k-近邻原理

K-近邻原理

对于未知类别数据集中的点与当前点的距离
1. 计算已知类别数据集中的点与当前点的距离
2.按照距离依次排序
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概率
5.返回前k个点出现频率最高的类别作为当前点预测分类

概述：
KNN算法本身简单有效，它是一种lazy-learning算法；
分类器不需要使用训练集进行训练，训练时间复杂度为0；
KNN分类的计算复杂度和训练集中的文档数目成正比，也就是说，如果训练集中文档总数为n，那么KNN的分类时间复杂度为O(n)。

该算法的三个基本要素：
1. k值的选择；
2. 距离度量；
3. 分类决策规则

问题：
该算法在分类时有个主要的不足是，当样本不平衡时，如一个类的样本容量很大，而其他类样本容量很小时，有可能导致当输入一个新样本时，该样本的k个邻居大容量的样本占多数。

解决：
不同的样本给予不同权重项。

代码如下：

import numpy as np
import operator

def createDataSet():
    group = np.array([[1.0,1.1],[1.0,1.0],[0.0,0.0],[0,0.1]])
    labels = ['A','A','B','B']
    return group,labels

def classify0(inX,dataSet,labels,k):
    dataSetSize = dataSet.shape[0]
    diffMat = np.tile(inX, (dataSetSize,1)) - dataSet
    sqDiffMat = diffMat ** 2
    sqDistances = sqDiffMat.sum(axis = 1)
    distance = sqDistances **0.5
    sortedDistIndicies = distance.argsort()
    classCount = {}
    for i in range(k):
        voteLabel = labels[sortedDistIndicies[i]]
        classCount[voteLabel] = classCount.get(voteLabel,0) + 1
    sortedClassCount = sorted(classCount.iteritems(),key=operator.itemgetter(1),reverse=True)
    return sortedClassCount[0][0]

def file2matrix(filename):
    fr = open(filename)
    arrayOflines = fr.readlines()
    numOfLines = len(arrayOflines)
    returnMat = np.zeros((numOfLines,3))
    classLabelVector = []
    index = 0
    for line in arrayOflines:
        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
    m = dataSet.shape[0]
    normDataSet = np.zeros(np.shape(dataSet))
    normDataSet = dataSet - np.tile(minVals,(m,1))
    normDataSet = normDataSet / np.tile(ranges,(m,1))
    return normDataSet,ranges,minVals

def datingClassTest():
    hoRatio = 0.1
    datingDataMat,datingLabels = file2matrix('datingTestSet2.txt')
    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],4)
        print ('the classifier came back with: %d , the real answer is : %d' %(classifierResult, datingLabels[i]))
        if (classifierResult != datingLabels[i]):
            errorCount += 1.0
    print ('total result is : %f' %(errorCount / float(numTestVecs))

def classifyperson():
    resultList = ['not at all', 'in small does','in large does']
    input_man= [20000, 10, 5]
    datingDataMat,datingLabels = file2matrix('datingTestSet2.txt')
    normMat,ranges,minVals = autoNorm(datingDataMat) 
    result = classify0((input_man - minVals) / ranges,normMat,datingLabels,3)
    print ('you will probably like this person:' ,  resultList[result-1])

if __name__ == '__main__':
#     group,labels = createDataSet()
#     test = classify0([3,3],group,labels,3)
#     print test
    classifyperson()

output: A