Image.fromarray(int_X_reshape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([7, 2, 1, 0, 4, 1, 4, 9, 5, 9, 0, 6, 9, 0, 1, 5, 9, 7, 3, 4])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 猜測的 Y 前20筆\n",
    "y_predict[:20]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([7, 2, 1, 0, 4, 1, 4, 9, 5, 9, 0, 6, 9, 0, 1, 5, 9, 7, 3, 4])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#測試資料的 Y 前 20 筆\n",
    "test_set[1][:20]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9708"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 正確率\n",
    "(y_predict == test_set[1]).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# 用 PCA 降低維度到 60\n",
    "from sklearn.decomposition import PCA\n",
    "pca = PCA(n_components=60)\n",
    "train_X = pca.fit_transform(train_set[0])\n",
    "test_X = pca.transform(test_set[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "train_X /= np.linalg.norm(train_X, axis=1, keepdims=True)\n",
    "test_X /= np.linalg.norm(test_X, axis=1, keepdims=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# 矩陣乘法\n",
    "A = test_X @ train_X.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "y_predict = train_set[1][A.argmax(axis=1)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.97030000000000005"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 正確率\n",
    "(y_predict == test_set[1]).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "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": "3.5.2+"
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 },
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