k-近邻算法概述
- 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。
- 适用数据范围:数值型和标称型(标称型:标称型目标变量的结果只在有限目标集中取值,如真与假。标称型目标变量主要用于分类)
- 工作原理:存在一个样本数据集合,并且样本集中每个数据都存在标签。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(近邻)的k个数据(k一般不大于20)的分类标签,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。
kNN分类算法实现
伪代码如下:
对未知类别属性的数据集中的每个点一次执行以下操作:
- 计算已知类别数据集中的点与当前点之间的距离;
- 按照距离递增次序排序;
- 选取与当前点距离最小的k个点;
- 确定前k个点所在类别的出现频率;
- 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;
对于距离的度量我们使用欧式距离,公式为
实例:使用k-近邻算法改进约会网站的配对效果
特征:每年获得的飞行常客里程数、玩视频游戏所消时间百分比、每周消费的冰淇淋公升数
标签:将人分为三种,分别为:不喜欢的人、魅力一般的人和极具魅力的人
准备数据:从文本文件中解析数据
api:
file2matrix(filename) @return matVector, labelVector
str.strip()截取掉所有的回车字符
np.zero(shape: tuple(row, col))
分析数据:使用Matplotlib创建散点图
api:
plt.figure() @return fig
fig.add_subplot() @return ax
ax.scatter(X, Y)
准备数据:归一化数值
公式:
api:
autoNorm(dataset) @return normDataSet, ranges, minVals
np.array.min(axis) @param axis 1|0 分别代表行和列
np.tile(A, reps) 返回A根据reps重复后的矩阵 @return np.ndarray @param reps (row, col)
实现kNN邻近分类
api:
classify0(inX, dataSet, labels, k)
sorted(iterable, key=None, reverse=False) Return a new list containing all items from the iterable in ascending order.
dict.get(key, default)
测试算法
datingClassTest函数首先使用了file2matrix和autoNorm函数从文件中读取数据并将其转换为归一化特征值。接着计算测试向量的数量,此步决定了normMat kNN分类器classify0。最后,函数计算错误率并输出结果
参考代码:
'''
Created on Sep 16, 2010
kNN: k Nearest Neighbors
Input: inX: vector to compare to existing dataset (1xN)
dataSet: size m data set of known vectors (NxM)
labels: data set labels (1xM vector)
k: number of neighbors to use for comparison (should be an odd number)
Output: the most popular class label
@author: pbharrin
'''
from numpy import *
import operator
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.iteritems(), key=operator.itemgetter(1), reverse=True)
return sortedClassCount[0][0]
def createDataSet():
group = array([[1.0,1.1],[1.0,1.0],[0,0],[0,0.1]])
labels = ['A','A','B','B']
return group, labels
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 = normDataSet/tile(ranges, (m,1)) #element wise divide
return normDataSet, ranges, minVals
def datingClassTest():
hoRatio = 0.50 #hold out 10%
datingDataMat,datingLabels = file2matrix('datingTestSet2.txt') #load data setfrom file
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 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') #load the training set
m = len(trainingFileList)
trainingMat = zeros((m,1024))
for i in range(m):
fileNameStr = trainingFileList[i]
fileStr = fileNameStr.split('.')[0] #take off .txt
classNumStr = int(fileStr.split('_')[0])
hwLabels.append(classNumStr)
trainingMat[i,:] = img2vector('trainingDigits/%s' % fileNameStr)
testFileList = listdir('testDigits') #iterate through the test set
errorCount = 0.0
mTest = len(testFileList)
for i in range(mTest):
fileNameStr = testFileList[i]
fileStr = fileNameStr.split('.')[0] #take off .txt
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))