k-近邻算法（KNN）识别手写数字

k-近邻算法（KNN）

目录 trainingDigits 中包含了大约 2000 个例子，每个例子内容如下图所示，每个数字大约有 200 个样本；目录 testDigits 中包含了大约 900 个测试数据。

将一个32x32的二进制图像矩阵转化为1x1024的向量。

函数img2vector，将图像转化为向量，该函数创建1x1024的数组，然后打开给定的文件，循环读出文件的前32行，并将每行的头32个字值存储在NumPy数组种，最后返回数组。

#将图像文本数据转换为向量
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

将这些数据输入到分类器，检测分类器的执行效果。

#测试算法
def handwritingClassTest():
    hwLabels = []
    trainingFileList = listdir('trainingDigits')           #加载训练集
    m = len(trainingFileList)
    trainingMat = zeros((m,1024))
    for i in range(m):
        fileNameStr = trainingFileList[i]
        fileStr = fileNameStr.split('.')[0]     
        classNumStr = int(fileStr.split('_')[0])
        hwLabels.append(classNumStr)
        trainingMat[i,:] = img2vector('trainingDigits/%s' % fileNameStr)
    testFileList = listdir('testDigits')        #遍历
    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 "
the total number of errors is: %d" % errorCount
    print "
the total error rate is: %f" % (errorCount/float(mTest))

 测试算法：编写函数使用提供的部分数据集作为测试样本，如果预测分类与实际类别不同，则标记为一个错误

classify0）()函数有4个参数：用于分类的输入向量是inX，训练集为dataSet，标签向量为labels，，k表示用于选择最近邻居的数目，其中标签向量的元素数目和矩阵dataSet的行数相同。

def classify0(inX, dataSet, labels, k):
    dataSetSize = dataSet.shape[0]
    diffMat = tile(inX, (dataSetSize,1)) - dataSet   #把inX二维数组化，dataSetSize表示生成数组后的行数，1表示列的倍数。实现了矩阵之间的减法。
    sqDiffMat = diffMat**2
    sqDistances = sqDiffMat.sum(axis=1)。#axis=1：参数等于1，矩阵中行之间的数的求和
    distances = sqDistances**0.5
    sortedDistIndicies = distances.argsort()  #argsort()：对一个数组进行非降序排序   
    classCount={}          
    for i in range(k):
        voteIlabel = labels[sortedDistIndicies[i]]
        #访问下标键为voteIlabel的项
        classCount[voteIlabel] = classCount.get(voteIlabel,0) + 1
    sortedClassCount = sorted(classCount.iteritems(), key=operator.itemgetter(1), reverse=True)
    return sortedClassCount[0][0]

 代码

from numpy import *
import operator
from os import listdir

def classify0(inX, dataSet, labels, k):
    dataSetSize = dataSet.shape[0]
    diffMat = tile(inX, (dataSetSize,1)) - dataSet   #把inX二维数组化，dataSetSize表示生成数组后的行数，1表示列的倍数。实现了矩阵之间的减法。
    sqDiffMat = diffMat**2
    sqDistances = sqDiffMat.sum(axis=1)。#axis=1：参数等于1，矩阵中行之间的数的求和
    distances = sqDistances**0.5
    sortedDistIndicies = distances.argsort()  #argsort()：对一个数组进行非降序排序   
    classCount={}          
    for i in range(k):
        voteIlabel = labels[sortedDistIndicies[i]]
        #访问下标键为voteIlabel的项
        classCount[voteIlabel] = classCount.get(voteIlabel,0) + 1
    sortedClassCount = sorted(classCount.iteritems(), key=operator.itemgetter(1), reverse=True)
    return sortedClassCount[0][0]


#将图像文本数据转换为向量
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


#测试算法
def handwritingClassTest():
    hwLabels = []
    trainingFileList = listdir('trainingDigits')           #加载训练集
    m = len(trainingFileList)
    trainingMat = zeros((m,1024))
    for i in range(m):
        fileNameStr = trainingFileList[i]
        fileStr = fileNameStr.split('.')[0]     
        classNumStr = int(fileStr.split('_')[0])
        hwLabels.append(classNumStr)
        trainingMat[i,:] = img2vector('trainingDigits/%s' % fileNameStr)
    testFileList = listdir('testDigits')        #遍历
    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 "
the total number of errors is: %d" % errorCount
    print "
the total error rate is: %f" % (errorCount/float(mTest))

 运行：

>>> import kNN
>>> kNN.handwritingClassTest()
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
.
.
.
the classifier came back with: 3, the real answer is: 3

the total number of errors is: 11

the total error rate is: 0.011628