KNN详解

KNN算法，又称K-近邻算法

简单来说，KNN采用测量不同特征值之间的距离来进行分类

• 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

 

kNN算法的核心思想

       如果一个样本在特征空间中的k个最相邻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，并具有这个类别上样本的特性。该方法在确定分类决策上只依据最邻近的一个或者几个样本的类别来决定待分样本所属的类别。 kNN方法在类别决策时，只与极少量的相邻样本有关。由于kNN方法主要靠周围有限的邻近的样本，而不是靠判别类域的方法来确定所属类别的，因此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。

 

KNN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. 测试算法：计算错误率
5. 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KNN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

 

以下是机器学习实战里面的源码，如需运行，需要下载数据集，并改动本地路径

from numpy import *
import operator #运算符模块
from os import listdir


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

# inX: input vector
#   k: the number of the nearest data
def classify0(inX, dataSet, labels, k):

    #calculate the distance
    dataSetSize = dataSet.shape[0]  #group.shape[0]==4
    diffMat = tile(inX, (dataSetSize,1)) - dataSet
    sqDiffMat = diffMat**2
    sqDistances = sqDiffMat.sum(axis=1)
    distances = sqDistances**0.5

    #select the most nearest k data
    sortedDistIndicies = distances.argsort()
    classCount={}
    for i in range(k):
        voteIlabel = labels[sortedDistIndicies[i]]
        classCount[voteIlabel] = classCount.get(voteIlabel,0) + 1

    #sort and retrun
    sortedClassCount = sorted(classCount.items(), key=operator.itemgetter(1), reverse=True)
    return sortedClassCount[0][0]

def file2matrix(filename):
    love_dictionary={'largeDoses':3, 'smallDoses':2, 'didntLike':1}
    fr = open(filename)
    arrayOLines = fr.readlines()
    numberOfLines = len(arrayOLines)            #get the number of lines in the file
    returnMat = zeros((numberOfLines,3))        #prepare matrix to return
    classLabelVector = []                       #prepare labels return
    index = 0
    for line in arrayOLines:
        line = line.strip()
        listFromLine = line.split('\t')
        returnMat[index,:] = listFromLine[0:3]
        if(listFromLine[-1].isdigit()):
            classLabelVector.append(int(listFromLine[-1]))
        else:
            classLabelVector.append(love_dictionary.get(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 = 0.10      #10%拿去测试
    datingDataMat,datingLabels = file2matrix('/home/torres/PycharmProjects/MachineLearning/venv/c2/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('/home/torres/PycharmProjects/MachineLearning/venv/c2/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: %s" % 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('/home/torres/PycharmProjects/MachineLearning/venv/c2/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('/home/torres/PycharmProjects/MachineLearning/venv/c2/trainingDigits/%s' % fileNameStr)
    testFileList = listdir('/home/torres/PycharmProjects/MachineLearning/venv/c2/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('/home/torres/PycharmProjects/MachineLearning/venv/c2/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)))

###########################################################################################
#task 1:try KNN
group,labels = createDataSet()
# print(group.shape[0])  #4
result = classify0([0,0],group,labels,3)
print(result)



###########################################################################################
# task2: open file(care the path of the local file)
datingDataMat,datingLabels = file2matrix('/home/torres/PycharmProjects/MachineLearning/venv/c2/datingTestSet2.txt')
print(datingDataMat)
print(datingLabels)

#using matplotlib to draw a picture
import matplotlib
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.add_subplot(111)
# ax.scatter(datingDataMat[:,1], datingDataMat[:,2])
# ax.scatter(datingDataMat[:,1], datingDataMat[:,2],15.0*array(datingLabels),15.0*array(datingLabels))  #draw with color
ax.scatter(datingDataMat[:,0], datingDataMat[:,1],15.0*array(datingLabels),15.0*array(datingLabels))    #better performance
plt.show()

print(datingDataMat[:,0])
print(datingDataMat[:,0:2])   #尝试用切片的方法去截取矩阵


###########################################################################################
#task3 nomalize the dataset
normMat,ranges,minVals = autoNorm(datingDataMat)
print(normMat)
print(ranges)
print(minVals)


###########################################################################################
#task4 testing
datingClassTest()


###########################################################################################
#task4 using
classifyPerson()


###########################################################################################
# task5 手写识别系统
testVector = img2vector('/home/torres/PycharmProjects/MachineLearning/venv/c2/testDigits/0_13.txt')
print(testVector)
handwritingClassTest()

 

总结

• KNN算法是基于实例的学习，使用算法时我们必须有接近实际数据的训练样本数据
• KNN算法由于必须对数据集中的每个数据计算距离值，实际使用时可能非常耗时
• KNN算法的另一个缺陷是，它无法给出任何数据的基础结构信息，因此我们也无法知晓平均实例样本和典型实例样本具有什么特征