机器学习(1)：k-近邻算法

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 $d = \sqrt{(xA_{0} - xB_{0})^{2} + (xA_{1} - xB_{1})^{2}}$

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： $newValue = (oldValue - min) / (max - min)$

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))