K邻近算法

存在一个样本数据集合，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。输入没有标签的新数据后，将新数据的每个特征与样本集中数据对应的特征进行比较，然后算法提取样本集中特征最相似（最邻近）的分类标签。

K邻近模型由三个基本要素--距离度量、K值选择和分类决策规则决定

1. 使用python导入数据

from numpy import *
import operator #提供排序操作需要的函数def createDataSet():group = array([[1.0, 1.1], [1.0,1.1],[0, 0], [0, 0.1]])labels = ['A', 'A', 'B', 'B']return group, labels

group, labels = createDataSet()

group

array([[1. , 1.1],[1. , 1.1],[0. , 0. ],[0. , 0.1]])

labels

['A', 'A', 'B', 'B']

2.实施KNN算法

伪代码如下：

1. 计算已知类别数据集中的点与当前点之间的距离
2. 按照距离递增次序排序
3. 选取与当前点距离最小的k个点
4. 确定前k个点所在类别的出现频率
5. 返回前k个点出现频率最高的类别作为当前点的预测分类

def classify0(inX, dataSet, labels, k):             #inX是输入（待分类）dataSetSize = dataSet.shape[0]                  #利用属性shape[0]得到样本的个数diffMat = tile(inX, (dataSetSize, 1)) - dataSet sqDiffMat = diffMat**2sqDistances = sqDiffMat.sum(axis=1)distances = sqDistances**0.5                       #距离计算sortedDistIndicies = distances.argsort()            #对距离进行排序classCount = {}for i in range(k):                                 #选取临近的k个样本voteIlabel = labels[sortedDistIndicies[i]]     #获得样本标签classCount[voteIlabel] = classCount.get(voteIlabel, 0) + 1 #样本标签统计#对样本标签进行从大到小排序，返回出现次数最多的那个标签值sortedClassCount = sorted(classCount.items(), key=operator.itemgetter(1), reverse=True)return sortedClassCount[0][0]

注：

1.numpy.tile()函数可以将原矩阵纵向或横向地复制，复制的方向取决于第二个参数。在这里inX被纵向地复制了四次，然后减去dataset，这样一次减法就将inX和样本集中的每个样本做了减法。形如inX = [x1，x2]. tile之后变成[[x1,x2],[x1,x2],[x1,x2],[x1,x2]]，原dataset的数据形式为[[a1,b1],[a2,b2],[a3,b3],[a4,b4]]。结合代码不难理解这里的距离计算了。

2.numpy.argsort()返回数组值从小到大的索引值

3.classCount.get(voteIlabel,0).这里用到python字典的方法get(). 其使用的语法为：dict.get(key, default=None)。其中key是字典中要查找的键，如果指定的键不在，那么返回default的值。

4.对标签数目排序用的是numpy.sorted，其与numpy.sort有一定区别。后者是用在列表对象上，前者则适用与所有可迭代的对象。classCount.iteritems()的作用是返回字典列表操作之后的迭代(python3x中已经废除)。key=operator.itemgetter(1)的意思定义了获取字典第一维上（也就是每个标签数目）的数据的函数，itemgetter()返回的是一个函数，因为key的参数可以是lamda表达式或者函数。

classify0([0,0], group, labels, 3)

'B'

3.实例1--利用knn算法改进约会网站的配对效果

Step1:准备数据：从文本文件中解析数据

def file2matrix(filename):fr = open(filename)arrayOLines = fr.readlines()    #arrayOLines是一个列表，包括所有的行numberOfLines = len(arrayOLines)  #获得行数returnMat = zeros((numberOfLines,3)) #创建一个返回的NumPy矩阵classLabelVector = []          #类标签index = 0for line in arrayOLines:line = line.strip()        #去掉换行符listFromLine = line.split('\t')  returnMat[index, :] = listFromLine[0:3] #将数据装填到returnMatlabels = {'didntLike':1, 'smallDoses':2, 'largeDoses':3}classLabelVector.append(labels[(listFromLine[-1])]) #获得每个样例的标签index += 1return returnMat, classLabelVector

datingDataMat, datingLabels = file2matrix('datingTestSet.txt')

datingDataMat

array([[4.0920000e+04, 8.3269760e+00, 9.5395200e-01],[1.4488000e+04, 7.1534690e+00, 1.6739040e+00],[2.6052000e+04, 1.4418710e+00, 8.0512400e-01],...,[2.6575000e+04, 1.0650102e+01, 8.6662700e-01],[4.8111000e+04, 9.1345280e+00, 7.2804500e-01],[4.3757000e+04, 7.8826010e+00, 1.3324460e+00]])

datingLabels[0:20]

[3, 2, 1, 1, 1, 1, 3, 3, 1, 3, 1, 1, 2, 1, 1, 1, 1, 1, 2, 3]

注：

1.readlines()是python文件的方法，它返回一个列表，包含所有的行

2.split()是字符串方法，通过指定分隔符对字符串进行切片，返回一个字符串列表。如果参数 num 有指定值，则分隔 num+1 个子字符串，语法是str.split(str="", num=string.count(str)).，str是分隔符，有'\n','\t'等，num是分隔的次数，默认-1，即分割所有。

Step2:分析数据：使用Matplotlib创建散点图

%matplotlib inline
import matplotlib
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.add_subplot(111)
ax.scatter(datingDataMat[:,0], datingDataMat[:,1],15.0*array(datingLabels),15.0*array(datingLabels))
plt.show()

Step3:归一化特征值

def autoNorm(dataset):minVals = dataset.min(0)  maxVals = dataset.max(0)  #获得每一列的最大、最小值ranges = maxVals - minVals #获得范围normDataSet = zeros(shape(dataset)) m = dataset.shape[0]  #数据集的个数normDataSet = dataset - tile(minVals, (m,1)) normDataSet = normDataSet/tile(ranges, (m,1))#归一化的公式，再次用到tile()return normDataSet, ranges, minVals

normMat, ranges, minVals = autoNorm(datingDataMat)
normMat

array([[0.44832535, 0.39805139, 0.56233353],[0.15873259, 0.34195467, 0.98724416],[0.28542943, 0.06892523, 0.47449629],...,[0.29115949, 0.50910294, 0.51079493],[0.52711097, 0.43665451, 0.4290048 ],[0.47940793, 0.3768091 , 0.78571804]])

ranges

array([9.1273000e+04, 2.0919349e+01, 1.6943610e+00])

minVals

array([0.      , 0.      , 0.001156])

Step4:对分类器进行测试

def datingClassTest():hoRatio = 0.10datingDataMat, datingLabels = file2matrix('datingTestSet.txt')  #读取文件normMat, ranges, minVals = autoNorm(datingDataMat)            #归一化m = normMat.shape[0]                                       #获得样本总体数目numTestVecs = int(m*hoRatio)                        #选出一部分作为测试，另一部分作为训练errorCount = 0.0for i in range(numTestVecs):classifierResult = classify0(normMat[i,:], normMat[numTestVecs:m,:],\datingLabels[numTestVecs:m],3) #得到分类结果print("the classifier came back with: %d, the real answer is: %d"\%(classifierResult, datingLabels[i]))         if(classifierResult != datingLabels[i]): errorCount += 1.0 #如果错误就记录print("the total error rate is: %f" %(errorCount/float(numTestVecs))) #计算错误率

datingClassTest()

the classifier came back with: 3, the real answer is: 3
the classifier came back with: 2, the real answer is: 2
the classifier came back with: 1, the real answer is: 1
the classifier came back with: 1, the real answer is: 1
the classifier came back with: 1, the real answer is: 1
the classifier came back with: 1, the real answer is: 1
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: 1, the real answer is: 1
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 1, the real answer is: 1
the classifier came back with: 1, the real answer is: 1
the classifier came back with: 2, the real answer is: 2
the classifier came back with: 1, the real answer is: 1
the classifier came back with: 1, the real answer is: 1
the classifier came back with: 1, the real answer is: 1
the classifier came back with: 1, the real answer is: 1
the classifier came back with: 1, the real answer is: 1
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: 2, the real answer is: 2
the classifier came back with: 1, the real answer is: 1
the classifier came back with: 3, the real answer is: 2
the classifier came back with: 3, the real answer is: 3
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: 2, the real answer is: 2
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 2, the real answer is: 2
the classifier came back with: 1, the real answer is: 1
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 1, the real answer is: 1
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 1, the real answer is: 1
the classifier came back with: 2, the real answer is: 2
the classifier came back with: 1, the real answer is: 1
the classifier came back with: 1, the real answer is: 1
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: 1, the real answer is: 1
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
the classifier came back with: 1, the real answer is: 1
the classifier came back with: 1, the real answer is: 1
the classifier came back with: 1, the real answer is: 1
the classifier came back with: 1, the real answer is: 1
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: 1, the real answer is: 1
the classifier came back with: 3, the real answer is: 3
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: 1, the real answer is: 1
the classifier came back with: 2, the real answer is: 2
the classifier came back with: 1, the real answer is: 1
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: 2, the real answer is: 2
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 1, the real answer is: 1
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: 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: 1
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 1, the real answer is: 1
the classifier came back with: 1, the real answer is: 1
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: 1, the real answer is: 1
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: 1
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 1, the real answer is: 1
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: 1, the real answer is: 1
the classifier came back with: 1, the real answer is: 1
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 2, the real answer is: 3
the classifier came back with: 1, the real answer is: 1
the classifier came back with: 2, the real answer is: 2
the classifier came back with: 1, the real answer is: 1
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: 2, the real answer is: 2
the classifier came back with: 1, the real answer is: 1
the classifier came back with: 3, the real answer is: 1
the total error rate is: 0.050000