【Machine Learning in Action --2】K-近邻算法构造手写识别系统

　　为了简单起见，这里构造的系统只能识别数字0到9，需要识别的数字已经使用图形处理软件，处理成具有相同的色彩和大小：宽高是32像素的黑白图像。尽管采用文本格式存储图像不能有效地利用内存空间，但是为了方便理解，我们还是将图像转换为文本格式。

---1.收集数据：提供文本文件

　　该数据集合修改自“手写数字数据集的光学识别”-一文中的数据集合，该文登载于2010年10月3日的UCI机器学习资料库中http://archive.ics.uci.edu/ml。

      

---2.准备数据：将图像转换为测试向量

　　trainingDigits中包含了大约2000个例子，每个数字大约有200个样本；testDigits中包含了大约900个测试数据。两组数据没有重叠。

　　我们先将图像格式化处理为一个向量。我们将一个32*32的二进制图像矩阵转换为1*1024的向量。

　　我们首先编写函数img2vector，将图像转换为向量：该函数创建1*1024的NumPy数组，然后打开指定的文件，循环读出文件的前32行，并将每行的前32个字符值存储在NumPy数组中，最后返回数组。

#!/usr/bin/python
# -*- coding: utf-8 -*-
from numpy import *     #引入科学计算包numpy
from os import listdir
import operator         #经典python函数库，运算符模块

#算法核心
#inX：用户分类的输入向量，即将对其进行分类
#dataSet:训练样本集
#labels：标签向量
def classifyO(inX,dataSet,labels,k):
    #距离计算
    dataSetSize=dataSet.shape[0] #得到数组的行数，即知道有几个训练数据
    diffMat=tile(inX,(dataSetSize,1))-dataSet  #tile是numpy中的函数，tile将原来的一个数组，扩充成了4个一样的数组；diffMat得到目标与训练数值之间的差值
    sqDiffMat=diffMat**2         #各个元素分别平方
    sqDistances=sqDiffMat.sum(axis=1)
    distances=sqDistances**0.5   #开方，得到距离
    sortedDistIndicies=distances.argsort()  #升序排列
    #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
    #排序
    sortedClassCount=sorted(classCount.iteritems(),key=operator.itemgetter(1),reverse=True)
    return sortedClassCount[0][0]

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

　　在python命令行中输入下列命令测试img2vector函数，然后与本文编辑器打开的文件进行比较：

>>> import kNN
>>> testVector=kNN.img2vector('digits/testDigits/0_13.txt') #根据自己的目录写
>>> testVector[0,0:31]
array([ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
        0.,  1.,  1.,  1.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
        0.,  0.,  0.,  0.,  0.])
>>> testVector[0,32:63]
array([ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.,
        1.,  1.,  1.,  1.,  1.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
        0.,  0.,  0.,  0.,  0.])

---3.测试算法：使用k-近邻算法识别手写数字

　　我们已经将数据处理成分类器可以识别的格式，现在要做的是将这些数据输入到分类器，检查分类器的执行结果。handwritingClassTest()是测试分类器的代码，将其写入kNN.py文件中。在写入之前，保证将from os import listdir写入文件的起始部分。这段代码主要功能是从os模块中导入函数listdir，它可以列出给定目录的文件名。

def handwritingClassTest():
    hwLabels=[]
    trainingFileList=listdir('E:\\python excise\\digits\\trainingDigits')
    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('digits/trainingDigits/%s' %fileNameStr)
    testFileList=listdir('E:/python excise/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=classifyO(vectorUnderTest,trainingMat,hwLabels,3)
        print "the classifier came back with:%d,the real answeris:%d" %(classifierResult,classNumStr)
        if(classifierResult !=classNumStr):errorCount+=1.0
    print "\nthe total number of error is:%d"%errorCount
    print "\nthe total error rate is:%f"%(errorCount/float(mTest))

　　解释：将E:\\python excise\\digits\\trainingDigits目录中的文件内容存储到列表trainingFileList中，然后可以得到文件中有有多少文件，并将其存储在变量m中。接着，代码创建一个m行1024列的训练矩阵，该矩阵的每行数据存储一个图像。我们可以从文件名中解析出分类数字，该目录下的文件按照规则命名，如文件9_45.txt的分类是9，它是数字9的第45个实例。然后我们可以将类代码存储到hwLabels向量中，使用前面的img2vector函数载入图像。

　　下一步中，对E:/python excise/digits/testDigits目录中文件执行相似的操作，不同的是我们并不将这个目录下的文件载入矩阵，而是使用classifyO()函数测试该目录下的每个文件。由于文件中的值已经在0和1之间，所以不用归一化。

　　在python命令提示符中输入kNN.handwritingClassTest()，测试该函数的输出结果。依赖于机器速度，夹在数据集可能需要话费很长时间，然后函数依次测试每个文件：

>>> kNN.handwritingClassTest()
the classifier came back with:0,the real answeris:0
the classifier came back with:0,the real answeris:0
the classifier came back with:0,the real answeris:0
the classifier came back with:0,the real answeris:0
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the classifier came back with:0,the real answeris:0
the classifier came back with:0,the real answeris:0
the classifier came back with:0,the real answeris:0
the classifier came back with:0,the real answeris:0
the classifier came back with:0,the real answeris:0
the classifier came back with:1,the real answeris:1
the classifier came back with:1,the real answeris:1
the classifier came back with:1,the real answeris:1
the classifier came back with:1,the real answeris:1
...
the classifier came back with:9,the real answeris:9
the classifier came back with:9,the real answeris:9
the classifier came back with:9,the real answeris:9
the classifier came back with:9,the real answeris:9
the classifier came back with:9,the real answeris:9
the classifier came back with:9,the real answeris:9
the classifier came back with:9,the real answeris:9
the classifier came back with:9,the real answeris:9
the classifier came back with:9,the real answeris:9
the classifier came back with:9,the real answeris:9
the classifier came back with:9,the real answeris:9
the classifier came back with:9,the real answeris:9
the classifier came back with:9,the real answeris:9
the classifier came back with:9,the real answeris:9
the classifier came back with:9,the real answeris:9

the total number of error is:11

the total error rate is:0.011628

总结
　　k-近邻算法识别手写数字数据集，错误率为1.2%。改变变量k的值、修改函数handwritingClassTest随机选取训练样本、改变训练样本的数目，都会对k-近邻算法的错误率产生影响。