Chapter2.2.2.1.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 导入numpy工具包"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 初始化一个2*2的线性相关矩阵"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "M = np.array([[1,2],[2,4]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 计算矩阵的秩"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.matrix_rank(M,tol=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 使用pandas分别读取训练数据与测试数据集。\n",
    "digits_train = pd.read_csv('https://archive.ics.uci.edu/ml/machine-learning-databases/optdigits/optdigits.tra', header=None)\n",
    "digits_test = pd.read_csv('https://archive.ics.uci.edu/ml/machine-learning-databases/optdigits/optdigits.tes', header=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 分割训练数据的特征向量和标记"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_digits = digits_train[np.arange(64)]\n",
    "y_digits = digits_train[64]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 从sklearn.decomposition 导入PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.decomposition import  PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "estimator = PCA(n_components=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_pca=estimator.fit_transform(X_digits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 显示这10类手写体数字图片经PCA压缩后的2维空间分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYoAAAEKCAYAAAAMzhLIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nKIIgCIJc/g93HMVFsMbvEAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11595da50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_pca_scatter():\n",
    "    colors = ['black','blue','purple','yellow','white','red','lime','cyan','orange','gray']\n",
    "    for i in xrange(len(colors)):\n",
    "        px = X_pca[:, 0][y_digits.as_matrix() == i]\n",
    "        py = X_pca[:, 1][y_digits.as_matrix()== i]\n",
    "        plt.scatter(px,py,c=colors[i])\n",
    "        \n",
    "    plt.legend(np.arange(0,10).astype(str))\n",
    "    plt.xlabel('First Principal Component')\n",
    "    plt.ylabel('Second Principal Component')\n",
    "    plt.show()\n",
    "\n",
    "plot_pca_scatter()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 对训练数据／测试数据进行特征向量（图片像素）与分类目标的隔离"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train = digits_train[np.arange(64)]\n",
    "y_train = digits_train[64]\n",
    "X_test = digits_test[np.arange(64)]\n",
    "y_test = digits_test[64]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 导入基于线性核的支持向量机分类器"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.svm import LinearSVC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 初始化线性核的支持向量机的分类器"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "svc = LinearSVC()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearSVC(C=1.0, class_weight=None, dual=True, fit_intercept=True,\n",
       "     intercept_scaling=1, loss='squared_hinge', max_iter=1000,\n",
       "     multi_class='ovr', penalty='l2', random_state=None, tol=0.0001,\n",
       "     verbose=0)"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "svc.fit(X_train,y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_pred = svc.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 使用PCA将原64维德图像压缩为20个纬度"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "estimator = PCA(n_components=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 利用训练特征决定20个正交纬度的方向，并转化原训练特征\n",
    "pca_X_train = estimator.fit_transform(X_train)\n",
    "pca_X_test = estimator.transform(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 格式化LinearSVC，对压缩后的数据进行建模，并作出预测"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "psc_svc = LinearSVC()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "psc_svc.fit(pca_X_train,y_train)\n",
    "pca_y_pred = psc_svc.predict(pca_X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 ..., 8 9 8]\n"
     ]
    }
   ],
   "source": [
    "# print pca_y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import classification_report"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.93489148581\n"
     ]
    }
   ],
   "source": [
    "print svc.score(X_test,y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "             precision    recall  f1-score   support\n",
      "\n",
      "          0       0.98      0.98      0.98       178\n",
      "          1       0.92      0.90      0.91       182\n",
      "          2       0.96      0.98      0.97       177\n",
      "          3       0.95      0.92      0.94       183\n",
      "          4       0.94      0.97      0.95       181\n",
      "          5       0.90      0.97      0.93       182\n",
      "          6       0.99      0.98      0.98       181\n",
      "          7       0.98      0.92      0.95       179\n",
      "          8       0.85      0.90      0.87       174\n",
      "          9       0.90      0.84      0.87       180\n",
      "\n",
      "avg / total       0.94      0.93      0.93      1797\n",
      "\n",
      "0.925431274346\n",
      "             precision    recall  f1-score   support\n",
      "\n",
      "          0       0.97      0.97      0.97       178\n",
      "          1       0.91      0.80      0.85       182\n",
      "          2       0.97      0.97      0.97       177\n",
      "          3       0.97      0.94      0.96       183\n",
      "          4       0.93      0.97      0.95       181\n",
      "          5       0.89      0.98      0.93       182\n",
      "          6       0.98      0.98      0.98       181\n",
      "          7       0.96      0.89      0.92       179\n",
      "          8       0.87      0.87      0.87       174\n",
      "          9       0.82      0.88      0.85       180\n",
      "\n",
      "avg / total       0.93      0.93      0.93      1797\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print classification_report(y_test,y_pred,target_names=np.arange(10).astype(str))\n",
    "print psc_svc.score(pca_X_test,y_test)\n",
    "print classification_report(y_test,pca_y_pred,target_names=np.arange(10).astype(str))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}