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00000000000011111110000000000000

00000000001111111111000000000000

00000001111111111111100000000000

00000001111111011111100000000000

00000011111110000011110000000000

00000011111110000000111000000000

00000011111110000000111100000000

00000011111110000000011100000000

00000011111110000000011100000000

00000011111100000000011110000000

00000011111100000000001110000000

00000011111100000000001110000000

00000001111110000000000111000000

00000001111110000000000111000000

00000001111110000000000111000000

00000001111110000000000111000000

00000011111110000000001111000000

00000011110110000000001111000000

00000011110000000000011110000000

00000001111000000000001111000000

00000001111000000000011111000000

00000001111000000000111110000000

00000001111000000001111100000000

00000000111000000111111000000000

00000000111100011111110000000000

00000000111111111111110000000000

00000000011111111111110000000000

00000000011111111111100000000000

00000000001111111110000000000000

00000000000111110000000000000000

这就是经过数字图像处理的手写字体了，格式是32x32。

#inX：用于分类的输入向量。即将对其进行分类。

#dataSet：训练样本集

#labels:标签向量

def classify0(inX, dataSet, labels, k):

    dataSetSize = dataSet.shape[0]#得到训练样本集的行数，即有几个训练数据

    diffMat = tile(inX, (dataSetSize,1)) - dataSet #tile:numpy中的函数。tile将原来的一个数组，扩充成了dataSetSize个一样的数组。diffMat得到了目标与训练数值之间的差值。

    sqDiffMat = diffMat**2#差值的平方

    sqDistances = sqDiffMat.sum(axis=1)#对应列相乘，即距离和

    distances = sqDistances**0.5 #开根号 即距离

    sortedDistIndicies = distances.argsort()#升序排列

    classCount={}         #创建一个字典classCount  选择距离最小的k个点,

    for i in range(k):     #k次遍历

        voteIlabel = labels[sortedDistIndicies[i]]

        classCount[voteIlabel] = classCount.get(voteIlabel,0) + 1

    sortedClassCount = sorted(classCount.items(), key=operator.itemgetter(1), reverse=True) #原书是iteritems() py3改为items()

    return sortedClassCount[0][0]
#计算完所有点后，数据按从小到大排序，然后确定前k个距离最小元素所在的主要分类，输入k总是正整数，最后，将classCount字典分解为元组列表，然后此处的排序为逆序，
返回发生频率最高的元素标签。

　　我们要知道的是在python中。classfiy0就是一个函数，而inX, dataSet, labels, k是输入参数，其中k就是KNN算法的K。

　　shape是numpy库中的函数。.shape用于计算array各维度的长度，在python中都是从0开始的。

　　tile 也是 numpy中的函数，它可以在行和列上重复一个矩阵。

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alt="" width="803" height="312" />

那  tile(inX, (dataSetSize,1))的意思就是，让inX矩阵，在列重复1次。在行方向上重复dataSetSize次了。diffMat得到了目标与训练数值之间的差值。

　而 sum(axis=1) 为什么这样写呢，因为python和c不一样。 小编开始也不懂然后 在命令行输入help(sum) 出来很多有用的帮助。自己亲手敲了几行就懂了。

 axis=None, will sum all of the elements of the input array.  If

        axis is negative it counts from the last to the first axis.

　写到这想必大家也懂了。如果想搞机器学习，还需要了解很多python数学函数啊。

下面是get() 它是dictionary（字典）的一个函数。

所以classCount[voteIlabel] = classCount.get(voteIlabel,0) + 1 的意思就是查找classcount字典中和voteIlabel相同的元素，默认返回0，因为是从0开始的，所以要加1

 

 '''

 Created on Sep 16, 2010

 kNN: k Nearest Neighbors

 Input:      inX: vector to compare to existing dataset (1xN)

             dataSet: size m data set of known vectors (NxM)

             labels: data set labels (1xM vector)

             k: number of neighbors to use for comparison (should be an odd number)

 Output:     the most popular class label

  @author: pbharrin

 '''

 from numpy import *

 import operator   #运算符模块

 from os import listdir

 #inX：用于分类的输入向量。即将对其进行分类。

 #dataSet：训练样本集

 #labels:标签向量

 def classify0(inX, dataSet, labels, k):

     dataSetSize = dataSet.shape[0]#得到数组的行数，即有几个训练数据

     diffMat = tile(inX, (dataSetSize,1)) - dataSet #tile: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得到了目标与训练数值之间的差值。

     sqDiffMat = diffMat**2#差值的平方

     sqDistances = sqDiffMat.sum(axis=1)#对应列相乘，即距离和

     distances = sqDistances**0.5 #开根号

     sortedDistIndicies = distances.argsort()#升序排列

     classCount={}         #选择距离最小的k个点

     for i in range(k):

         voteIlabel = labels[sortedDistIndicies[i]]

         classCount[voteIlabel] = classCount.get(voteIlabel,0) + 1

     sortedClassCount = sorted(classCount.items(), key=operator.itemgetter(1), reverse=True)

     return sortedClassCount[0][0]

 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 file2matrix(filename):

     fr = open(filename)

     numberOfLines = len(fr.readlines())         #get the number of lines in the file

     returnMat = zeros((numberOfLines,3))        #prepare matrix to return

     classLabelVector = []                       #prepare labels return

     fr = open(filename)

     index = 0

     for line in fr.readlines():

         line = line.strip()                     #Python strip() 方法用于移除字符串头尾指定的字符（默认为空格）。

         listFromLine = line.split('\t')          #将line按'\t'进行分割

         returnMat[index,:] = listFromLine[0:3]

         classLabelVector.append(int(listFromLine[-1]))  #倒数第一个元素

         index += 1

     return returnMat,classLabelVector

  #归一化特征值

  #使得所有参量在0到1之间

 def autoNorm(dataSet):

     minVals = dataSet.min(0)

     maxVals = dataSet.max(0)

     ranges = maxVals - minVals

     normDataSet = zeros(shape(dataSet))

     m = dataSet.shape[0]  #返回矩阵第二维长度(列数)

     normDataSet = dataSet - tile(minVals, (m,1))

     normDataSet = normDataSet/tile(ranges, (m,1))   #element wise divide

     return normDataSet, ranges, minVals

 def datingClassTest():

     hoRatio = 0.50 #hold out 10%

     datingDataMat,datingLabels = file2matrix('datingTestSet2.txt')       #load data setfrom file

     normMat, ranges, minVals = autoNorm(datingDataMat)

     m = normMat.shape[0]       #m:目录中有多少文件#shape函数是numpy.core.fromnumeric中的函数，它的功能是查看矩阵或者数组的维数。

     numTestVecs = int(m*hoRatio)

     errorCount = 0.0

     for i in range(numTestVecs):

         classifierResult = classify0(normMat[i,:],normMat[numTestVecs:m,:],datingLabels[numTestVecs:m],3)

 #inX：用于分类的输入向量。即将对其进行分类。normMat[i,:],

 #dataSet：训练样本集.normMat[numTestVecs:m,:]

 #labels:标签向量.datingLabels[numTestVecs:m]

 #k: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)))

     print (errorCount)

 '''

 我们将一个32x32二进制图像矩阵转换为1x1024的向量

 '''

 def img2vector(filename):   #图片转化为向量

     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

 #安照先训练再测试的模式

 def handwritingClassTest():

     hwLabels = []

     trainingFileList = listdir('trainingDigits')           #load the training set listdir法用于返回指定的文件夹包含的文件或文件夹的名字的列表

     m = len(trainingFileList)  #获取文件长度

     trainingMat = zeros((m,1024))

     for i in range(m):

         fileNameStr = trainingFileList[i]      #从文件名解析分类数字

         fileStr = fileNameStr.split('.')[0]     #take off .txt

         classNumStr = int(fileStr.split('_')[0])

         hwLabels.append(classNumStr)

         trainingMat[i,:] = img2vector('trainingDigits/%s' % fileNameStr)  #将文件名

     testFileList = listdir('testDigits')        #iterate through the test set

     errorCount = 0.0

     mTest = len(testFileList)

     for i in range(mTest):

         fileNameStr = testFileList[i]

         fileStr = fileNameStr.split('.')[0]     #take off .txt

         classNumStr = int(fileStr.split('_')[0])

         vectorUnderTest = img2vector('testDigits/%s' % fileNameStr)

         classifierResult = classify0(vectorUnderTest, trainingMat, hwLabels, 4)

         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)))

 # main part

 handwritingClassTest();

k临近算法手写识别，错误率为1.2%，改变k的值，修改函数handwriting - classTest 随机选取的训练样本，改变训练样本的个数，都会对k临近算法错误率产生影响。