一、KNN（k-近邻算法）工作原理
一句话：从训练集中找出k个最接近测试数据的训练样本，再从这k个样本中找出出现次数最多的分类，作为测试数据的分类。
存在一个样本数据集合（训练样本集）且样本集中每个数据都存在标签（即我们知道样本集中每一数据与所属分类的对应关系）；
输入没有标签的数据后，将该数据的每个特征与样本集中数据对应的特征进行比较，并提取样本集中特征最相似数据（最近邻）的分类标签；
选择样本集中前k个最相似的数据（这就是k-近邻算法中k的出处，通常k是不大于20的整数）；
选择k个最相似数据中出现次数最多的分类，作为新数据的分类。
二、优缺点
优点：
1、理论成熟、思想简单、易理解和实现；
2、可用于分类（包括非线性分类）、回归；
3、计算时间和空间线性于训练集的规模（训练时间复杂度比支持向量机之类的算法低，O(n)）
4、适合单标签多分类和多标签分类问题；
5、对于类域的交叉或重叠较多的待分类样本集较为适合；
缺点：
1、计算量大（尤其是特征数比较多的时候）
2、对不平衡数据集（数据集中各个类别的样本量极不均衡）效果差（可采用加权投票法改进）
3、k值的选择对分类效果有很大影响（较小的话对噪声敏感，需估计最佳k值）
4、可解释性不强
三、代码
代码来自于《机器学习实践》，添加了一些小注释和一些测试代码
1 #encoding:utf-8
2 '''
3 Created on Sep 16, 2010
4 kNN: k Nearest Neighbors
5
6 Input: inX: vector to compare to existing dataset (1xN)
7 dataSet: size m data set of known vectors (NxM)
8 labels: data set labels (1xM vector)
9 k: number of neighbors to use for comparison (should be an odd number)
10
11 Output: the most popular class label
12
13 @author: pbharrin
14 '''
15 from numpy import *
16 import operator
17 from os import listdir
18
19 #inX:用于分类的输入向量，即将对其进行分类
20 #dataSet：训练样本集
21 #labels：标签向量
22 def classify0(inX, dataSet, labels, k):
23 dataSetSize = dataSet.shape[0] # 得到数组的行数。即知道有几个训练数据
24 diffMat = tile(inX, (dataSetSize,1)) - dataSet #tile将原来的一个数组，行数扩充dataSetSize个，列数不扩充。diffMat得到了目标与训练数值之间的差值
25 sqDiffMat = diffMat**2 #各个元素分别平方
26 sqDistances = sqDiffMat.sum(axis=1) # 对沿着轴1的方向进行数据相加处理，即得到一个每一个距离的平方
27 distances = sqDistances**0.5 # 开方的距离
28 sortedDistIndices = distances.argsort() #升序排列
29 classCount={} # 定义字典
30 for i in range(k):
31 voteIlabel = labels[sortedDistIndices[i]] # 从排序好的list中依次获取索引，并根据该索引，获得相应距离对应的标签值
32 classCount[voteIlabel] = classCount.get(voteIlabel,0) + 1 # 从字典中，获取该标签值对应的统计数，若还没有标签值，则取默认值0，并且+1
33 sortedClassCount = sorted(classCount.items(), key=operator.itemgetter(1), reverse=True)
34 return sortedClassCount[0][0]
35
36 def createDataSet():
37 group = array([[1.0,1.1],[1.0,1.0],[0,0],[0,0.1]])
38 labels = ['A','A','B','B']
39 return group, labels
40
41 def file2matrix(filename):
42 fr = open(filename)
43 numberOfLines = len(fr.readlines()) #get the number of lines in the file
44 returnMat = zeros((numberOfLines,3)) #prepare matrix to return
45 print(type(returnMat))
46 classLabelVector = [] #prepare labels return
47 fr = open(filename)
48 index = 0
49 for line in fr.readlines():
50 line = line.strip()
51 listFromLine = line.split(' ')
52 returnMat[index,:] = listFromLine[0:3] # numpy数组赋值方式
53 classLabelVector.append(int(listFromLine[-1]))
54 index += 1
55 return returnMat,classLabelVector
56
57 def autoNorm(dataSet):
58 minVals = dataSet.min(0) # 0 表示纵轴，1表示横轴，与matrix刚好相反。注意这里保留了所有列的平均值
59 maxVals = dataSet.max(0)
60 ranges = maxVals - minVals
61 normDataSet = zeros(shape(dataSet))
62 m = dataSet.shape[0]
63 normDataSet = dataSet - tile(minVals, (m,1))
64 normDataSet = normDataSet/tile(ranges, (m,1)) #element wise divide
65 return normDataSet, ranges, minVals
66
67 def datingClassTest():
68 hoRatio = 0.10 #hold out 10%
69 datingDataMat,datingLabels = file2matrix('datingTestSet2.txt') #load data setfrom file
70 normMat, ranges, minVals = autoNorm(datingDataMat)
71 m = normMat.shape[0]
72 numTestVecs = int(m*hoRatio)
73 errorCount = 0.0
74 for i in range(numTestVecs):
75 classifierResult = classify0(normMat[i,:],normMat[numTestVecs:m,:],datingLabels[numTestVecs:m],3)
76 print("the classifier came back with: %d, the real answer is: %d" % (classifierResult, datingLabels[i]))
77 if (classifierResult != datingLabels[i]): errorCount += 1.0
78 print("the total error rate is: %f" % (errorCount/float(numTestVecs)))
79 print(errorCount)
80
81 def img2vector(filename):
82 returnVect = zeros((1,1024))
83 fr = open(filename)
84 for i in range(32):
85 lineStr = fr.readline()
86 for j in range(32):
87 returnVect[0,32*i+j] = int(lineStr[j])
88 return returnVect
89
90 def handwritingClassTest():
91 hwLabels = []
92 trainingFileList = listdir('trainingDigits') #load the training set
93 m = len(trainingFileList)
94 trainingMat = zeros((m,1024))
95 for i in range(m):
96 fileNameStr = trainingFileList[i]
97 fileStr = fileNameStr.split('.')[0] #take off .txt
98 classNumStr = int(fileStr.split('_')[0])
99 hwLabels.append(classNumStr)
100 trainingMat[i,:] = img2vector('trainingDigits/%s' % fileNameStr)
101 testFileList = listdir('testDigits') #iterate through the test set
102 errorCount = 0.0
103 mTest = len(testFileList)
104 for i in range(mTest):
105 fileNameStr = testFileList[i]
106 fileStr = fileNameStr.split('.')[0] #take off .txt
107 classNumStr = int(fileStr.split('_')[0])
108 vectorUnderTest = img2vector('testDigits/%s' % fileNameStr)
109 classifierResult = classify0(vectorUnderTest, trainingMat, hwLabels, 3)
110 print("the classifier cam e back with: %d, the real answer is: %d" % (classifierResult, classNumStr))
111 if (classifierResult != classNumStr): errorCount += 1.0
112 print ("
the total number of errors is: %d" % errorCount)
113 print ("
the total error rate is: %f" % (errorCount/float(mTest)))
114
115
116 if __name__ == '__main__':
117 trainingMat = zeros((10,4))
118 print(trainingMat)
119 m = len(trainingMat)
120 for i in range(m):
121 trainingMat[i,:] = [1,2,3,4]
122 print ('-----------------')
123 print (trainingMat)
124
125 a = array([[3,2,3,4],[3,4,5,6]])
126 a = a**2
127 print (a)
128 print ('-----------')
129 sqDistances = a.sum(axis=0) # 按y轴（纵轴）相加
130 print (sqDistances)
131 sqDistances2 = a.sum(axis=1) # 沿x轴（横轴）相加
132 print (sqDistances2)
133 distances = sqDistances**0.5
134 print (distances)
135 print (distances.argsort())
136 print (distances[0])
137
138 x = array([1,4,3,-1,6,9])
139 print (x.argsort()[-1])
140 y = x.argsort()
141 print (x)
142 print (y)
143 print (x[y[0]])
144
145 classCount = {0:3, 5:2, 4:6}
146 print(classCount)
147 sortedClassCount = sorted(classCount.items(), key=operator.itemgetter(1), reverse=True)
148 print(sortedClassCount)
149 print (sortedClassCount[0][0])
150
151 handwritingClassTest() # 手写字体分类测试
152 datingClassTest() # 约会对象分类测试
四、绘制里程数与玩视频游戏所占比例的数据散点图
代码如下：
''' Created on Oct 6, 2010 @author: Peter ''' from numpy import * import matplotlib import matplotlib.pyplot as plt from matplotlib.patches import Rectangle n = 1000 #number of points to create xcord1 = []; ycord1 = [] xcord2 = []; ycord2 = [] xcord3 = []; ycord3 = [] markers =[] colors =[] fw = open('testSet.txt','w') for i in range(n): [r0,r1] = random.standard_normal(2) # 正态分布函数中区数据个数 myClass = random.uniform(0,1) # 从0到1中取随机值，将0.66%（即66分以上的，标识为喜欢） if (myClass <= 0.16): # fFlyer = random.uniform(22000, 60000) # 自定义里程数 tats = 3 + 1.6*r1 # 自定义玩视频游戏时间的函数（这个蛮有意思的） markers.append(20) # 大小定义 colors.append(2.1) # 颜色定义 classLabel = 1 #'didntLike' xcord1.append(fFlyer); ycord1.append(tats) elif ((myClass > 0.16) and (myClass <= 0.33)): fFlyer = 6000*r0 + 70000 tats = 10 + 3*r1 + 2*r0 markers.append(20) colors.append(1.1) classLabel = 1 #'didntLike' if (tats < 0): tats =0 # 异常值处理 if (fFlyer < 0): fFlyer =0 # 异常值处理 xcord1.append(fFlyer); ycord1.append(tats) elif ((myClass > 0.33) and (myClass <= 0.66)): fFlyer = 5000*r0 + 10000 tats = 3 + 2.8*r1 markers.append(30) colors.append(1.1) classLabel = 2 #'smallDoses' if (tats < 0): tats =0 if (fFlyer < 0): fFlyer =0 xcord2.append(fFlyer); ycord2.append(tats) else: fFlyer = 10000*r0 + 35000 # 自定义：里程多又爱玩游戏的超级喜欢（里程多，所以会玩） tats = 10 + 2.0*r1 # 自定义：里程多又爱玩游戏的超级喜欢（玩游戏时间多，可以和自己一起玩） markers.append(50) colors.append(0.1) classLabel = 3 #'largeDoses' if (tats < 0): tats =0 if (fFlyer < 0): fFlyer =0 xcord3.append(fFlyer); ycord3.append(tats) fw.close() fig = plt.figure() ax = fig.add_subplot(111) #ax.scatter(xcord,ycord, c=colors, s=markers) type1 = ax.scatter(xcord1, ycord1, s=20, c='red') type2 = ax.scatter(xcord2, ycord2, s=30, c='green') type3 = ax.scatter(xcord3, ycord3, s=50, c='blue') ax.legend([type1, type2, type3], ["Did Not Like", "Liked in Small Doses", "Liked in Large Doses"], loc=2) ax.axis([-5000,100000,-2,25]) # 定义x轴和y轴的起始点 plt.xlabel('Frequent Flyier Miles Earned Per Year') # 定义x轴标签描述 plt.ylabel('Percentage of Time Spent Playing Video Games') # 定义x轴标签描述 plt.show()