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$k$-近邻算法（kNN）的工作原理：存在一个训练样本集，样本集中的每个数据都存在标签，即我们知道样本集中每一数据与所属分类的对于关系。输入没有标签的新数据后，将新数据的每一个特征与样本集中数据对应的特征进行比较，然后算法提取样本集中特征最相似数据（最近邻）的分类标签。一般来说，我们只选择样本数据集中前 $k$ 个最相似的数据，这就是$k$-近邻算法中$k$的出处，通常$k$是不大于20的整数。最后，选择$k$个最相似的数据中出现次数最多的分类，作为新数据的分类。 |
1. Putting the kNN classification algorithm into action
For every point in our dataset: calculate the distance between inX and the current point sort the distances in increasing order take k items with lowest distances to inX find the majority class among these items return the majority class as our prediction for the class of inX
一个简单的例子：kNN.py
# coding=utf-8 from numpy import * import operator def createDataSet(): group = array([[1.0,1.1], [1.0,1.0], [0,0], [0,0.1]]) labels = ['A', 'A', 'B', 'B'] return group, labels def classify0(inX, dataSet, labels, k): dataSetSize = dataSet.shape[0] diffMat = tile(inX, (dataSetSize,1)) - dataSet sqDiffMat = diffMat**2 sqDistances = sqDiffMat.sum(axis=1) # 按行求和 distances = sqDistances**0.5 sortedDistIndicies = distances.argsort() # 将索引按照距离从小到大顺序排列 classCount={} # 以dict形式存储 for i in range(k): voteIlabel = labels[sortedDistIndicies[i]] # 第i最靠近的样本的标签 # dict是按照key-value的形式构成的，classCount.get(voteIlabel,0)是取出classCount中key是voteIlabel的value，如果key不存在，则定义返回0 classCount[voteIlabel] = classCount.get(voteIlabel,0) +1 # classCount.items()以(key, value) tuple 形式返回list sortedClassCount = sorted(classCount.items(), key=operator.itemgetter(1), reverse=True) return sortedClassCount[0][0] group, labels = createDataSet() label = classify0([0.2,0.2], group, labels, 3) print label
createDataSet() 函数为我们准备了四个简单的训练数据。
classify0() 函数是一个简单的$k$-近邻算法实现，函数有四个参数：待预测样本的输入特征inX，训练样本集特征集合dataSet，训练样本集标签向量labels，最近邻数目$k$。
2. Example: improving matches from a dating site with kNN
Example: using kNN on results from a dating site 1. Collect: Text file provided. 2. Prepare: Parse a text file in Python. 3. Analyze: Use Matplotlib to make 2D plots of our data. 4. Train: Doesn’t apply to the kNN algorithm. 5. Test: Write a function to use some portion of the data Hellen gave us as test examples. The test examples are classified against the non-test examples. If the predicted class doesn’t match the real class, we’ll count that as an error. 6. Use: Build a simple command-line program Hellen can use to predict whether she’ll like someone based on a few inputs.
2.1 Prepare: parsing data from a text file
所有训练数据存放在文本文件datingTestSet.txt中，样本容量大小为1000。样本主要包含以下三种特征：
■ Number of frequent flyer miles earned per year
■ Percentage of time spent playing video games
■ Liters of ice cream consumed per week
设计分类器之前，我们首先要把原始数据读入到python中。在kNN.py中创建名为file2matrix的函数，以此来处理原始数据。该函数的输入为文件名字符串，输出为训练样本矩阵和类标签向量。
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largeDoses 12556 3.690342 0.462281 smallDoses 39432 3.563706 0.242019 didntLike 38010 1.065870 1.141569 didntLike 69306 6.683796 1.456317 didntLike 38000 1.712874 0.243945 didntLike 46321 13.109929 1.280111 largeDoses 66293 11.327910 0.780977 didntLike 22730 4.545711 1.233254 didntLike 5952 3.367889 0.468104 smallDoses 72308 8.326224 0.567347 didntLike 60338 8.978339 1.442034 didntLike 13301 5.655826 1.582159 smallDoses 27884 8.855312 0.570684 largeDoses 11188 6.649568 0.544233 smallDoses 56796 3.966325 0.850410 didntLike 8571 1.924045 1.664782 smallDoses 4914 6.004812 0.280369 smallDoses 10784 0.000000 0.375849 smallDoses 39296 9.923018 0.092192 largeDoses 13113 2.389084 0.119284 smallDoses 70204 13.663189 0.133251 didntLike 46813 11.434976 0.321216 largeDoses 11697 0.358270 1.292858 smallDoses 44183 9.598873 0.223524 largeDoses 2225 6.375275 0.608040 smallDoses 29066 11.580532 0.458401 largeDoses 4245 5.319324 1.598070 smallDoses 34379 4.324031 1.603481 didntLike 44441 2.358370 1.273204 didntLike 2022 0.000000 1.182708 smallDoses 26866 12.824376 0.890411 largeDoses 57070 1.587247 1.456982 didntLike 32932 8.510324 1.520683 largeDoses 51967 10.428884 1.187734 largeDoses 44432 8.346618 0.042318 largeDoses 67066 7.541444 0.809226 didntLike 17262 2.540946 1.583286 smallDoses 79728 9.473047 0.692513 didntLike 14259 0.352284 0.474080 smallDoses 6122 0.000000 0.589826 smallDoses 76879 12.405171 0.567201 didntLike 11426 4.126775 0.871452 smallDoses 2493 0.034087 0.335848 smallDoses 19910 1.177634 0.075106 smallDoses 10939 0.000000 0.479996 smallDoses 17716 0.994909 0.611135 smallDoses 31390 11.053664 1.180117 largeDoses 20375 0.000000 1.679729 smallDoses 26309 2.495011 1.459589 didntLike 33484 11.516831 0.001156 largeDoses 45944 9.213215 0.797743 largeDoses 4249 5.332865 0.109288 smallDoses 6089 0.000000 1.689771 smallDoses 7513 0.000000 1.126053 smallDoses 27862 12.640062 1.690903 largeDoses 39038 2.693142 1.317518 didntLike 19218 3.328969 0.268271 smallDoses 62911 7.193166 1.117456 didntLike 77758 6.615512 1.521012 didntLike 27940 8.000567 0.835341 largeDoses 2194 4.017541 0.512104 smallDoses 37072 13.245859 0.927465 largeDoses 15585 5.970616 0.813624 smallDoses 25577 11.668719 0.886902 largeDoses 8777 4.283237 1.272728 smallDoses 29016 10.742963 0.971401 largeDoses 21910 12.326672 1.592608 largeDoses 12916 0.000000 0.344622 smallDoses 10976 0.000000 0.922846 smallDoses 79065 10.602095 0.573686 didntLike 36759 10.861859 1.155054 largeDoses 50011 1.229094 1.638690 didntLike 1155 0.410392 1.313401 smallDoses 71600 14.552711 0.616162 didntLike 30817 14.178043 0.616313 largeDoses 54559 14.136260 0.362388 didntLike 29764 0.093534 1.207194 didntLike 69100 10.929021 0.403110 didntLike 47324 11.432919 0.825959 largeDoses 73199 9.134527 0.586846 didntLike 44461 5.071432 1.421420 didntLike 45617 11.460254 1.541749 largeDoses 28221 11.620039 1.103553 largeDoses 7091 4.022079 0.207307 smallDoses 6110 3.057842 1.631262 smallDoses 79016 7.782169 0.404385 didntLike 18289 7.981741 0.929789 largeDoses 43679 4.601363 0.268326 didntLike 22075 2.595564 1.115375 didntLike 23535 10.049077 0.391045 largeDoses 25301 3.265444 1.572970 smallDoses 32256 11.780282 1.511014 largeDoses 36951 3.075975 0.286284 didntLike 31290 1.795307 0.194343 didntLike 38953 11.106979 0.202415 largeDoses 35257 5.994413 0.800021 didntLike 25847 9.706062 1.012182 largeDoses 32680 10.582992 0.836025 largeDoses 62018 7.038266 1.458979 didntLike 9074 0.023771 0.015314 smallDoses 33004 12.823982 0.676371 largeDoses 44588 3.617770 0.493483 didntLike 32565 8.346684 0.253317 largeDoses 38563 6.104317 0.099207 didntLike 75668 16.207776 0.584973 didntLike 9069 6.401969 1.691873 smallDoses 53395 2.298696 0.559757 didntLike 28631 7.661515 0.055981 largeDoses 71036 6.353608 1.645301 didntLike 71142 10.442780 0.335870 didntLike 37653 3.834509 1.346121 didntLike 76839 10.998587 0.584555 didntLike 9916 2.695935 1.512111 smallDoses 38889 3.356646 0.324230 didntLike 39075 14.677836 0.793183 largeDoses 48071 1.551934 0.130902 didntLike 7275 2.464739 0.223502 smallDoses 41804 1.533216 1.007481 didntLike 35665 12.473921 0.162910 largeDoses 67956 6.491596 0.032576 didntLike 41892 10.506276 1.510747 largeDoses 38844 4.380388 0.748506 didntLike 74197 13.670988 1.687944 didntLike 14201 8.317599 0.390409 smallDoses 3908 0.000000 0.556245 smallDoses 2459 0.000000 0.290218 smallDoses 32027 10.095799 1.188148 largeDoses 12870 0.860695 1.482632 smallDoses 9880 1.557564 0.711278 smallDoses 72784 10.072779 0.756030 didntLike 17521 0.000000 0.431468 smallDoses 50283 7.140817 0.883813 largeDoses 33536 11.384548 1.438307 largeDoses 9452 3.214568 1.083536 smallDoses 37457 11.720655 0.301636 largeDoses 17724 6.374475 1.475925 largeDoses 43869 5.749684 0.198875 largeDoses 264 3.871808 0.552602 smallDoses 25736 8.336309 0.636238 largeDoses 39584 9.710442 1.503735 largeDoses 31246 1.532611 1.433898 didntLike 49567 9.785785 0.984614 largeDoses 7052 2.633627 1.097866 smallDoses 35493 9.238935 0.494701 largeDoses 10986 1.205656 1.398803 smallDoses 49508 3.124909 1.670121 didntLike 5734 7.935489 1.585044 smallDoses 65479 12.746636 1.560352 didntLike 77268 10.732563 0.545321 didntLike 28490 3.977403 0.766103 didntLike 13546 4.194426 0.450663 smallDoses 37166 9.610286 0.142912 largeDoses 16381 4.797555 1.260455 smallDoses 10848 1.615279 0.093002 smallDoses 35405 4.614771 1.027105 didntLike 15917 0.000000 1.369726 smallDoses 6131 0.608457 0.512220 smallDoses 67432 6.558239 0.667579 didntLike 30354 12.315116 0.197068 largeDoses 69696 7.014973 1.494616 didntLike 33481 8.822304 1.194177 largeDoses 43075 10.086796 0.570455 largeDoses 38343 7.241614 1.661627 largeDoses 14318 4.602395 1.511768 smallDoses 5367 7.434921 0.079792 smallDoses 37894 10.467570 1.595418 largeDoses 36172 9.948127 0.003663 largeDoses 40123 2.478529 1.568987 didntLike 10976 5.938545 0.878540 smallDoses 12705 0.000000 0.948004 smallDoses 12495 5.559181 1.357926 smallDoses 35681 9.776654 0.535966 largeDoses 46202 3.092056 0.490906 didntLike 11505 0.000000 1.623311 smallDoses 22834 4.459495 0.538867 didntLike 49901 8.334306 1.646600 largeDoses 71932 11.226654 0.384686 didntLike 13279 3.904737 1.597294 smallDoses 49112 7.038205 1.211329 largeDoses 77129 9.836120 1.054340 didntLike 37447 1.990976 0.378081 didntLike 62397 9.005302 0.485385 didntLike 0 1.772510 1.039873 smallDoses 15476 0.458674 0.819560 smallDoses 40625 10.003919 0.231658 largeDoses 36706 0.520807 1.476008 didntLike 28580 10.678214 1.431837 largeDoses 25862 4.425992 1.363842 didntLike 63488 12.035355 0.831222 didntLike 33944 10.606732 1.253858 largeDoses 30099 1.568653 0.684264 didntLike 13725 2.545434 0.024271 smallDoses 36768 10.264062 0.982593 largeDoses 64656 9.866276 0.685218 didntLike 14927 0.142704 0.057455 smallDoses 43231 9.853270 1.521432 largeDoses 66087 6.596604 1.653574 didntLike 19806 2.602287 1.321481 smallDoses 41081 10.411776 0.664168 largeDoses 10277 7.083449 0.622589 smallDoses 7014 2.080068 1.254441 smallDoses 17275 0.522844 1.622458 smallDoses 31600 10.362000 1.544827 largeDoses 59956 3.412967 1.035410 didntLike 42181 6.796548 1.112153 largeDoses 51743 4.092035 0.075804 didntLike 5194 2.763811 1.564325 smallDoses 30832 12.547439 1.402443 largeDoses 7976 5.708052 1.596152 smallDoses 14602 4.558025 0.375806 smallDoses 41571 11.642307 0.438553 largeDoses 55028 3.222443 0.121399 didntLike 5837 4.736156 0.029871 smallDoses 39808 10.839526 0.836323 largeDoses 20944 4.194791 0.235483 smallDoses 22146 14.936259 0.888582 largeDoses 42169 3.310699 1.521855 didntLike 7010 2.971931 0.034321 smallDoses 3807 9.261667 0.537807 smallDoses 29241 7.791833 1.111416 largeDoses 52696 1.480470 1.028750 didntLike 42545 3.677287 0.244167 didntLike 24437 2.202967 1.370399 didntLike 16037 5.796735 0.935893 smallDoses 8493 3.063333 0.144089 smallDoses 68080 11.233094 0.492487 didntLike 59016 1.965570 0.005697 didntLike 11810 8.616719 0.137419 smallDoses 68630 6.609989 1.083505 didntLike 7629 1.712639 1.086297 smallDoses 71992 10.117445 1.299319 didntLike 13398 0.000000 1.104178 smallDoses 26241 9.824777 1.346821 largeDoses 11160 1.653089 0.980949 smallDoses 76701 18.178822 1.473671 didntLike 32174 6.781126 0.885340 largeDoses 45043 8.206750 1.549223 largeDoses 42173 10.081853 1.376745 largeDoses 69801 6.288742 0.112799 didntLike 41737 3.695937 1.543589 didntLike 46979 6.726151 1.069380 largeDoses 79267 12.969999 1.568223 didntLike 4615 2.661390 1.531933 smallDoses 32907 7.072764 1.117386 largeDoses 37444 9.123366 1.318988 largeDoses 569 3.743946 1.039546 smallDoses 8723 2.341300 0.219361 smallDoses 6024 0.541913 0.592348 smallDoses 52252 2.310828 1.436753 didntLike 8358 6.226597 1.427316 smallDoses 26166 7.277876 0.489252 largeDoses 18471 0.000000 0.389459 smallDoses 3386 7.218221 1.098828 smallDoses 41544 8.777129 1.111464 largeDoses 10480 2.813428 0.819419 smallDoses 5894 2.268766 1.412130 smallDoses 7273 6.283627 0.571292 smallDoses 22272 7.520081 1.626868 largeDoses 31369 11.739225 0.027138 largeDoses 10708 3.746883 0.877350 smallDoses 69364 12.089835 0.521631 didntLike 37760 12.310404 0.259339 largeDoses 13004 0.000000 0.671355 smallDoses 37885 2.728800 0.331502 didntLike 52555 10.814342 0.607652 largeDoses 38997 12.170268 0.844205 largeDoses 69698 6.698371 0.240084 didntLike 11783 3.632672 1.643479 smallDoses 47636 10.059991 0.892361 largeDoses 15744 1.887674 0.756162 smallDoses 69058 8.229125 0.195886 didntLike 33057 7.817082 0.476102 largeDoses 28681 12.277230 0.076805 largeDoses 34042 10.055337 1.115778 largeDoses 29928 3.596002 1.485952 didntLike 9734 2.755530 1.420655 smallDoses 7344 7.780991 0.513048 smallDoses 7387 0.093705 0.391834 smallDoses 33957 8.481567 0.520078 largeDoses 9936 3.865584 0.110062 smallDoses 36094 9.683709 0.779984 largeDoses 39835 10.617255 1.359970 largeDoses 64486 7.203216 1.624762 didntLike 0 7.601414 1.215605 smallDoses 39539 1.386107 1.417070 didntLike 66972 9.129253 0.594089 didntLike 15029 1.363447 0.620841 smallDoses 44909 3.181399 0.359329 didntLike 38183 13.365414 0.217011 largeDoses 37372 4.207717 1.289767 didntLike 0 4.088395 0.870075 smallDoses 17786 3.327371 1.142505 smallDoses 39055 1.303323 1.235650 didntLike 37045 7.999279 1.581763 largeDoses 6435 2.217488 0.864536 smallDoses 72265 7.751808 0.192451 didntLike 28152 14.149305 1.591532 largeDoses 25931 8.765721 0.152808 largeDoses 7538 3.408996 0.184896 smallDoses 1315 1.251021 0.112340 smallDoses 12292 6.160619 1.537165 smallDoses 49248 1.034538 1.585162 didntLike 9025 0.000000 1.034635 smallDoses 13438 2.355051 0.542603 smallDoses 69683 6.614543 0.153771 didntLike 25374 10.245062 1.450903 largeDoses 55264 3.467074 1.231019 didntLike 38324 7.487678 1.572293 largeDoses 69643 4.624115 1.185192 didntLike 44058 8.995957 1.436479 largeDoses 41316 11.564476 0.007195 largeDoses 29119 3.440948 0.078331 didntLike 51656 1.673603 0.732746 didntLike 3030 4.719341 0.699755 smallDoses 35695 10.304798 1.576488 largeDoses 1537 2.086915 1.199312 smallDoses 9083 6.338220 1.131305 smallDoses 47744 8.254926 0.710694 largeDoses 71372 16.067108 0.974142 didntLike 37980 1.723201 0.310488 didntLike 42385 3.785045 0.876904 didntLike 22687 2.557561 0.123738 didntLike 39512 9.852220 1.095171 largeDoses 11885 3.679147 1.557205 smallDoses 4944 9.789681 0.852971 smallDoses 73230 14.958998 0.526707 didntLike 17585 11.182148 1.288459 largeDoses 68737 7.528533 1.657487 didntLike 13818 5.253802 1.378603 smallDoses 31662 13.946752 1.426657 largeDoses 86686 15.557263 1.430029 didntLike 43214 12.483550 0.688513 largeDoses 24091 2.317302 1.411137 didntLike 52544 10.069724 0.766119 largeDoses 61861 5.792231 1.615483 didntLike 47903 4.138435 0.475994 didntLike 37190 12.929517 0.304378 largeDoses 6013 9.378238 0.307392 smallDoses 27223 8.361362 1.643204 largeDoses 69027 7.939406 1.325042 didntLike 78642 10.735384 0.705788 didntLike 30254 11.592723 0.286188 largeDoses 21704 10.098356 0.704748 largeDoses 34985 9.299025 0.545337 largeDoses 31316 11.158297 0.218067 largeDoses 76368 16.143900 0.558388 didntLike 27953 10.971700 1.221787 largeDoses 152 0.000000 0.681478 smallDoses 9146 3.178961 1.292692 smallDoses 75346 17.625350 0.339926 didntLike 26376 1.995833 0.267826 didntLike 35255 10.640467 0.416181 largeDoses 19198 9.628339 0.985462 largeDoses 12518 4.662664 0.495403 smallDoses 25453 5.754047 1.382742 smallDoses 12530 0.000000 0.037146 smallDoses 62230 9.334332 0.198118 didntLike 9517 3.846162 0.619968 smallDoses 71161 10.685084 0.678179 didntLike 1593 4.752134 0.359205 smallDoses 33794 0.697630 0.966786 didntLike 39710 10.365836 0.505898 largeDoses 16941 0.461478 0.352865 smallDoses 69209 11.339537 1.068740 didntLike 4446 5.420280 0.127310 smallDoses 9347 3.469955 1.619947 smallDoses 55635 8.517067 0.994858 largeDoses 65889 8.306512 0.413690 didntLike 10753 2.628690 0.444320 smallDoses 7055 0.000000 0.802985 smallDoses 7905 0.000000 1.170397 smallDoses 53447 7.298767 1.582346 largeDoses 9194 7.331319 1.277988 smallDoses 61914 9.392269 0.151617 didntLike 15630 5.541201 1.180596 smallDoses 79194 15.149460 0.537540 didntLike 12268 5.515189 0.250562 smallDoses 33682 7.728898 0.920494 largeDoses 26080 11.318785 1.510979 largeDoses 19119 3.574709 1.531514 smallDoses 30902 7.350965 0.026332 largeDoses 63039 7.122363 1.630177 didntLike 51136 1.828412 1.013702 didntLike 35262 10.117989 1.156862 largeDoses 42776 11.309897 0.086291 largeDoses 64191 8.342034 1.388569 didntLike 15436 0.241714 0.715577 smallDoses 14402 10.482619 1.694972 smallDoses 6341 9.289510 1.428879 smallDoses 14113 4.269419 0.134181 smallDoses 6390 0.000000 0.189456 smallDoses 8794 0.817119 0.143668 smallDoses 43432 1.508394 0.652651 didntLike 38334 9.359918 0.052262 largeDoses 34068 10.052333 0.550423 largeDoses 30819 11.111660 0.989159 largeDoses 22239 11.265971 0.724054 largeDoses 28725 10.383830 0.254836 largeDoses 57071 3.878569 1.377983 didntLike 72420 13.679237 0.025346 didntLike 28294 10.526846 0.781569 largeDoses 9896 0.000000 0.924198 smallDoses 65821 4.106727 1.085669 didntLike 7645 8.118856 1.470686 smallDoses 71289 7.796874 0.052336 didntLike 5128 2.789669 1.093070 smallDoses 13711 6.226962 0.287251 smallDoses 22240 10.169548 1.660104 largeDoses 15092 0.000000 1.370549 smallDoses 5017 7.513353 0.137348 smallDoses 10141 8.240793 0.099735 smallDoses 35570 14.612797 1.247390 largeDoses 46893 3.562976 0.445386 didntLike 8178 3.230482 1.331698 smallDoses 55783 3.612548 1.551911 didntLike 1148 0.000000 0.332365 smallDoses 10062 3.931299 0.487577 smallDoses 74124 14.752342 1.155160 didntLike 66603 10.261887 1.628085 didntLike 11893 2.787266 1.570402 smallDoses 50908 15.112319 1.324132 largeDoses 39891 5.184553 0.223382 largeDoses 65915 3.868359 0.128078 didntLike 65678 3.507965 0.028904 didntLike 62996 11.019254 0.427554 didntLike 36851 3.812387 0.655245 didntLike 36669 11.056784 0.378725 largeDoses 38876 8.826880 1.002328 largeDoses 26878 11.173861 1.478244 largeDoses 46246 11.506465 0.421993 largeDoses 12761 7.798138 0.147917 largeDoses 35282 10.155081 1.370039 largeDoses 68306 10.645275 0.693453 didntLike 31262 9.663200 1.521541 largeDoses 34754 10.790404 1.312679 largeDoses 13408 2.810534 0.219962 smallDoses 30365 9.825999 1.388500 largeDoses 10709 1.421316 0.677603 smallDoses 24332 11.123219 0.809107 largeDoses 45517 13.402206 0.661524 largeDoses 6178 1.212255 0.836807 smallDoses 10639 1.568446 1.297469 smallDoses 29613 3.343473 1.312266 didntLike 22392 5.400155 0.193494 didntLike 51126 3.818754 0.590905 didntLike 53644 7.973845 0.307364 largeDoses 51417 9.078824 0.734876 largeDoses 24859 0.153467 0.766619 didntLike 61732 8.325167 0.028479 didntLike 71128 7.092089 1.216733 didntLike 27276 5.192485 1.094409 largeDoses 30453 10.340791 1.087721 largeDoses 18670 2.077169 1.019775 smallDoses 70600 10.151966 0.993105 didntLike 12683 0.046826 0.809614 smallDoses 81597 11.221874 1.395015 didntLike 69959 14.497963 1.019254 didntLike 8124 3.554508 0.533462 smallDoses 18867 3.522673 0.086725 smallDoses 80886 14.531655 0.380172 didntLike 55895 3.027528 0.885457 didntLike 31587 1.845967 0.488985 didntLike 10591 10.226164 0.804403 largeDoses 70096 10.965926 1.212328 didntLike 53151 2.129921 1.477378 didntLike 11992 0.000000 1.606849 smallDoses 33114 9.489005 0.827814 largeDoses 7413 0.000000 1.020797 smallDoses 10583 0.000000 1.270167 smallDoses 58668 6.556676 0.055183 didntLike 35018 9.959588 0.060020 largeDoses 70843 7.436056 1.479856 didntLike 14011 0.404888 0.459517 smallDoses 35015 9.952942 1.650279 largeDoses 70839 15.600252 0.021935 didntLike 3024 2.723846 0.387455 smallDoses 5526 0.513866 1.323448 smallDoses 5113 0.000000 0.861859 smallDoses 20851 7.280602 1.438470 smallDoses 40999 9.161978 1.110180 largeDoses 15823 0.991725 0.730979 smallDoses 35432 7.398380 0.684218 largeDoses 53711 12.149747 1.389088 largeDoses 64371 9.149678 0.874905 didntLike 9289 9.666576 1.370330 smallDoses 60613 3.620110 0.287767 didntLike 18338 5.238800 1.253646 smallDoses 22845 14.715782 1.503758 largeDoses 74676 14.445740 1.211160 didntLike 34143 13.609528 0.364240 largeDoses 14153 3.141585 0.424280 smallDoses 9327 0.000000 0.120947 smallDoses 18991 0.454750 1.033280 smallDoses 9193 0.510310 0.016395 smallDoses 2285 3.864171 0.616349 smallDoses 9493 6.724021 0.563044 smallDoses 2371 4.289375 0.012563 smallDoses 13963 0.000000 1.437030 smallDoses 2299 3.733617 0.698269 smallDoses 5262 2.002589 1.380184 smallDoses 4659 2.502627 0.184223 smallDoses 17582 6.382129 0.876581 smallDoses 27750 8.546741 0.128706 largeDoses 9868 2.694977 0.432818 smallDoses 18333 3.951256 0.333300 smallDoses 3780 9.856183 0.329181 smallDoses 18190 2.068962 0.429927 smallDoses 11145 3.410627 0.631838 smallDoses 68846 9.974715 0.669787 didntLike 26575 10.650102 0.866627 largeDoses 48111 9.134528 0.728045 largeDoses 43757 7.882601 1.332446 largeDoses
这里我们还需要先把标签替换成数字型的以便识别，largeDoses -> 3, smallDoses -> 2, didntLike -> 1
def file2matrix(filename): fr = open(filename) arrayOLines = fr.readlines() numberOfLines = len(arrayOLines) returnMat = zeros((numberOfLines,3)) classLabelVector = [] index = 0; for line in arrayOLines: line = line.strip() # 去掉所有的回车符 listFromLine = line.split(' ') # 按照tab字符分割成list returnMat[index,:] = listFromLine[0:3] # 我们必须明确地将标签值转换成整型，否则python语言会将其当做字符串处理 classLabelVector.append(int(listFromLine[-1])) index += 1 return returnMat, classLabelVector
接下来我们可以采用图形化的方式直观的展示数据。
2.2 Analyze: creating scatter plots with Matplotlib
我们在cmd中定位到源码所在路径，然后绘制原始数据的散点图：
>>> import kNN >>> datingDataMat, datingLabels = kNN.file2matrix('datingTestSet2.txt') >>> import matplotlib >>> import matplotlib.pyplot as plt >>> fig = plt.figure() >>> ax = fig.add_subplot(111) >>> ax.scatter(datingDataMat[:,1], datingDataMat[:,2]) >>> plt.show()
由于没有使用样本分类的label，我们很难从上图看到任何有用的数据模式信息。为了更好的理解数据信息，我们可以使用色彩或者其他记号来区别标记
datingDataMat, datingLabels = file2matrix('datingTestSet2.txt') from matplotlib.font_manager import FontProperties import matplotlib.pyplot as plt zhfont1 = FontProperties(fname='C:WindowsFontssimkai.ttf',size=16) fig = plt.figure() ax = fig.add_subplot(111) ax.scatter(datingDataMat[:,1], datingDataMat[:,2], 15.0*array(datingLabels), 15.0*array(datingLabels)) plt.xlabel(u'玩游戏所耗时间百分比', fontproperties=zhfont1) plt.ylabel(u'每周消费的冰淇淋公升数', fontproperties=zhfont1) plt.show()
2.3 Prepare: normalizing numeric values
newValue = (oldValue-min)/(max-min)
def autoNorm(dataSet): minVals = dataSet.min(0) # 比较每行获得特征矩阵最小值 maxVals = dataSet.max(0) # 比较每行获得特征矩阵最大值 ranges = maxVals - minVals normDataSet = zeros(shape(dataSet)) m = dataSet.shape[0] # 特征向量行数 normDataSet = dataSet - tile(minVals, (m,1)) # tile函数将变量内容复制成dataSet同样大小的矩阵 normDataSet = normDataSet/tile(ranges, (m,1)) return normDataSet, ranges, minVals
2.4 Test: testing the classifier as a whole program
机器学习算法一个很重要的工作就是评估算法的正确率，通常我们只提供已有数据的90%作为训练样本来训练分类器，而使用其余的10%数据去测试分类器，检测分类器的正确率。
这里我们可以随机选择这10%的测试样本，也可以顺序选择。
最终我们可以选择错误率来检测分类器的性能。
def datingClassTest(): hoRatio = 0.10 # 测试集所占比例 datingDataMat, datingLabels = file2matrix('datingTestSet2.txt') # 读入样本集 normMat ,ranges, minVals = autoNorm(datingDataMat) # 特征归一化 m = normMat.shape[0] numTestVecs = int(m*hoRatio) errorCount = 0.0 # 对于每个测试样本，测试结果，并统计错误次数 for i in range(numTestVecs): classifierResult = classify0(normMat[i,:], normMat[numTestVecs:m,:], datingLabels[numTestVecs:m], 3) print "the classifier came back with: %d, the real answer is: %d" % (classifierResult, datingLabels[i]) if classifierResult != datingLabels[i]: errorCount += 1.0 print "the total error rate is: %f" % (errorCount/float(numTestVecs))
2.5 Use: putting together a useful system
def classifyPerson(): resultList = ['not at all', 'in small doses', 'in large doses'] percentTats = float(raw_input("percentage of time spent playing video games?")) ffMiles = float(raw_input("ferquent fliter miles earned per year?")) iceCream = float(raw_input("liters of ice cream consumed per year?")) datingDataMat, datingLabels = file2matrix('datingTestSet2.txt') # 读入样本集 normMat, ranges, minVals = autoNorm(datingDataMat) # 特征归一化 inArr = array([ffMiles, percentTats, iceCream]) # 预测样本特征 classifierResult = classify0((inArr-minVals)/ranges, normMat, datingLabels, 3) print "You will probably like the person: ", resultList[classifierResult-1]
到此为止，一个简单的约会对象匹配算法就完成了！
3. Example: a handwriting recognition system
3.1 Prepare: converting images into test vectors
为了简单起见，这里构造的系统只能识别数字0-9。需要识别的数字已经使用图形处理软件，处理成具有相同的色彩和大小：宽高是32像素$ imes$32像素的黑白图像。尽管采用文本格式存储图形不能有效地利用内存空间，但是为了方便理解，我们还是将图像转换为文本格式。
def img2vector(filename): returnVect = zeros((1,1024)) fr = open(filename) for i in range(32): lineStr = fr.readline() # 读取一行数据 for j in range(32): returnVect[0,32*i+j] = int(lineStr[j]) # 数据默认都是以字符形式读入，需要强制转换 return returnVect testVector = img2vector('testDigits/0_13.txt') print testVector[0,0:31]
这样我们就可以借助于之前的kNN算法代码测试了
Test: kNN on handwritten digits
from os import listdir def handwritingClasstest(): hwLabels = [] trainingFileList = listdir('trainingDigits') # 获得路径下所有文件名 m = len(trainingFileList) # 训练样本数 trainingMat = zeros((m,1024)) for i in range(m): fileNameStr = trainingFileList[i] fileStr = fileNameStr.split('.')[0] classNumStr = int(fileStr.split('_')[0]) # 训练样本标签 hwLabels.append(classNumStr) trainingMat[i,:] = img2vector('trainingDigits/%s' % fileNameStr) # 读取样本 testFileList = listdir('testDigits') errorCount = 0.0 mTest = len(testFileList) # 测试样本数 for i in range(mTest): fileNameStr = testFileList[i] fileStr = fileNameStr.split('.')[0] classNumStr = int(fileStr.split('_')[0]) # 测试样本标签 vectorUnderTest = img2vector('testDigits/%s' % fileNameStr) classifierResult = classify0(vectorUnderTest, trainingMat, hwLabels, 3) # 预测样本类别 print "the classifier came back with: %d, the real answer is: %d" % (classifierResult, classNumStr) if classifierResult != classNumStr: errorCount += 1.0 # 统计错误分类数 print " the total number of errors is: %d" % errorCount print " the total error rate is: %f" % (errorCount/mTest) handwritingClasstest()
实际使用这个算法是，算法的执行效率并不高。因为预测时，测试样本要和所有样本做距离计算。后面我们会使用一种$k$决策树算法来节省计算开销。