K近邻算法
概述:
K最近邻(k-Nearest Neighbor,以下简称KNN)分类算法,是一个理论上比较成熟的方法,也是最简单的机器学习算法之一。该方法的思路是:如果一个样本在特征空间中的k个最相似(即特征空间中最邻近)的样本中的大多数属于某一个类别,则该样本也属于这个类别。(来自百度词条)
利弊分析:
KNN 是分类数据最简单最有效的算法,他的核心思想是基于实例的学习,使用时我们必须有接近实际数据的训练样本数据,并且需要保存全部的数据集,消耗的存储空间也比较多,由于要对每个数据计算欧式距离,计算量比较大也比较费时,另一个缺点是无法给出平均实例样本的特征。训练复杂度为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),对于类域的交叉或重叠较多的待分样本集来说,KNN方法较其他方法更为适合。
要点:
K 近邻算法使用的模型实际上对应于对特征空间的划分。K 值的选择,距离度量和分类决策规则是该算法的三个基本要素:
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K 值的选择会对算法的结果产生重大影响。K值较小意味着只有与输入实例较近的训练实例才会对预测结果起作用,但容易发生过拟合;如果 K 值较大,优点是可以减少学习的估计误差,但缺点是学习的近似误差增大,这时与输入实例较远的训练实例也会对预测起作用,使预测发生错误。在实际应用中,K 值一般选择一个较小的数值,通常采用交叉验证的方法来选择最优的 K 值。随着训练实例数目趋向于无穷和 K=1 时,误差率不会超过贝叶斯误差率的2倍,如果K也趋向于无穷,则误差率趋向于贝叶斯误差率。
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该算法中的分类决策规则往往是多数表决,即由输入实例的 K 个最临近的训练实例中的多数类决定输入实例的类别
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距离度量一般采用 Lp 距离,当p=2时,即为欧氏距离,在度量之前,应该将每个属性的值规范化,这样有助于防止具有较大初始值域的属性比具有较小初始值域的属性的权重过大。
KNN算法不仅可以用于分类,还可以用于回归。
Python实现(非框架):
以下代码来自机器学习实战,我之后会有一些补充,对于可能会遇到的实际问题作出修改:
from numpy import *
import operator
import matplotlib
import matplotlib.pyplot as plt
from os import listdir
def classify0(inX, dataSet, labels, k):
dataSetSize = dataSet.shape[0]
diffMat = tile(inX, (dataSetSize,1)) - dataSet
sqDiffMat = diffMat**2
sqDistances = sqDiffMat.sum(axis=1)
distances = sqDistances**0.5
sortedDistIndicies = distances.argsort()
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]
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 = dataSet / tile(ranges,(m,1))
return normDataSet,ranges,minVals
def datingClassTest():
horatio = 0.50
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],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 classifyPerson():
resultList = ['not at all','in small doses','in large doses']
percentTats = input("percentage of time spent playing video games?")
ffMiles = input("frequent flier miles earmed per year?")
iceCrea, =input("liters of ice cream consumed per year?")
datingDataMat,ranges,minVals = autoNorm(datingDataMat)
datingDataMat,datingLabels = file2matrix('datingTestSet2.txt')
inArr = array([ffMiles,percentTats,icerCream])
classifierResult = classify0((inArr-minVals)/ranges,normMat,datingLabels,3)
print("You will probably like this person:",resultList[classifierResult-1])
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('trainingDigits')
m = len(trainingFileList)
trainingMat = zeros((m,1024))
for i in range(m):
fileNameStr = trainingFileList[i]
fileStr = fileNameStr.split('.')[0]
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(fileNameStr.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
print("\nThe total number of errors is: %d"% errorCount)
print("\nThe total error rate is: %f"% (errorCount/float(mTest)))
Tips:关于源码以及数据集可以在www.manning.com/MachineLearninginAction下载到