​ 简单地说，k-近邻算法采用测量不同特征值之间的距离方法进行分类。

• 工作原理：

  存在一个样本数据集合，也称为训练样本集，并且样本集中每个数据都存在标签。输入没有标签的新数据后，将新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。最后，选择k个最相似数据中出现次数最多的分类，作为新数据的分类。

• 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。

• 代码：

# -*- coding: utf-8 -*
from numpy import *
import operator
import matplotlib
import matplotlib.pyplot as plt
from os import listdir


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 # tile：获得dataSetSize行1列的 inX向量（横着）
    sqDiffMat = diffMat**2
    sqDistances = sqDiffMat.sum(axis=1) # axis=1：将一个矩阵的每一行向量内部相加
    distances = sqDistances**0.5
    sortedDistIndicies = distances.argsort()  # argsort() 返回数组值从小到大的索引值
    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]


# 将文本记录解析为为 训练样本矩阵，类标签向量
def file2matrix(filename):
    fr = open(filename)
    arrayOfLines = fr.readlines()    # 按行读
    numberOfLines = len(arrayOfLines)
    returnMat = zeros((numberOfLines, 3))
    classLabelVector = []
    index = 0
    for line in arrayOfLines:
        line = line.strip() # 截取掉所有的回车字符
        listFromLine = line.split('\t')     # 使用tab字符将整行数据分割成一个元素列表
        returnMat[index, :] = listFromLine[0:3]
        classLabelVector.append(int(listFromLine[-1]))
        index += 1
    return returnMat, classLabelVector

# datingDataMat, datingLables = file2matrix('datingTestSet2.txt')
# fig = plt.figure()
# ax = fig.add_subplot(111)
# ax.scatter(datingDataMat[:,0], datingDataMat[:,1], 15.0*array(datingLables), 15.0*array(datingLables))
# plt.show()


# 归一化特征值
def autoNorm(dataSet):
    minVals = dataSet.min(0)    # min(0)返回该矩阵中每一列的最小值 / min(1)返回该矩阵中每一行的最小值
    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))
    return normDataSet, ranges, minVals

# normMat, ranges, minVals = autoNorm(datingDataMat)


# 测试集的错误率
def datingClassTest():
    hoRatio = 0.10
    datingDataMat, datingLables = file2matrix('datingTestSet2.txt')
    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, :], datingLables[numTestVecs:m], 3)
        print("the classifier came back with: %d, the real answer is: %d" % (classifierResult, datingLables[i]))
        if(classifierResult != datingLables[i]): errorCount += 1.0
    print("the total error rate is: %f" % (errorCount/float(numTestVecs)))


# 预测具体的人
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, datingLables = file2matrix("datingTestSet2.txt")
    normMat, ranges, minVals = autoNorm(datingDataMat)
    inArr = array([percentTats, ffMiles, iceCream])
    classifierResult = classify0((inArr-minVals)/ranges, normMat,datingLables,3)
    print("You will probably like this person: ", resultList[classifierResult-1])


# 准备数据（将32*32的二进制图像矩阵转换为1*1024的向量）
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


def handwritingClassTest():
    hwLabels = []   # 标签集
    trainingFileList = listdir('trainingDigits')    # 列出给定目录下的文件名
    m = len(trainingFileList)
    trainingMat = zeros((m, 1024))
    for i in range(m):
        fileNameStr = trainingFileList[i]   # 文件名 如'9_45.txt',数字9的第45个实例
        fileStr = fileNameStr.split('.')[0] # '9_45'
        classNumStr = int(fileStr.split('_')[0])   # 9
        hwLabels.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, hwLabels, 3)
        print("the classifier came back with: %d, the real answer is: %d" % (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)))