使用 k 近邻算法改进网站的配对效果

说明：

将数据集文件 ‘datingTestSet2.txt’ 放在当前文件夹

# 导入程序所需要的模块 import numpy as np import operator

定义数据集导入函数

file2matrix函数实现的功能是读取文件数据，函数返回的returnMat和classLabelVector分别是数据集的特征矩阵和输出标签向量。

def file2matrix(filename): love_dictionary = {'largeDoses':3, 'smallDoses':2, 'didntLike':1} # 三个类别 # 打开文件 fr = open(filename) # 逐行打开,readlines()方法用于读取所有行(直到结束符 EOF)并返回列表，该列表可以由 Python 的 for... in ... 结构进行处理。 arrayOLines = fr.readlines() #得到文件的行数 numberOfLines = len(arrayOLines) #返回numpy矩阵,numberOfLines行，3列的零元素矩阵//初始化特征矩阵 returnMat = np.zeros((numberOfLines, 3)) #返回分类的标签向量//初始化输出标签向量 classLabelVector = [] #行的索引值 index = 0 for line in arrayOLines: # 删去字符串首尾空格 line = line.strip() # 按'\t'对字符串进行分割，listFromLine 是列表 listFromLine = line.split('\t') #将数据前三列提取出来，存放到returnMat的numpy矩阵中，也就是不含标签变量，只有特征变量。 # listFromLine的0,1,2元素是特征，赋值给returnMat的当前行 #一行一行的存储 returnMat[index, :] = listFromLine[0:3] # 如果listFromLine最后一个元素是数字 if(listFromLine[-1].isdigit()): # 直接赋值给classLabelVector classLabelVector.append(int(listFromLine[-1])) else: # 如果listFromLine最后一个元素不是数字，而是字符串。根据字典love_dictionary转化为数字 # Python 字典(Dictionary) get() 函数返回指定键的值 classLabelVector.append(love_dictionary.get(listFromLine[-1])) index += 1 return returnMat, classLabelVector # 返回的类别标签classLabelVector是1,2,3 returnMat,classLabelVector=file2matrix('datingTestSet2.txt') print(returnMat) print(classLabelVector) print(returnMat.shape) [[4.0920000e+04 8.3269760e+00 9.5395200e-01] [1.4488000e+04 7.1534690e+00 1.6739040e+00] [2.6052000e+04 1.4418710e+00 8.0512400e-01] ... [2.6575000e+04 1.0650102e+01 8.6662700e-01] [4.8111000e+04 9.1345280e+00 7.2804500e-01] [4.3757000e+04 7.8826010e+00 1.3324460e+00]] [3, 2, 1, 1, 1, 1, 3, 3, 1, 3, 1, 1, 2, 1, 1, 1, 1, 1, 2, 3, 2, 1, 2, 3, 2, 3, 2, 3, 2, 1, 3, 1, 3, 1, 2, 1, 1, 2, 3, 3, 1, 2, 3, 3, 3, 1, 1, 1, 1, 2, 2, 1, 3, 2, 2, 2, 2, 3, 1, 2, 1, 2, 2, 2, 2, 2, 3, 2, 3, 1, 2, 3, 2, 2, 1, 3, 1, 1, 3, 3, 1, 2, 3, 1, 3, 1, 2, 2, 1, 1, 3, 3, 1, 2, 1, 3, 3, 2, 1, 1, 3, 1, 2, 3, 3, 2, 3, 3, 1, 2, 3, 2, 1, 3, 1, 2, 1, 1, 2, 3, 2, 3, 2, 3, 2, 1, 3, 3, 3, 1, 3, 2, 2, 3, 1, 3, 3, 3, 1, 3, 1, 1, 3, 3, 2, 3, 3, 1, 2, 3, 2, 2, 3, 3, 3, 1, 2, 2, 1, 1, 3, 2, 3, 3, 1, 2, 1, 3, 1, 2, 3, 2, 3, 1, 1, 1, 3, 2, 3, 1, 3, 2, 1, 3, 2, 2, 3, 2, 3, 2, 1, 1, 3, 1, 3, 2, 2, 2, 3, 2, 2, 1, 2, 2, 3, 1, 3, 3, 2, 1, 1, 1, 2, 1, 3, 3, 3, 3, 2, 1, 1, 1, 2, 3, 2, 1, 3, 1, 3, 2, 2, 3, 1, 3, 1, 1, 2, 1, 2, 2, 1, 3, 1, 3, 2, 3, 1, 2, 3, 1, 1, 1, 1, 2, 3, 2, 2, 3, 1, 2, 1, 1, 1, 3, 3, 2, 1, 1, 1, 2, 2, 3, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 2, 3, 2, 3, 3, 3, 3, 1, 2, 3, 1, 1, 1, 3, 1, 3, 2, 2, 1, 3, 1, 3, 2, 2, 1, 2, 2, 3, 1, 3, 2, 1, 1, 3, 3, 2, 3, 3, 2, 3, 1, 3, 1, 3, 3, 1, 3, 2, 1, 3, 1, 3, 2, 1, 2, 2, 1, 3, 1, 1, 3, 3, 2, 2, 3, 1, 2, 3, 3, 2, 2, 1, 1, 1, 1, 3, 2, 1, 1, 3, 2, 1, 1, 3, 3, 3, 2, 3, 2, 1, 1, 1, 1, 1, 3, 2, 2, 1, 2, 1, 3, 2, 1, 3, 2, 1, 3, 1, 1, 3, 3, 3, 3, 2, 1, 1, 2, 1, 3, 3, 2, 1, 2, 3, 2, 1, 2, 2, 2, 1, 1, 3, 1, 1, 2, 3, 1, 1, 2, 3, 1, 3, 1, 1, 2, 2, 1, 2, 2, 2, 3, 1, 1, 1, 3, 1, 3, 1, 3, 3, 1, 1, 1, 3, 2, 3, 3, 2, 2, 1, 1, 1, 2, 1, 2, 2, 3, 3, 3, 1, 1, 3, 3, 2, 3, 3, 2, 3, 3, 3, 2, 3, 3, 1, 2, 3, 2, 1, 1, 1, 1, 3, 3, 3, 3, 2, 1, 1, 1, 1, 3, 1, 1, 2, 1, 1, 2, 3, 2, 1, 2, 2, 2, 3, 2, 1, 3, 2, 3, 2, 3, 2, 1, 1, 2, 3, 1, 3, 3, 3, 1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 3, 2, 1, 3, 3, 2, 2, 2, 3, 1, 2, 1, 1, 3, 2, 3, 2, 3, 2, 3, 3, 2, 2, 1, 3, 1, 2, 1, 3, 1, 1, 1, 3, 1, 1, 3, 3, 2, 2, 1, 3, 1, 1, 3, 2, 3, 1, 1, 3, 1, 3, 3, 1, 2, 3, 1, 3, 1, 1, 2, 1, 3, 1, 1, 1, 1, 2, 1, 3, 1, 2, 1, 3, 1, 3, 1, 1, 2, 2, 2, 3, 2, 2, 1, 2, 3, 3, 2, 3, 3, 3, 2, 3, 3, 1, 3, 2, 3, 2, 1, 2, 1, 1, 1, 2, 3, 2, 2, 1, 2, 2, 1, 3, 1, 3, 3, 3, 2, 2, 3, 3, 1, 2, 2, 2, 3, 1, 2, 1, 3, 1, 2, 3, 1, 1, 1, 2, 2, 3, 1, 3, 1, 1, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 2, 2, 2, 3, 1, 3, 1, 2, 3, 2, 2, 3, 1, 2, 3, 2, 3, 1, 2, 2, 3, 1, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 3, 2, 1, 3, 3, 3, 1, 1, 3, 1, 2, 3, 3, 2, 2, 2, 1, 2, 3, 2, 2, 3, 2, 2, 2, 3, 3, 2, 1, 3, 2, 1, 3, 3, 1, 2, 3, 2, 1, 3, 3, 3, 1, 2, 2, 2, 3, 2, 3, 3, 1, 2, 1, 1, 2, 1, 3, 1, 2, 2, 1, 3, 2, 1, 3, 3, 2, 2, 2, 1, 2, 2, 1, 3, 1, 3, 1, 3, 3, 1, 1, 2, 3, 2, 2, 3, 1, 1, 1, 1, 3, 2, 2, 1, 3, 1, 2, 3, 1, 3, 1, 3, 1, 1, 3, 2, 3, 1, 1, 3, 3, 3, 3, 1, 3, 2, 2, 1, 1, 3, 3, 2, 2, 2, 1, 2, 1, 2, 1, 3, 2, 1, 2, 2, 3, 1, 2, 2, 2, 3, 2, 1, 2, 1, 2, 3, 3, 2, 3, 1, 1, 3, 3, 1, 2, 2, 2, 2, 2, 2, 1, 3, 3, 3, 3, 3, 1, 1, 3, 2, 1, 2, 1, 2, 2, 3, 2, 2, 2, 3, 1, 2, 1, 2, 2, 1, 1, 2, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 1, 3, 3, 2, 3, 2, 3, 3, 2, 2, 1, 1, 1, 3, 3, 1, 1, 1, 3, 3, 2, 1, 2, 1, 1, 2, 2, 1, 1, 1, 3, 1, 1, 2, 3, 2, 2, 1, 3, 1, 2, 3, 1, 2, 2, 2, 2, 3, 2, 3, 3, 1, 2, 1, 2, 3, 1, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 1, 3, 3, 3] (1000, 3)

定义特征归一化函数

这里为什么要对特征进行归一化？

因为在处理这种不同取值范围的特征值时，数值归一化能够将不同特征的取值范围限定在同一区间例如[0,1]之间，让不同特征对距离的计算影响相同。具体可看《机器学习实战》第2.2.3节内容。

#归一化特征变量中的数据 #归一化公式为 : newValue = (oldvalue-min)/(max-min) def autoNorm(dataSet): #获得数据每一列的最小值和最大值 #b.min(k)就是b.min(axis=k)，就是在他的第k个轴上投影求最小 minVals = dataSet.min(0) maxVals = dataSet.max(0) #最大值和最小值的范围 ranges = maxVals - minVals #创建numpy矩阵，里面全是零元素 normDataSet = np.zeros(np.shape(dataSet)) #返回dataSet的行数 m = dataSet.shape[0] #原始值减去最小值。np.tile: 重复n次 normDataSet = dataSet - np.tile(minVals, (m, 1)) #除以最大和最小值的差，得到归一化的数据 #normDataSet值被限定在[0,1]之间 normDataSet = normDataSet/np.tile(ranges, (m, 1)) return normDataSet, ranges, minVals normDataSet,ranges,minVals=autoNorm(returnMat) print(normDataSet) print(ranges) print(minVals) [[0.44832535 0.39805139 0.56233353] [0.15873259 0.34195467 0.98724416] [0.28542943 0.06892523 0.47449629] ... [0.29115949 0.50910294 0.51079493] [0.52711097 0.43665451 0.4290048 ] [0.47940793 0.3768091 0.78571804]] [9.1273000e+04 2.0919349e+01 1.6943610e+00] [0. 0. 0.001156]

定义k近邻算法

def classify0(inX, dataSet, labels, k): # inX是测试集，dataSet是训练集，labels是训练样本标签，k是取的最近邻个数 #训练数据集行数,训练样本个数 dataSetSize = dataSet.shape[0] #在行向量方向上重复inx共datasetSize次，在列向量方向上重复inx共1次 diffMat = np.tile(inX,(dataSetSize,1)) - dataSet #二维特征相减之后的平方 sqDiffMat = diffMat**2 #sum()所有元素相加，sum(0)列相加，sum(1)行相加 sqDistances = sqDiffMat.sum(axis=1) #开方，计算出距离。distance是inX与dataSet的欧氏距离 distances = sqDistances**0.5 #argsort函数返回的是数组值从小到大的索引值。即返回distances中元素从小到大排序后的索引值。后续sortedDistIndicies[i]要用到。 sortedDistIndicies = distances.argsort() #定义一个记录类别（label）次数的字典，字典存储k近邻不同label出现的次数 classCount = {} #遍历前k个，记录次数。选择距离最小的k个点 for i in range(k): voteIlabel = labels[sortedDistIndicies[i]] # classCount中若有此key，对应label加1；classCount中若无此key，则默认为0 classCount[voteIlabel] = classCount.get(voteIlabel, 0) + 1 # operator.itemgetter 获取对象的哪个维度的数据 # key=operator.itemgetter(1)根据字典的值进行排序 # key=operator.itemgetter(0)根据字典的键进行排序 # reverse=True降序排列 sortedClassCount = sorted(classCount.items(), key=operator.itemgetter(1), reverse=True) # 返回k近邻中所属类别最多的那一类 return sortedClassCount[0][0]

测试算法：作为完整程序验证分类器

def datingClassTest(): #整个数据集的10%用来测试 hoRatio = 0.10 #导入数据集。将返回的特征矩阵和分类向量分别存储到datingDataMat, datingLabels datingDataMat, datingLabels = file2matrix('datingTestSet2.txt') #数据归一化,返回归一化后的矩阵,数据范围,数据最小值 normMat, ranges, minVals = autoNorm(datingDataMat) #样本个数 m = normMat.shape[0] #测试样本的个数 numTestVecs = int(m*hoRatio) #分类错误计数 errorCount = 0.0 for i in range(numTestVecs): #前numTestVecs个数据作为测试集,后m-numTestVecs个数据作为训练集 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))) # 打印错误率 print(errorCount) # 打印错误个数 datingClassTest() the classifier came back with: 3, the real answer is: 3 the classifier came back with: 2, the real answer is: 2 the classifier came back with: 1, the real answer is: 1 the classifier came back 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使用算法：构建完整可用系统

根据用户输入，在线判断类别。

def classifyPerson(): resultList = ['not at all', 'in small doses', 'in large doses'] percentTats = float(input(\ "percentage of time spent playing video games?")) ffMiles = float(input("frequent flier miles earned per year?")) iceCream = float(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, 5) print("You will probably like this person: %s" % resultList[classifierResult - 1]) classifyPerson() percentage of time spent playing video games?10 frequent flier miles earned per year?100 liters of ice cream consumed per year?1 You will probably like this person: in small doses