Chapter2.2.1.1.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 使用K均值算法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 分别导入pandas分别读取训练集和测试集"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 读取训练集\n",
    "digits_train = pd.read_csv('https://archive.ics.uci.edu/ml/machine-learning-databases/optdigits/optdigits.tra', header=None)\n",
    "# 读取测试集\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": 189,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 从训练集和测试集上都分离出64维度的相素特征与一维的数字特征"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_train = digits_train[np.arange(64)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_train = digits_train[64]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_test  = digits_test[np.arange(64)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_test = digits_test[64]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 从sklearn.cluster中导入Kmeans模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from  sklearn.cluster  import KMeans"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 初始化Kmeans模型，并导入聚类中心数量为10\n",
    "kmeans = KMeans(n_clusters=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KMeans(algorithm='auto', copy_x=True, init='k-means++', max_iter=300,\n",
       "    n_clusters=10, n_init=10, n_jobs=1, precompute_distances='auto',\n",
       "    random_state=None, tol=0.0001, verbose=0)"
      ]
     },
     "execution_count": 198,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 使用kmeans对模型进行训练\n",
    "kmeans.fit(X_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 逐条判断每个测试图像所属的聚类中心"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_pred = kmeans.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 使用ARI进行Kmeans聚类性能评估"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn import metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.663057794933\n"
     ]
    }
   ],
   "source": [
    "# print metrics.adjusted_rand_score(y_test,y_pred)\n",
    "# 使用ARI进行KMeans聚类性能评估。\n",
    "print metrics.adjusted_rand_score(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 从sklearn.metrics导入silhouette_score用于计算轮廓系数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import  silhouette_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 分割出3*2=6个子图，并在1号子图作图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11a2fe310>"
      ]
     },
     "execution_count": 207,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.subplot(3,2,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x1 = np.array([1,2,3,1,5,6,5,5,6,7,8,9,7,9])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x2 = np.array([1,3,2,2,8,6,7,6,7,1,2,1,1,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = np.array(zip(x1,x2)).reshape(len(x1),2) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 在1号子图中作出原始数据点阵的分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 10)"
      ]
     },
     "execution_count": 212,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.xlim([0,10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 10)"
      ]
     },
     "execution_count": 213,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.ylim([0,10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x11c33f650>"
      ]
     },
     "execution_count": 214,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.title('Instance')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 215,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x11a2fe0d0>"
      ]
     },
     "execution_count": 215,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.scatter(x1,x2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "colors = ['b','g','r','c','m','y','k','b']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "markers = ['o','s','D','v','^','p','*','+']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "clusters = [2,3,4,5,8]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "subplot_counter = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sc_scores=[]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "metadata": {},
   "outputs": [],
   "source": [
    "for t  in clusters:\n",
    "    subplot_counter+=1\n",
    "    plt.subplot(3,2,subplot_counter)\n",
    "    kmeans_model = KMeans(n_clusters=t).fit(X)\n",
    "    for i,l in enumerate(kmeans_model.labels_):\n",
    "            plt.plot(x1[i],x2[i],color=colors[l],marker=markers[l],ls='None')\n",
    "    plt.xlim([0,10])\n",
    "    plt.ylim([0,10])\n",
    "    sc_score = silhouette_score(X,kmeans_model.labels_,metric='euclidean')\n",
    "    \n",
    "    sc_scores.append(sc_score)\n",
    "    \n",
    "    plt.title('k=%s,silhouette coefficient=%0.03f'%(t,sc_score))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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mbcPITexPehuGYRjliTkMwzAMIxTmMAzDMIxQmMMwDMMwQhH5g3tGtPS5tw/r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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c260610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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9mrBg/V76vbyIrfuOex3LBDE3BSNRRKY6p4+uFJGpgJt5UGsB/p3Sdjnrcuoq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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11148e8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plt.plot(clusters,sc_scores,'bx-')\n",
    "plt.figure()\n",
    "plt.plot(clusters, sc_scores, '*-')\n",
    "plt.xlabel('Number of Clusters')\n",
    "plt.ylabel('Silhouette Coefficient Score')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 244,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.spatial.distance import cdist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "cluster1 = np.random.uniform(0.5,1.5,(2,10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "cluster2 = np.random.uniform(5.5,6.5,(2,10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "cluster3 = np.random.uniform(3.0,4.0,(2,10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = np.hstack((cluster1,cluster2,cluster3)).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 235,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x11a490f10>"
      ]
     },
     "execution_count": 235,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.scatter(X[:,0],X[:,1])\n",
    "plt.xlabel('x1')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 236,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x111876ad0>"
      ]
     },
     "execution_count": 236,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.ylabel('x2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 237,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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mZ9+02gHLmfcAellfB36nbZdW7Zjz3yhWsgOWvj+AXtbXq3SGB4dVm681fLyT65ec/4bQ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\n4cenr7U/AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1118fd610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "K = range(1,10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 240,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "meandistortions=[]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 245,
   "metadata": {},
   "outputs": [],
   "source": [
    "for k in K:\n",
    "    kmeans = KMeans(n_clusters=k)\n",
    "    kmeans.fit(X)\n",
    "    meandistortions.append(sum(np.min(cdist(X,kmeans.cluster_centers_,'euclidean'),axis=1))/X.shape[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 246,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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lRScxs0riolCldtoJRoxI13F+//2i05hZpXBRqGJjxsCrr8LVVxedxMwqRVmL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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1118be2d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(K,meandistortions,'bx-')\n",
    "plt.xlabel('K')\n",
    "plt.ylabel('Average Dispersion')\n",
    "plt.title('Selecting K whith the Elbow Method')\n",
    "plt.show()"
   ]
  },
  {
   "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
}