K-近邻算法（KNN）

原理：

存在一个样数据集合，样本集中每个数据都存在标签，输入没有标签的新数据之后，将新数据的每个特征与样本数据的对应特征进行比较，算法提取出样本集中特征最相似的k个数据，然后这k个数据中出现次数最多的分类作为新数据的分类。

k越大，决策边界越平滑。实际中选择k,cross validation!

优缺点：

精度高，对异常值不敏感。

缺点：计算复杂度高，空间复杂的高。

kNN基本代码，数字识别代码：

# _*_ coding:UTF8 _*_
# 测试demo 约会网站 数字识别
'''
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
from os import listdir

def classify0(inX, dataSet, labels, k):
    dataSetSize = dataSet.shape[0]
    diffMat = tile(inX, (dataSetSize,1)) - dataSet #tile函数复制
    sqDiffMat = diffMat**2
    print type(sqDiffMat)
    sqDistances = sqDiffMat.sum(axis=1) #按照行相加
    distances = sqDistances**0.5
    sortedDistIndicies = distances.argsort() #  存储的是下标
    classCount={}          
    for i in range(k):
        voteIlabel = labels[sortedDistIndicies[i]]
        classCount[voteIlabel] = classCount.get(voteIlabel,0) + 1
    sortedClassCount = sorted(classCount.iteritems(), 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('digits/trainingDigits')           #load the training set
    m = len(trainingFileList)
    trainingMat = zeros((m,1024))
    for i in range(m):
        fileNameStr = trainingFileList[i]
        fileStr = fileNameStr.split('.')[0]     #take off .txt
        if fileStr == '' :
            continue
        classNumStr = int(fileStr.split('_')[0])
        hwLabels.append(classNumStr)
        trainingMat[i,:] = img2vector('digits/trainingDigits/%s' % fileNameStr)
    testFileList = listdir('digits/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
        if fileStr == '':
            continue
        classNumStr = int(fileStr.split('_')[0])
        vectorUnderTest = img2vector('digits/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))

 Kaggle 数字识别kNN代码

def kaggleHandWriting():
    data = loadData('Kaggle/train.csv')
    m = len(data)
    n = len(data[0]) - 1
    hwLabels = []
    trainData = zeros((m, n))
    for i in range(m):
        hwLabels.append(int(data[i][0]))
        for j in range(n):
            trainData[i][j] = int(data[i][j + 1])
    testData = loadData('Kaggle/test.csv')
    mTest = len(testData)
    predictLabels = []
    for i in range(mTest):
        curTest = []
        for j in range(n):
            curTest.append(int(testData[i][j]))
        label = classify0(curTest, trainData, hwLabels, 5)
        predictLabels.append(label)
        print '第 %d 个数为：%d'%(i,label)
    saveResult(predictLabels)

def loadData(filename):
    data = []
    f = file(filename, 'rb')
    lines = csv.reader(f)
    for line in lines:
        print ','.join(line)
        data.append(line)
    del(data[0])
    f.close()
    return data
def saveResult(result):
    f = file('Kaggle/sample_submission.csv','wb')
    myWriter = csv.writer(f)
    myWriter.writerow(['ImageId','Label'])
    m = len(result)
    for i in range(m):
        myWriter.writerow([i,result[i]])
    f.close()