机器学习笔记之K近邻算法

算法概述

简单地说，k-近邻算法采用测量不同特征值之间的距离的方法进行分类。
算法优点：精度高、对异常值不敏感、无数据输入假定。
算法缺点：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。

工作原理：
存在一个样本数据集合，也称作训练样本集，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。

KNN伪代码

对未知类别属性的数据集中的每个点依次执行以下操作：
(1) 计算已知类别数据集中的点与当前点之间的距离；
(2) 按照距离递增次序排序；
(3) 选取与当前点距离最小的k个点；
(4) 确定前k个点所在类别的出现频率；
(5) 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。

## K-近邻算法
import numpy as np
import operator

def classify0(inX, dataSet, labels, k):
    dataSetSize = dataSet.shape[0]
    ## 计算欧式距离
    diffMat = np.tile(inX, (dataSetSize, 1)) - dataSet  #tile是np的一个函数，使得inX与dataSet相同行数
    sqDiffMat = diffMat ** 2
    sqDistances = sqDiffMat.sum(axis = 1)
    distances = sqDistances ** 0.5
    sortedDistIndicies = distances.argsort()   #argsort是np的一个函数，返回的是数组从小到大的索引值
    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]

classify0()函数有4个输入参数：用于分类的输入向量是inX，输入的训练样本集为dataSet，
标签向量为labels，最后的参数k表示用于选择最近邻居的数目，其中标签向量的元素数目和矩
阵dataSet的行数相同。程序使用欧氏距离公式计算所有特征间的距离

group = np.array([[1.0, 1.1], [1.0, 1.0], [0, 0], [0, 0.1]])
labels = ['A', 'A', 'B', 'B']

classify0([[0, 6]], group, labels, 3)

'A'

示例1：使用K-近邻算法改进约会网站的配对效果

## 将文本记录转成Numpy的解析程序
def file2matrix(filename):
    fr = open(filename)
    arrayOLines = fr.readlines()
    numberOfLines = len(arrayOLines)
    returnMat = np.zeros((numberOfLines, 3))
    classLabelVector = []
    index = 0
    for line in arrayOLines:
        line = line.strip()
        listFromLine = line.split('\t')
        returnMat[index, :] = listFromLine[0:3]
        classLabelVector.append(int(listFromLine[-1]))
        index += 1
    return returnMat, classLabelVector

datingDataMat, datingLabels = file2matrix('D:\BaiduNetdiskDownload\ml_action\Ch02\datingTestSet2.txt')

## 分析数据：使用Matplotlib创建散点图
import matplotlib
import matplotlib.pyplot as plt

fig = plt.figure()
ax = fig.add_subplot(111)
ax.scatter(datingDataMat[:, 1], datingDataMat[:, 2])
plt.show()

## 数据归一化，将数据转换到0到1之间
def autoNorm(dataSet):
    minVals = dataSet.min(0)
    maxVals = dataSet.max(0)
    ranges = maxVals - minVals
    normDataSet = np.zeros(dataSet.shape)
    m = dataSet.shape[0]
    normDataSet = dataSet - np.tile(minVals, (m, 1))
    normDataSet = normDataSet/np.tile(ranges, (m, 1))
    
    return normDataSet, ranges, minVals

normMat, ranges, minVals = autoNorm(datingDataMat)

## 分类器针对约会网站的测试代码
def datingClassTest():
    hoRatio = 0.1 #抽样比率
    datingDataMat, datingLabels = file2matrix('D:\BaiduNetdiskDownload\ml_action\Ch02\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 calssifier 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)))
      
    

datingClassTest()

the calssifier came back with: 3, the real answer is : 3
the calssifier came back with: 2, the real answer is : 2
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 3, the real answer is : 3
the calssifier came back with: 3, the real answer is : 3
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 3, the real answer is : 3
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 2, the real answer is : 2
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 2, the real answer is : 2
the calssifier came back with: 3, the real answer is : 3
the calssifier came back with: 2, the real answer is : 2
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 3, the real answer is : 2
the calssifier came back with: 3, the real answer is : 3
the calssifier came back with: 2, the real answer is : 2
the calssifier came back with: 3, the real answer is : 3
the calssifier came back with: 2, the real answer is : 2
the calssifier came back with: 3, the real answer is : 3
the calssifier came back with: 2, the real answer is : 2
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 3, the real answer is : 3
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 3, the real answer is : 3
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 2, the real answer is : 2
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 2, the real answer is : 2
the calssifier came back with: 3, the real answer is : 3
the calssifier came back with: 3, the real answer is : 3
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 2, the real answer is : 2
the calssifier came back with: 3, the real answer is : 3
the calssifier came back with: 3, the real answer is : 3
the calssifier came back with: 3, the real answer is : 3
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 2, the real answer is : 2
the calssifier came back with: 2, the real answer is : 2
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 3, the real answer is : 3
the calssifier came back with: 2, the real answer is : 2
the calssifier came back with: 2, the real answer is : 2
the calssifier came back with: 2, the real answer is : 2
the calssifier came back with: 2, the real answer is : 2
the calssifier came back with: 3, the real answer is : 3
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 2, the real answer is : 2
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 2, the real answer is : 2
the calssifier came back with: 2, the real answer is : 2
the calssifier came back with: 2, the real answer is : 2
the calssifier came back with: 2, the real answer is : 2
the calssifier came back with: 2, the real answer is : 2
the calssifier came back with: 3, the real answer is : 3
the calssifier came back with: 2, the real answer is : 2
the calssifier came back with: 3, the real answer is : 3
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 2, the real answer is : 2
the calssifier came back with: 3, the real answer is : 3
the calssifier came back with: 2, the real answer is : 2
the calssifier came back with: 2, the real answer is : 2
the calssifier came back with: 3, the real answer is : 1
the calssifier came back with: 3, the real answer is : 3
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 3, the real answer is : 3
the calssifier came back with: 3, the real answer is : 3
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 2, the real answer is : 2
the calssifier came back with: 3, the real answer is : 3
the calssifier came back with: 3, the real answer is : 1
the calssifier came back with: 3, the real answer is : 3
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 2, the real answer is : 2
the calssifier came back with: 2, the real answer is : 2
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 3, the real answer is : 3
the calssifier came back with: 2, the real answer is : 3
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 2, the real answer is : 2
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 3, the real answer is : 3
the calssifier came back with: 3, the real answer is : 3
the calssifier came back with: 2, the real answer is : 2
the calssifier came back with: 1, the real answer is : 1
the calssifier came back with: 3, the real answer is : 1
the total error rate is: 0.050000

##使用算法构建完整系统
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('D:\BaiduNetdiskDownload\ml_action\Ch02\datingTestSet2.txt')
    normMat, ranges, minVals = autoNorm(datingDataMat)
    inArr = np.array([ffMiles, percentTats, iceCream])
    classifierResult = classify0((inArr - minVals)/ranges, normMat, datingLabels, 3)
    print("You will probably like this person: ", resultList[classifierResult - 1])
    

classifyPerson()

percentage of time spent playing video games?10
frequent flier miles earned per year?10000
liters of ice cream consumed per year?0.5
You will probably like this person:  in small doses

示例2 手写识别系统

##准备数据：将图像转换成测试向量
def img2vector(filename):
    returnVect = np.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

img2vector('D:/BaiduNetdiskDownload/ml_action/Ch02/digits/trainingDigits/0_13.txt')

array([[0., 0., 0., ..., 0., 0., 0.]])

##手写数字识别系统
import os
def handwritingClassTest():
    hwLabels = []
    trainingFileList = os.listdir('D:/BaiduNetdiskDownload/ml_action/Ch02/digits/trainingDigits')
    m = len(trainingFileList)
    trainingMat = np.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('D:/BaiduNetdiskDownload/ml_action/Ch02/digits/trainingDigits' + '/' + fileNameStr)
    testFileList = os.listdir('D:/BaiduNetdiskDownload/ml_action/Ch02/digits/trainingDigits')
    errorCount = 0.0
    mTest = len(testFileList)
    for i in range(mTest):
        fileNameStr = testFileList[i]
        fileStr = fileNameStr.split('.')[0]
        classNumStr = int(fileStr.split('_')[0])
        vectorUnderTest = img2vector('D:/BaiduNetdiskDownload/ml_action/Ch02/digits/trainingDigits' + '/' + 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)))
    

handwritingClassTest()

the classifier came back with: 0, the real answer is: 0
the classifier came back with: 0, the real answer is: 0
the classifier came back with: 0, the real answer is: 0
the classifier came back with: 0, the real answer is: 0
the classifier came back with: 0, the real answer is: 0
the classifier came back with: 0, the real answer is: 0
the classifier came back with: 0, the real answer is: 0
the classifier came back with: 0, the real answer is: 0
the classifier came back with: 0, the real answer is: 0
the classifier came back with: 0, the real answer is: 0
the classifier came back with: 0, the real answer is: 0
the classifier came back with: 0, the real answer is: 0
the classifier came back with: 0, the real answer is: 0
the classifier came back with: 0, the real answer is: 0
the classifier came back with: 0, the real answer is: 0
the classifier came back with: 0, the real answer is: 0
the classifier came back with: 0, the real answer is: 0
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the classifier came back with: 6, the real answer is: 0
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the classifier came back with: 1, the real answer is: 1
the classifier came back with: 1, the real answer is: 1
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the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 5, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
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the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
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the classifier came back with: 4, the real answer is: 4
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the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
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the classifier came back with: 4, the real answer is: 4
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the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
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the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
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the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
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the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 9, the real answer is: 5
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the classifier came back with: 5, the real answer is: 5
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the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 9, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 9, the real answer is: 5
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the classifier came back with: 5, the real answer is: 5
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the classifier came back with: 6, the real answer is: 6
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the classifier came back with: 6, the real answer is: 6
the classifier came back with: 6, the real answer is: 6
the classifier came back with: 6, the real answer is: 6
the classifier came back with: 6, the real answer is: 6
the classifier came back with: 6, the real answer is: 6
the classifier came back with: 6, the real answer is: 6
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the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 4, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 3, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 7, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9

the total number of errors is: 23

the total error rate is: 0.011892