k-近邻算法2（kNN）手写识别系统

这里构造的系统只能识别数字0-9

目录trainingDigits中包含了1934个文件

目录testDigits中包含了946个文件

文件形式

 

（1）准备数据：将图像转换为测试向量

 

# 将图像格式化处理为一个向量
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

 

（2）测试算法：使用k-近邻算法识别手写数字

def handwritingClassTest():
    hwLabels = []
    # 获取目录内容
    trainingFileList = listdir('digits/trainingDigits')
    m = len(trainingFileList)
    trainingMat = zeros((m, 1024))
    for i in range(m):
        # 从文件名解析分类数字
        # 1、获取文件名
        fileNameStr = trainingFileList[i]
        # 2、去掉文件后缀
        fileStr = fileNameStr.split('.')[0]
        # 3、这个文件内的图像所表示的数字，即分类
        classNumStr = int(fileStr.split('_')[0])
        hwLabels.append(classNumStr)
        trainingMat[i, :] = img2vector('digits/trainingDigits/%s' % fileNameStr)
    testFileList = listdir('digits/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('digits/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)))

def classify0(inX, dataSet, labels, k):
    dataSetSize = dataSet.shape[0]
    # 1距离计算
    diffMat = tile(inX, (dataSetSize, 1)) - dataSet
    sqDiffMat = diffMat ** 2
    sqDistances = sqDiffMat.sum(axis=1)
    distances = sqDistances ** 0.5
    sortedDistIndicies = distances.argsort()
    # 2选择距离最小的k个点
    classCount = {}
    for i in range(k):
        voteIlabel = labels[sortedDistIndicies[i]]
        classCount[voteIlabel] = classCount.get(voteIlabel, 0) + 1
    # 3排序
    sortedClassCount = sorted(classCount.items(), key=operator.itemgetter(1), reverse=True)
    return sortedClassCount[0][0]

 

上篇+这篇的全部代码

#!usr/bin/env python3
# -*-coding:utf-8 -*-

from numpy import *
import operator
import matplotlib
import matplotlib.pyplot as plt


def createDataSet():
    group = array([[1.0, 1.1], [1.0, 1.], [0, 0.], [0, 0.1]])
    labels = ['A', 'A', 'B', 'B']
    return group, labels


def classify0(inX, dataSet, labels, k):
    dataSetSize = dataSet.shape[0]
    # 1距离计算
    diffMat = tile(inX, (dataSetSize, 1)) - dataSet
    sqDiffMat = diffMat ** 2
    sqDistances = sqDiffMat.sum(axis=1)
    distances = sqDistances ** 0.5
    sortedDistIndicies = distances.argsort()
    # 2选择距离最小的k个点
    classCount = {}
    for i in range(k):
        voteIlabel = labels[sortedDistIndicies[i]]
        classCount[voteIlabel] = classCount.get(voteIlabel, 0) + 1
    # 3排序
    sortedClassCount = sorted(classCount.items(), key=operator.itemgetter(1), reverse=True)
    return sortedClassCount[0][0]


def file2matrix(filename):
    fr = open(filename)
    arrayOLines = fr.readlines()
    # 得到文件行数
    numberOfLines = len(arrayOLines)
    # 创建以0填充的矩阵
    returnMat = zeros((numberOfLines, 3))
    classLabelVector = []
    index = 0
    for line in arrayOLines:
        # 截取掉所有回车字符
        line = line.strip()
        # 将整行数据分割成一个元素列表
        listFromLine = line.split('\t')
        returnMat[index, :] = listFromLine[0:3]
        classLabelVector.append(int(listFromLine[-1]))
        index += 1
    return returnMat, classLabelVector


# newValue=(oldValue-min)/(max-min)
def autoNorm(dataSet):
    # 参数0使得函数可以从列中选取最小值
    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))
    return normDataSet, ranges, minVals


def datingClassTest():
    # 测试数据所占的比例
    hoRatio = 0.1
    datingDataMat, datingLabels = file2matrix('datingTestSet2.txt')
    normMat, ranges, minVals = autoNorm(datingDataMat)
    # 矩阵第一维大小
    m = normMat.shape[0]
    # 测试向量的数量
    numTestVecs = int(m * hoRatio)
    errorCount = 0.0
    for 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 += 1.0
    print("the total error rate is: %f" % (errorCount / float(numTestVecs)))


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 = array([ffMiles, percentTats, iceCream])
    classifierResult = classify0(inArr, datingDataMat, datingLabels, 3)
    print("You will probably like this person: ", resultList[classifierResult - 1])


def draw():
    fig = plt.figure()  # figure创建一个绘图对象
    ax = fig.add_subplot(111)  # 若参数为349，意思是：将画布分割成3行4列，图像画在从左到右从上到下的第9块，
    datingDataMat, datingLabels = file2matrix('datingTestSet2.txt')

    '''
    matplotlib.pyplot.scatter(x, y, s=20, c='b', marker='o', cmap=None,
    norm=None, vmin=None, vmax=None, alpha=None, linewidths=None, verts=None, hold=None,**kwargs)
    其中，xy是点的坐标，s是点的大小
    maker是形状可以maker=（5，1）5表示形状是5边型，1表示是星型（0表示多边形，2放射型，3圆形）
    alpha表示透明度；facecolor=‘none’表示不填充。
    '''

    type1_x = []
    type1_y = []
    type2_x = []
    type2_y = []
    type3_x = []
    type3_y = []
    for i in range(len(datingLabels)):
        if datingLabels[i] == 1:  # 不喜欢
            type1_x.append(datingDataMat[i][0])
            type1_y.append(datingDataMat[i][1])

        if datingLabels[i] == 2:  # 魅力一般
            type2_x.append(datingDataMat[i][0])
            type2_y.append(datingDataMat[i][1])

        if datingLabels[i] == 3:  # 极具魅力
            type3_x.append(datingDataMat[i][0])
            type3_y.append(datingDataMat[i][1])

    type1 = ax.scatter(type1_x, type1_y, s=20, c='red')
    type2 = ax.scatter(type2_x, type2_y, s=30, c='green')
    type3 = ax.scatter(type3_x, type3_y, s=40, c='blue')

    # ax.scatter(datingDataMat[:, 1], datingDataMat[:, 2])
    # 设置字体防止中文乱码
    zhfont = matplotlib.font_manager.FontProperties(fname='C:\Windows\Fonts\STXINGKA.TTF')
    plt.xlabel('每年获取的飞行常客里程数', fontproperties=zhfont)
    plt.ylabel('玩视频游戏所耗时间百分比', fontproperties=zhfont)
    # ax.scatter(datingDataMat[:, 0], datingDataMat[:, 1],
    # 15.0 * array(datingLabels), 15.0 * array(datingLabels))
    ax.legend((type1, type2, type3), (u'不喜欢', u'魅力一般', u'极具魅力'), loc=2, prop=zhfont)
    plt.show()


from os import listdir


# 将图像格式化处理为一个向量
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 = []
    # 获取目录内容
    trainingFileList = listdir('digits/trainingDigits')
    m = len(trainingFileList)
    trainingMat = zeros((m, 1024))
    for i in range(m):
        # 从文件名解析分类数字
        # 1、获取文件名
        fileNameStr = trainingFileList[i]
        # 2、去掉文件后缀
        fileStr = fileNameStr.split('.')[0]
        # 3、这个文件内的图像所表示的数字，即分类
        classNumStr = int(fileStr.split('_')[0])
        hwLabels.append(classNumStr)
        trainingMat[i, :] = img2vector('digits/trainingDigits/%s' % fileNameStr)
    testFileList = listdir('digits/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('digits/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)))


if __name__ == "__main__":
    handwritingClassTest()
    # classifyPerson()

handwritingClassTest()运行结果,只截取了最后的部分

 

实际使用这个算法时，算法的执行效率不高。因为算法需要为每个测试向量做2000次距离计算，每个距离计算包括了1024个维度浮点运算，总计执行900次。

此外，还要为测试向量准备2MB的存储空间。（k决策树是k-近邻算法的优化版，可以节省大量的计算开销）

 

小结

k-近邻算法时分类数据最简单最有效的算法。是基于实例的学习，使用算法时我们必须有接近实际数据的训练样本数据。

此算法必须保存全部数据集，如果训练集很大，必须使用大量的存储空间。此外，由于必须对数据集中的每个数据计算距离值，实际使用时可能非常耗时。

它无法给出任何数据的基础结构信息，也无法知晓平均实例样本和典型实例样本具有什么特征。