K-近邻算法
K-近邻算法概述
工作原理:给定一个训练样本集,训练样本集中的每个数据都有自己所属的类别,输入一个不知道所属类别的新数据,在训练样本集中找到k个最邻近的数据,而这k个数据的大多数所属的类别将作为新数据所属的类别。
优点:精度高,对异常值不敏感,无数据输入假定
缺点:计算复杂度高,空间复杂度高
适用范围:数值型和标称型
算法初涉
import numpy as np
import operator
from os import listdir
def createDataSet():
group = np.array([[1.0,1.1],[1.0,1.0],[0,0],[0,0.1]])
labels = ['A','A','B','B']
return group, labels
group,labels = createDataSet()
def classify0(inX, dataSet, labels, k): #用于分类的输入向量,训练样本集,标签向量,选择最近邻居的数目
dataSetSize = dataSet.shape[0] #读取矩阵第一维度的长度(行数)
diffMat = np.tile(inX, (dataSetSize,1)) - dataSet #tile()把数组沿各个方向复制
sqDiffMat = diffMat**2
sqDistances = sqDiffMat.sum(axis=1) #对每一行进行求和
distances = sqDistances**0.5 #求出距离
sortedDistIndicies = distances.argsort() #按数值从小到大排序的索引
classCount={}
for i in range(k):
voteIlabel = labels[sortedDistIndicies[i]]
classCount[voteIlabel] = classCount.get(voteIlabel,0) + 1
sortedClassCount = sorted(classCount.items(),
key=operator.itemgetter(1), reverse=True)
return sortedClassCount[0][0]
classify0([0,0],group,labels,3) # B
使用K-近邻算法改进约会网站的配对效果
准备数据:从文本文件中解析数据
def file2matrix(filename):
fr = open(filename)
arrayOLines = fr.readlines()
numberOfLines = len(arrayOLines) #文件行数
returnMat = np.zeros((numberOfLines,3))
classLabelVector = []
index = 0
for line in arrayOLines:
line = line.strip()
listFromLine = line.split('\t')
returnMat[index,:] = listFromLine[0:3]
classLabelVector.append(int(listFromLine[-1]))
index += 1
return returnMat,classLabelVector
datingDataMat,datingLabels = file2matrix('datingTestSet2.txt')
分析数据:创建散点图
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.add_subplot(111)
ax.scatter(datingDataMat[:,1],datingDataMat[:,2],
15.0*np.array(datingLabels), 15.0*np.array(datingLabels))
plt.show()

归一化数值
def autoNorm(dataSet): #将数字特征值转化为0到1的区间
minVals = dataSet.min(0)
maxVals = dataSet.max(0)
ranges = maxVals - minVals
normDataSet = np.zeros(np.shape(dataSet))
m = dataSet.shape[0]
normDataSet = dataSet - np.tile(minVals, (m,1))
normDataSet = normDataSet/np.tile(ranges, (m,1))
return normDataSet, ranges, minVals
normMat, ranges, minVals = autoNorm(datingDataMat)
测试算法
这里使用90%的样本训练分类器,10%的样本测试分类器,检测分类器的正确性
def datingClassTest():
hoRatio = 0.10
datingDataMat,datingLabels = file2matrix('datingTestSet2.txt')
normMat, ranges, minVals = autoNorm(datingDataMat) #归一化数值
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)))
datingClassTest()
使用算法
def classifyPerson():
resultList = ['not at all','in small doses','in large doses']
percentTats = float(input("percentage of time spent playing video games?"))
ffMiles = float(input("frequent flier miles earned per year?"))
iceCream = float(input("liters of ice cream consumed per year?"))
datingDataMat,datingLabels = file2matrix("datingTestSet2.txt")
normMat, ranges, minVals = autoNorm(datingDataMat)
inArr = np.array([ffMiles,percentTats, iceCream])
classifierResult = classify0((inArr-minVals)/ranges,normMat,datingLabels,3)
print("You will probably like this person: ",
resultList[classifierResult - 1])
classifyPerson()
构造手写识别系统
准备数据
def img2vector(filename):
returnVect = np.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
testVector = img2vector('./testDigits/0_13.txt')
print(testVector[0,0:31])
print(testVector[0,32:63])
测试算法
def handwritingClassTest():
hwLabels = []
trainingFileList = listdir('trainingDigits') #获取训练集目录的文件名
m = len(trainingFileList)
trainingMat = np.zeros((m,1024))
for i in range(m):
fileNameStr = trainingFileList[i]
fileStr = fileNameStr.split('.')[0] #获得文件名
classNumStr = int(fileStr.split('_')[0])
hwLabels.append(classNumStr)
trainingMat[i,:] = img2vector('trainingDigits/%s' % fileNameStr)
testFileList = listdir('testDigits')
errorCount = 0.0
mTest = len(testFileList)
for i in range(mTest):
fileNameStr = testFileList[i]
fileStr = fileNameStr.split('.')[0]
classNumStr = int(fileStr.split('_')[0])
vectorUnderTest = img2vector('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)))
handwritingClassTest()