k近邻算法

《机器学习实战》学习总结

一言以蔽之

计算待分类点与训练集中每个点之间的距离，选取前k个最近的点，
其中出现频率最高的类别就是待分类点的类别。

伪代码

1.计算训练集中的点到当前点之间的距离；
2.按照距离递增顺序排序；
3.选取与当前点距离最小的k个点；
4.确定前k个点所在类别的出现频率；
5.返回前k个点出现频率最高的类别作为当前点的预测分类。

Pros & Cons

优点：精度高，对异常值不敏感，无数据输入假定。
缺点：计算复杂度高，空间复杂度高。
适用数据范围：数值型和标称型。

python代码实现

• 数据预处理
• 模型训练（KNN中没有该步骤）
• 性能测试
• 算法应用

# -*- coding: utf-8 -*-# kNN: k Nearest Neighbors#from numpy import *import operatorfrom os import listdir# knn algorithmdef classify0(inX,dataSet,labels,k):    dataSetSize = dataSet.shape[0]    diffMat = tile(inX, (dataSetSize,1)) - dataSet    sqDiffMat = diffMat**2    sqDistances = sqDiffMat.sum(axis=1)    distances = sqDistances**0.5    sortedDistIndicies = distances.argsort()    classCount={}    for i in range(k):        voteIlabel = labels[sortedDistIndicies[i]]        classCount[voteIlabel] = classCount.get(voteIlabel,0) + 1    sortedClassCount = sorted(classCount.iteritems(), key=operator.itemgetter(1), reverse=True)    return sortedClassCount[0][0]def file2matrix(filename):    fr = open(filename)    numberOfLines = len(fr.readlines())         #get the number of lines in the file    returnMat = zeros((numberOfLines,3))        #prepare matrix to return    classLabelVector = []                       #prepare labels return    fr = open(filename)    index = 0    for line in fr.readlines():        line = line.strip()        listFromLine = line.split('\t')        returnMat[index,:] = listFromLine[0:3]        classLabelVector.append(int(listFromLine[-1]))        index += 1    return returnMat,classLabelVector## normalizationdef autoNorm(dataSet):    minVals = dataSet.min(0)    maxVals = dataSet.max(0)    ranges = maxVals - minVals    normDataSet = zeros(shape(dataSet))    m = dataSet.shape[0]    normDataSet = dataSet - tile(minVals, (m,1))    normDataSet = normDataSet/tile(ranges, (m,1))   #element wise divide    return normDataSet, ranges, minVals## dating website exampledef datingClassTest():    hoRatio = 0.10      #hold out 10%    datingDataMat,datingLabels = file2matrix('datingTestSet2.txt')       #load data setfrom file    normMat, ranges, minVals = autoNorm(datingDataMat)    m = normMat.shape[0]    numTestVecs = int(m*hoRatio)    errorCount = 0.0    for i in range(numTestVecs):        classifierResult = classify0(normMat[i,:],normMat[numTestVecs:m,:],datingLabels[numTestVecs:m],3)        print "#%d: the classifier came back with: %d, the real answer is: %d" % (i,classifierResult, datingLabels[i])        if (classifierResult != datingLabels[i]): errorCount += 1.0    print "errorCount: %d" % errorCount    print "the total error rate is: %f" % (errorCount/float(numTestVecs))## applicationdef classifyPerson():    resultList = ['not at all','in small doses','in large doses']    # require input    percentGames = float(raw_input("percentage of time spent on playing video games: "))    ffMiles = float(raw_input("frequent flier miles earned per year: "))    iceCreams = float(raw_input("liters of ice cream consumed per year "))    # training data preprocessing    datingDataMat,datingLabels = file2matrix('datingTestSet2.txt')    normMat,ranges,minVals = autoNorm(datingDataMat)    # predict input    inArr = array([ffMiles,percentGames,iceCreams])    classifierResult = classify0((inArr-minVals)/ranges,normMat,datingLabels,3)    # test data need to be normalized    print "You will probably like this persion: " , resultList[classifierResult-1]def img2vector(filename):    returnVect = zeros((1,1024))    fr = open(filename)    for i in range(32):        lineStr = fr.readline()        for j in range(32):            returnVect[0,32*i+j] = int(lineStr[j])    return returnVect## handwriting exampledef handwritingClassTest():    hwLabels = []    trainingFileList = listdir('trainingDigits')           #load the training set    m = len(trainingFileList)    trainingMat = zeros((m,1024))    for i in range(m):        fileNameStr = trainingFileList[i]        fileStr = fileNameStr.split('.')[0]     #take off .txt        classNumStr = int(fileStr.split('_')[0])        hwLabels.append(classNumStr)        trainingMat[i,:] = img2vector('trainingDigits/%s' % fileNameStr)    testFileList = listdir('testDigits')        #iterate through the test set    errorCount = 0.0    mTest = len(testFileList)    for i in range(mTest):        fileNameStr = testFileList[i]        fileStr = fileNameStr.split('.')[0]     #take off .txt        classNumStr = int(fileStr.split('_')[0])        vectorUnderTest = img2vector('testDigits/%s' % fileNameStr)        classifierResult = classify0(vectorUnderTest, trainingMat, hwLabels, 3)        print "#%d: the classifier came back with: %d, the real answer is: %d" \            % (i,classifierResult, classNumStr)        if (classifierResult != classNumStr): errorCount += 1.0    print "\nthe total number of errors is: %d" % errorCount    print "\nthe total error rate is: %f" % (errorCount/float(mTest))## mainif __name__ == '__main__':    print "\n#-------------Dating website example------------------#\n"    print "\n-----------------test-----------------"    datingClassTest()    print "\n---------------prediction-------------"    classifyPerson()    print "\n#--------------Handwriting example-------------------#\n"    print "\n-----------------test-----------------"    handwritingClassTest()

matlab代码实现

• 主程序

%% KNN: K Nearest Neighborhood% Initializationclear;close all;clc;data_file_name = 'datingTestSet2.txt';%% load datadata = load(data_file_name);trainData = data(:,1:3);y = data(:,4);%% visualizationX = trainData(:,1:2);   % plot first two featuresfigure;hold on;idx1 = find(y==1);idx2 = find(y==2);idx3 = find(y==3);plot(X(idx1,1),X(idx1,2),'k+','LineWidth',2,'MarkerSize',7);plot(X(idx2,1),X(idx2,2),'ko','MarkerFaceColor','y','MarkerSize',7);plot(X(idx3,1),X(idx3,2),'b*');hold off;%% normalizationminVals = min(trainData,[],1);maxVals = max(trainData,[],1);ranges = maxVals-minVals;normData = zeros(size(trainData));num_example = size(trainData,1);normData = trainData-repmat(minVals,[num_example,1]);normData = normData./repmat(ranges,[num_example,1]);% knn algorithm%label_pred = my_knn(inX,data,label,k);% testhold_out_ratio = 0.1;error_count = 0;k = 3;num_test = round(num_example * hold_out_ratio); % round-四舍五入；floor-朝负无穷方向舍入；ceil-正无穷；fix-0.for i = 1:num_test    label_pred = my_knn(normData(i,:),normData(num_test:num_example,:),y(num_test:num_example),k);    fprintf('#%d: the classifier came back with label: %d, the real label is: %d.\n',i,label_pred,y(i));    if(label_pred ~= y(i))        error_count = error_count + 1;    endend% evaluateerr = error_count/num_test;fprintf('error count: %d\n',error_count);fprintf('the total error rate is %.2f%%.\n',err*100);

• knn算法实现(my_knn.m)

function label_pred = my_knn(inX,data,label,k)% INPUT: （归一化之后的数据）%     inX--待预测样本%     data--训练集数据%     label--训练集类标%     k--knn参数% OUTPUT:%     待预测样本的类标row_data = size(data,1);diffMat = data - repmat(inX,[row_data,1]);sqDiffMat = diffMat.^2;sqDistance = sum(sqDiffMat,2);distance = sqrt(sqDistance);[D,I] = sort(distance);vote_label = zeros(k,1);for i = 1:k    vote_label(i) = label(I(i));endunique_label = unique(vote_label);      % 找出每个出现过的类标n = histc(vote_label,unique_label);     % 计算每个类标出现的次数[~,idx] = max(n);label_pred = unique_label(idx);      % 找到出现次数最多的类标