K近邻算法——手写数字识别_k近邻算法实现手写数字识别

一、准备工作
前面的博客已讲述了K近邻的概念，这里是一个K近邻算法的应用。
准备内容：
1.手写数字训练集trainingDigits

2.手写数字测试集testDigits

程序的基本内容:
1.原算法的第一步是导入数据，并进行矩阵化处理，这里的第一步是将图片转化成向量。图片在数据集中是以数字的形式保存，3232，将二维图片转化成11024一维的向量。一共有接近2000的训练集和900多的测试集
2.将每一个测试样本都调用KNN算法，KNN算法的参数为1.测试向量 2.训练样本 3.类别 4.k值

代码：

import numpy as np
import operator
import os




# 图像转换为向量
def img2vector(filename):
    returnVect = np.zeros((1,1024))  # 生成一个1*1024的向量
    fr = open(filename)  # 打开文件
    for i in range(32):
        lineStr = fr.readline()  # 一行一行的读
        for j in range(32):
            returnVect[0,32*i+j] = int(lineStr[j]) # 一个一个的加入1*1024的向量中
    return returnVect  # 返回这个1*1024向量

# KNN
def classify0(inX,dataset,labels,k):
    dataSetSize = dataset.shape[0]
    #  下面计算距离
    diffMat = np.tile(inX,(dataSetSize,1))-dataset # tile()复制函数
    sqDiffMat = diffMat**2
    sqDistances = sqDiffMat.sum(axis=1)     # 进行行相加
    distances = sqDistances**0.5
    sortedDistIndicies = distances.argsort()  #argsort()按照从小到大排序返回原序列元素的序号。
    # 选择距离最小的K个点
    classCount={}
    for i in range(k):
        voteIlabel =labels[sortedDistIndicies[i]]   # 找到与数据最近的k个标签
        classCount[voteIlabel] = classCount.get(voteIlabel,0)+1   # 将各个标签的数量添加到字典中
    # operator.itemgetter(1)选择字典的value进行排序，拍完序reserve反转
    sortedClassCount = sorted(classCount.items(),key=operator.itemgetter(1),reverse=True)
    # print(sortedClassCount)
    return sortedClassCount[0][0]


# 测试手写数字识别
def handwritingClassTest():
    hwlabels = []
    trainingFileList = os.listdir('trainingDigits')
    m = len(trainingFileList)
    trainingMat = np.zeros((m,1024))
    for i in range(m):
        fileNameStr = trainingFileList[i]     # 获取训练样本名字
        fileStr = fileNameStr.split('.')[0]   #获取训练样本的名字去掉后缀
        classNumStr = int(fileStr.split('_')[0])  # 获取‘0_13’前面数字，代表数字
        hwlabels.append(classNumStr)  # 类别标签保存到列表中
        trainingMat[i,:] = img2vector('trainingDigits/%s' %fileNameStr)  # 将全部训练样本组成一个矩阵
    testFileList = os.listdir('testDigits')  # 获取测试样本的列表
    errorCount = 0.0   # 错误分类
    mTest = len(testFileList)  # 测试样本的数量
    for i in range(mTest):
        fileNameStr = testFileList[i]  # 获取测试样本的全部名称
        fileStr = fileNameStr.split('.')[0]  # 获取测试样本的名称
        classNumStr = int(fileStr.split('_')[0]) # 得到类别名
        vectorUnderTest = img2vector('testDigits/%s'%fileNameStr)  # 转化成1*1024向量
        classifierResult = classify0(vectorUnderTest,trainingMat,hwlabels,3)  # 类别预测结果
        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 error is : %d' %errorCount)
    print('the total error rate is :%f' % (errorCount/float(mTest)))


handwritingClassTest()
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结果：

the classifier came back with :0,the real answer is :0
the classifier came back with :0,the real answer is :0
the classifier came back with :0,the real answer is :0
the classifier came back with :0,the real answer is :0
the classifier came back with :0,the real answer is :0
the classifier came back with :0,the real answer is :0

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the classifier came back with :2,the real answer is :2
the classifier came back with :2,the real answer is :2
the classifier came back with :2,the real answer is :2
the classifier came back with :2,the real answer is :2
the classifier came back with :2,the real answer is :2
the classifier came back with :3,the real answer is :3
the classifier came back with :3,the real answer is :3
the classifier came back with :3,the real answer is :3

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the classifier came back with :9,the real answer is :9
the classifier came back with :9,the real answer is :9
the classifier came back with :9,the real answer is :9
the total number of error is : 11
the total error rate is :0.011628

Process finished with exit code 0

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可以看到预测的错误率为1.1%。通过更改变量K值和修改函数的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。

样本集下载：百度云链接
提取码：g64m