k-近邻算法 (K-Nearest Neighbors,KNN)

k-近邻算法概述

k-近邻算法采用测量不同特征值之间的距离方法进行分类。
工作原理：存在一个样本数据几何，也称作样本集，并且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数据（最近邻）的分类标签。一般来说，我们只选择样本数据集中前k个最相似的数据，这就是k-近邻算法中k的出处，通常k是不大于20的整数。最后，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。

• 有监督学习
• 分类算法

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

k-近邻算法的一般流程

1. 收集数据：可以使用任何方法
2. 准备数据：距离计算所需要的数值，最好是结构化的数据格式
3. 分析数据：可以使用任何方法
4. 训练算法：此步骤不适用于k-近邻算法
5. 测试算法：计算错误率
6. 使用算法：首先需要输入样本数据和结构化的输出结果，然后运行k-近邻算法判定输入数据分别属于哪个分类，最后应用对计算出的分类执行后续的处理

示例

kNN.py

"""
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.items(), 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 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 = array([ffMiles, percentTats, iceCream])
    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')  # 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)))

使用k-近邻算法改进约会网站的配对效果

'''
import kNN
from numpy import array
import matplotlib
import matplotlib.pyplot as plt

# 准备数据：从文本文件中解析数据
datingDataMat, datingLabels = kNN.file2matrix('datingTestSet2.txt')
print(datingDataMat)
print(datingLabels[0: 20])

# 分析数据：使用Matplotlib创建散点图
fig = plt.figure()
ax = fig.add_subplot(111)
# ax.scatter(datingDataMat[:, 1], datingDataMat[:, 2])
# plt.show()
ax.scatter(datingDataMat[:, 1], datingDataMat[:, 2], 15.0 * array(datingLabels), 15.0 * array(datingLabels))
plt.show()

# 准备数据：归一化数值
normMat, ranges, minVals = kNN.autoNorm(datingDataMat)
print(normMat)
print(ranges)
print(minVals)

# 测试算法：作为完整程序验证分类器
kNN.datingClassTest()

# 使用算法：构建完整可用系统
kNN.classifyPerson()

手写识别系统

import kNN


# 准备数据：将图像转换为测试向量
testVector = kNN.img2vector('testDigits/0_13.txt')
print(testVector[0, 0:31])

# 测试算法：使用k-近邻算法识别手写数字
kNN.handwritingClassTest()

[1]哈林顿李锐. 机器学习实战 : Machine learning in action[M]. 人民邮电出版社, 2013.
[2]代码和数据来源：https://www.manning.com/books/machine-learning-in-action
注意：原代码是基于python2.x，在3.x的python中部分兼容问题需要调整