k近邻算法(KNN)

k近邻算法

KNN定义：

给定新样本求其分类y，是从离x最近的k个点的类别中选取最多的分类(投票)，定义为x的分类y
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
适合数据范围：数值型和标称型

通常k是个不大于20的整数，选择样本数据集中前k个最相似的数据
k值减小意味着整体模型变得复杂，容易发生过拟合

代码伪码

1 计算已知类别数据集中的点与当前点之间的距离
2按照距离递增次序排序
3选取与当前距离最小的k个点
4确定前k个点所在类别出现的频率
5返回前k个频率最高的类别作为当前点的预测分类

代码

# coding=utf-8# __author__=Eshter Yuu#无需言，做自己import numpy as npfrom os import listdirimport operator##运行这个operator会产生pi，e以及gramma三个变量import matplotlib.pyplot as pltdef createDataSet():    group = np.array([[1.0,1.1],[1.0,1.0],[0,0],[0,0.1]])    labels = ['A','A','B','B']    return group, labels##k近邻算法def classify0(inX, dataSet, labels, k):    dataSetSize = np.shape(dataSet)[0]    diffMat =np.tile(inX, (dataSetSize,1)) - dataSet ##复制，相当于matlab的repmat    sqDiffMat = diffMat **2    sqDistances = sqDiffMat.sum(axis=1)    distances = sqDistances** 0.5    sortedDistIndicies = distances.argsort()    classCount ={}    for i in range(k):        votelabel = labels[sortedDistIndicies[i]]        classCount[votelabel] = classCount.get(votelabel,0) + 1    sortedClassCount = sorted(classCount.items(), key = operator.itemgetter(1), reverse=True)    return sortedClassCount[0][0]##将文本记录转换为numpy的解析程序def file2matrix (filename):    fr = open(filename)    arrayOLines = fr.readlines()    numberOfLines = len(arrayOLines)    returnMat = np.zeros((numberOfLines,3))    index= 0    classLabelsVector = []    for line in arrayOLines:        line = line.strip()        listFromLine = line.split('\t')        returnMat[index,:] = listFromLine[0:3]        classLabelsVector.append(int(listFromLine[-1]))        index += 1    return returnMat, classLabelsVector###归一化特征值---min-max归一化def autoNorm(dataSet):    minVals = dataSet.min(0)##对每一列求最小值，，max(1)是对每一行求最小值    maxVals = dataSet.max(0)##对每一列求最大值    ranges = maxVals- minVals    normDataSet = np.zeros(np.shape(dataSet))    m = dataSet.shape[0]    normDataSet = dataSet - np.tile(minVals,(m,1))    normDataSet =normDataSet/np.tile(ranges,(m,1))    return normDataSet, ranges, minValsdef datingClassTest():    hoRatio = 0.10    datingDataMat, datingLabels = file2matrix('datingTestSet2.txt')    normMat,ranges, minVals = autoNorm(datingDataMat)    m = normMat.shape[0]    numTestVecs = int(m * hoRatio)    errorCount = 0.0    for i  in range(numTestVecs):        classifierReult = classify0(normMat[i,:], normMat[numTestVecs:m,:], datingLabels[numTestVecs:m],3)        print("the classifier came back with:%d, the real answer is %d"% (classifierReult, datingLabels[i]))        if (classifierReult != datingLabels[i]): errorCount += 1.0    print("the total error rate is :%f"% (errorCount / float(numTestVecs)))##约会网络数据##raw_input 该函数允许用户输入文本行命令并返回用户所输入的命令# def classfyPerson():#   resultList = ['not at all ', 'in samll doses','in large doses']#   percentTats = float (raw_input("percentagy of time spent playing vodeo games?"))#   ffMiles = float(raw_input("frequent flier miles earned per year?"))#   iceCream = float(raw_input("liters of ice cream consumed per year?"))#   datingDataMat, datingLabels = file2matrix('datingTestSet2.txt')#   normMat, ranges, minVals = autoNorm(datingDataMat)#   inArr = np.array([ffMiles, percentTats, iceCream])#   classifierResult = classify0((inArr- minVals)/ranges, normMat, datingLabels,3)#   print(" you will probably like this person:", resultList[classifierResult -1])###手写体识别def img2vector(filename):    returnVect = np.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'''k近邻算法识别手写数字'''def handwritingClassTest():    hwLables = []    traingFileList = listdir('trainingDigits')    m = len(traingFileList)    trainingMat = np.zeros((m,1024))    for i in range(m):        fileNameStr = traingFileList[i]        fileStr = fileNameStr.split('.')[0]        classNumStr = int(fileStr.split('_')[0])        hwLables.append(classNumStr)        trainingMat[i,:] = img2vector('trainingDigits/%s'% fileNameStr)    testFileList = listdir('testDigits')    errorCount = 0.0    mTest = len(testFileList)    for i  in range(mTest):        fileNameStr = testFileList[i]        fileStr = fileNameStr.split('.')[0]        classNumStr = int(fileStr.split('_')[0])        vectorUnderTest = img2vector('testDigits/%s'% fileNameStr)        classifierResult = classify0(vectorUnderTest, trainingMat,hwLables,3)        print("the classifier came back with: %d, the real answer is :%d"%(classifierResult,classNumStr))        if (classifierResult != classNumStr) : errorCount += 1.0    print("\n the total number of errors is :%d"% errorCount)    print("\n the total error rate is :%f"% (errorCount/float(mTest)) )group,labels = createDataSet()print(group,'\n')print(labels)## b =classify0([0,0], group, labels,3)# print('类别为：',b)#datingDataMat, datingLabels = file2matrix('datingTestSet2.txt')# datingDataMat = np.mat(datingDataMat)# datingLabels = np.mat(datingLabels)# print(np.shape(datingDataMat)[0],'\n')# print(np.shape(datingLabels)[0])# fig = plt.figure()# ax = fig.add_subplot(111)# ax.scatter(datingDataMat[:,1],datingDataMat[:,2],15.0*np.array(datingLabels), 15.0*np.array(datingLabels))# plt.show()#normMat, ranges, minVals = autoNorm(datingDataMat)# print('ranges = ',ranges)# print('minVals', minVals)#datingClassTest()'''手写体识别'''# testVector = img2vector('testDigits/1_13.txt')# print(testVector[0,0:31])# handwritingClassTest()