k近邻法(k-nearest neighbor, k-NN)是1967年由Cover T和Hart P提出的一种基本分类与回归方法。它的工作原理是：存在一个样本数据集合，也称作为训练样本集，并且样本集中每个数据都存在标签，即我们知道样本集中每一个数据与所属分类的对应关系。输入没有标签的新数据后，将新的数据的每个特征与样本集中数据对应的特征进行比较，然后算法提取样本最相似数据(最近邻)的分类标签。
机器学习实战源码：
'''Created on Sep 16, kNN: k Nearest NeighborsInput:inX: vector to compare to existing dataset (1xN)dataSet: size m data set of known vectors (NxM)labels: data set labels (1xM vector)k: number of neighbors to use for comparison (should be an odd number)Output:the most popular class label@author: pbharrin'''from numpy import *import operatorfrom os import listdirdef classify0(inX, dataSet, labels, k):dataSetSize = dataSet.shape[0]diffMat = tile(inX, (dataSetSize, 1)) - dataSetsqDiffMat = diffMat ** 2sqDistances = sqDiffMat.sum(axis=1)distances = sqDistances ** 0.5sortedDistIndicies = distances.argsort()classCount = {}for i in range(k):voteIlabel = labels[sortedDistIndicies[i]]classCount[voteIlabel] = classCount.get(voteIlabel, 0) + 1sortedClassCount = sorted(classCount.items(), key=operator.itemgetter(1), reverse=True)return sortedClassCount[0][0]def createDataSet():group = array([[1.0, 1.1], [1.0, 1.0], [0, 0], [0, 0.1]])labels = ['A', 'A', 'B', 'B']return group, labelsdef file2matrix(filename):fr = open(filename)numberOfLines = len(fr.readlines()) # get the number of lines in the filereturnMat = zeros((numberOfLines, 3)) # prepare matrix to returnclassLabelVector = [] # prepare labels returnfr = open(filename)index = 0for line in fr.readlines():line = line.strip()listFromLine = line.split('\t')returnMat[index, :] = listFromLine[0:3]classLabelVector.append(int(listFromLine[-1]))index += 1return returnMat, classLabelVectordef autoNorm(dataSet):minVals = dataSet.min(0)maxVals = dataSet.max(0)ranges = maxVals - minValsnormDataSet = zeros(shape(dataSet))m = dataSet.shape[0]normDataSet = dataSet - tile(minVals, (m, 1))normDataSet = normDataSet / tile(ranges, (m, 1)) # element wise dividereturn normDataSet, ranges, minValsdef datingClassTest():hoRatio = 0.50 # hold out 10%datingDataMat, datingLabels = file2matrix('datingTestSet2.txt') # load data setfrom filenormMat, ranges, minVals = autoNorm(datingDataMat)m = normMat.shape[0]numTestVecs = int(m * hoRatio)errorCount = 0.0for 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 += 1.0print("the total error rate is: %f" % (errorCount / float(numTestVecs)))print(errorCount)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 returnVectdef handwritingClassTest():hwLabels = []trainingFileList = listdir('trainingDigits') # load the training setm = len(trainingFileList)trainingMat = zeros((m, 1024))for i in range(m):fileNameStr = trainingFileList[i]fileStr = fileNameStr.split('.')[0] # take off .txtclassNumStr = int(fileStr.split('_')[0])hwLabels.append(classNumStr)trainingMat[i, :] = img2vector('trainingDigits/%s' % fileNameStr)testFileList = listdir('testDigits') # iterate through the test seterrorCount = 0.0mTest = len(testFileList)for i in range(mTest):fileNameStr = testFileList[i]fileStr = fileNameStr.split('.')[0] # take off .txtclassNumStr = int(fileStr.split('_')[0])vectorUnderTest = img2vector('testDigits/%s' % fileNameStr)classifierResult = classify0(vectorUnderTest, trainingMat, hwLabels, 3)print("the classifier came back with: %d, the real answer is: %d" % (classifierResult, classNumStr))if (classifierResult != classNumStr): errorCount += 1.0print("\nthe total number of errors is: %d" % errorCount)print("\nthe total error rate is: %f" % (errorCount / float(mTest)))if __name__ == '__main__':handwritingClassTest()
运行结果：
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classifier came back with: 8, the real answer is: 8the classifier came back with: 8, the real answer is: 8the classifier came back with: 8, the real answer is: 8the classifier came back with: 8, the real answer is: 8the classifier came back with: 8, the real answer is: 8the classifier came back with: 8, the real answer is: 8the classifier came back with: 8, the real answer is: 8the classifier came back with: 8, the real answer is: 8the classifier came back with: 8, the real answer is: 8the classifier came back with: 8, the real answer is: 8the classifier came back with: 8, the real answer is: 8the classifier came back with: 8, the real answer is: 8the classifier came back with: 8, the real answer is: 8the classifier came back with: 8, the real answer is: 8the classifier came back with: 8, the real answer is: 8the classifier came back with: 8, the real answer is: 8the classifier came back with: 8, the real answer is: 8the classifier came back with: 8, the real answer is: 8the classifier came back with: 8, the real answer is: 8the classifier came back with: 8, the real answer is: 8the classifier came back with: 8, the real answer is: 8the classifier came back with: 8, the real answer is: 8the classifier came back with: 8, the real answer is: 8the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 1, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 7, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the classifier came back with: 9, the real answer is: 9the total number of errors is: 10the total error rate is: 0.010571Process finished with exit code 0
