KNN手写数字识别

kNN算法思想：从训练集中找到和新数据最接近的k条记录，然后根据他们中出现最多的分类来决定新数据的类别

1、KNN伪代码：

2、距离度量方式：

--欧氏距离

--曼哈顿距离

--切比雪夫距离

--余弦相似度（适合文本分析）衡量样本向量之间的差异

3、优缺点：

--优点：简单有效易于实现

--缺点：必须保存全部数据集，训练集很大时，保存数据消耗大量存储空间；

           必须对每个数据计算距离，实际使用时非常耗时

总结：k近邻算法没有训练过程

          k值较小时，对数据较敏感，抗噪能力差；k值过大，会因数据不平衡导致分类误差增大

代码实现：

# -*- coding: utf-8 -*-
#手写数字识别

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
    sqDiffMat = diffMat**2
    sqDistances = sqDiffMat.sum(axis=1)
    distances = sqDistances**0.5
    sortedDistIndicies = distances.argsort()     
    classCount={}          
    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()
        listFromLine = line.split('\t')
        returnMat[index,:] = listFromLine[0:3]
        classLabelVector.append(int(listFromLine[-1]))
        index += 1
    return returnMat,classLabelVector
    
def autoNorm(dataSet):
    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))   #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]
    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)))
    print (errorCount)
    
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 = []
    trainingFileList = listdir('trainingDigits')    #load the training set 指定目录下的文件列表
    m = len(trainingFileList)
    trainingMat = zeros((m,1024))
    for i in range(m):
        fileNameStr = trainingFileList[i]
        fileStr = fileNameStr.split('.')[0]     #take off .txt
        classNumStr = int(fileStr.split('_')[0])
        hwLabels.append(classNumStr)
        trainingMat[i,:] = img2vector('trainingDigits/%s' % fileNameStr)    #[i,:]表示切片
    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, 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)))

需要补充注释 最好每一行都有注释

运行结果如下：

》kNN.handWritingClassTest()
the total number of errors is: 10
the total error rate is: 0.010571