Maching learning in action，KNN(k-nearest neighbor)算法笔记

发表于   |   分类于   |  

Maching learning in action，KNN(k-nearest neighbor)算法笔记

KNN算法概述

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．输入没有标签的数据后，将新数据的每个特征值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的数据，这就是KNN算法Ｋ的出处．

KNN算法一般流程

  • 收集数据: 可以使用任何方法
  • 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．
  • 分析数据: 可以使用任何方法
  • 训练算法: 此步骤不适合用于KNN算法
  • 测试数据: 计算错误率
  • 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

使用python导入数据

1
2
3
4
5
6
7
import numpy as np
import operator

def createDataSet():
    group = np.array([[1.0, 1.1], [1.0, 1.0], [0, 0], [0, 0.1]])
    labels = ['A', 'A', 'B', 'B']
    return group, labels
1
2
group, labels = createDataSet()
group, labels
(array([[ 1. ,  1.1],
        [ 1. ,  1. ],
        [ 0. ,  0. ],
        [ 0. ,  0.1]]), ['A', 'A', 'B', 'B'])

实施KNN算法

对未知类别属性的数据集中的每个点依次执行一下操作：

  • 计算已知类别数据集中的点与当前点之间的距离
  • 排序
  • 选取距离最小的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

这样找出k个点，如果数据量特别大．显然是不可取的，这里可以改进成kd树的数据结构

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
def classify0(inX, dataSet, labels, k):
    dataSetSize = dataSet.shape[0]
    diffMat = np.tile(inX, (dataSetSize, 1)) - dataSet
    sqDiffMat = diffMat**2
    sqDistances = sqDiffMat.sum(axis=1)
    distances = sqDistances ** 0.5
    sortedDistIndices = distances.argsort()
    classCount={}
    for i in range(k):
        voteLables = labels[sortedDistIndices[i]]
        classCount[voteLables] = classCount.get(voteLables, 0) + 1
        
    sortedClassCount = sorted(classCount.iteritems(), key=lambda x: x[1], reverse=True)
#     print classCount
    return sortedClassCount[0][0]

这里的sorted函数书中写的是operator.itemgetter(1),这里使用lambda更好 

1
classify0([0, 0], group, labels, 3)
{'A': 1, 'B': 2}





'B'

使用KNN算法改进约会网站的配对效果

准备数据：从文本文件中解析数据

1
2
3
4
5
6
7
8
9
10
11
12
13
14
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
1
datingDataMat, datingLabels = file2matrix('datingTestSet2.txt')
1
datingDataMat[:10]
array([[  4.09200000e+04,   8.32697600e+00,   9.53952000e-01],
       [  1.44880000e+04,   7.15346900e+00,   1.67390400e+00],
       [  2.60520000e+04,   1.44187100e+00,   8.05124000e-01],
       [  7.51360000e+04,   1.31473940e+01,   4.28964000e-01],
       [  3.83440000e+04,   1.66978800e+00,   1.34296000e-01],
       [  7.29930000e+04,   1.01417400e+01,   1.03295500e+00],
       [  3.59480000e+04,   6.83079200e+00,   1.21319200e+00],
       [  4.26660000e+04,   1.32763690e+01,   5.43880000e-01],
       [  6.74970000e+04,   8.63157700e+00,   7.49278000e-01],
       [  3.54830000e+04,   1.22731690e+01,   1.50805300e+00]])

1
datingLabels[:10]
[3, 2, 1, 1, 1, 1, 3, 3, 1, 3]

分析数据: 使用Matplotlib创建散点图

1
2
3
4
5
6
import matplotlib
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.add_subplot(111)
ax.scatter(datingDataMat[:, 1], datingDataMat[:, 2])
plt.show()

1
2
3
4
5
fig = plt.figure()
ax = fig.add_subplot(111)
ax.scatter(datingDataMat[:, 0], datingDataMat[:, 1],
          15*np.array(datingLabels), 15*np.array(datingLabels))
plt.show()

准备数据: 归一化数值

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

1
2
3
4
5
6
7
8
9
def autoNorm(dataSet):
    minVals = dataSet.min(0)
    maxVals = dataSet.max(0)
    ranges = maxVals - minVals
    normDataSet = np.zeros(np.shape(dataSet))
    m = dataSet.shape[0]
    normDataSet = dataSet - np.tile(minVals, (m, 1))
    normDataSet = normDataSet/np.tile(ranges, (m, 1))
    return normDataSet, ranges, minVals
1
2
normMat, ranges, minVals = autoNorm(datingDataMat)
normMat
array([[ 0.44832535,  0.39805139,  0.56233353],
       [ 0.15873259,  0.34195467,  0.98724416],
       [ 0.28542943,  0.06892523,  0.47449629],
       ..., 
       [ 0.29115949,  0.50910294,  0.51079493],
       [ 0.52711097,  0.43665451,  0.4290048 ],
       [ 0.47940793,  0.3768091 ,  0.78571804]])

1
ranges
array([  9.12730000e+04,   2.09193490e+01,   1.69436100e+00])

1
minVals
array([ 0.      ,  0.      ,  0.001156])

测试算法: 作为完整程序验证分类器

1
2
3
4
5
6
7
8
9
10
11
12
13
def datingClassTest():
    hoRatio = 0.10
    datingDataMat, datingLabels = file2matrix('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 classifier came back with %d, the real answer is: %d" % (classifierResult, datingLabels[i])
        if classifierResult!=datingLabels[i]: errorCount += 1
            
    print "the total error rate is: %f" % (errorCount/float(numTestVecs))
1
datingClassTest()
the classifier came back with 3, the real answer is: 3
the classifier came back with 2, the real answer is: 2
the classifier came back with 1, the real answer is: 1
the classifier came back with 1, the real answer is: 1
the classifier came back with 1, the real answer is: 1
the classifier came back with 1, the real answer is: 1
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 1, the real answer is: 1
the classifier came back with 3, the real answer is: 3
the classifier came back with 1, the real answer is: 1
the classifier came back with 1, the real answer is: 1
the classifier came back with 2, the real answer is: 2
the classifier came back with 1, the real answer is: 1
the classifier came back with 1, the real answer is: 1
the classifier came back with 1, the real answer is: 1
the classifier came back with 1, the real answer is: 1
the classifier came back with 1, the real answer is: 1
the classifier came back with 2, the real answer is: 2
the classifier came back with 3, the real answer is: 3
the classifier came back with 2, the real answer is: 2
the classifier came back with 1, the real answer is: 1
the classifier came back with 1, the real answer is: 2
the classifier came back with 3, the real answer is: 3
the classifier came back with 2, the real answer is: 2
the classifier came back with 3, the real answer is: 3
the classifier came back with 2, the real answer is: 2
the classifier came back with 3, the real answer is: 3
the classifier came back with 2, the real answer is: 2
the classifier came back with 1, the real answer is: 1
the classifier came back with 3, the real answer is: 3
the classifier came back with 1, the real answer is: 1
the classifier came back with 3, the real answer is: 3
the classifier came back with 1, the real answer is: 1
the classifier came back with 2, the real answer is: 2
the classifier came back with 1, the real answer is: 1
the classifier came back with 1, the real answer is: 1
the classifier came back with 2, the real answer is: 2
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 1, the real answer is: 1
the classifier came back with 2, the real answer is: 2
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 1, the real answer is: 1
the classifier came back with 1, the real answer is: 1
the classifier came back with 1, the real answer is: 1
the classifier came back with 1, the real answer is: 1
the classifier came back with 2, the real answer is: 2
the classifier came back with 2, the real answer is: 2
the classifier came back with 1, the real answer is: 1
the classifier came back with 3, the real answer is: 3
the classifier came back with 2, the real answer is: 2
the classifier came back with 2, the real answer is: 2
the classifier came back with 2, the real answer is: 2
the classifier came back with 2, the real answer is: 2
the classifier came back with 3, the real answer is: 3
the classifier came back with 1, the real answer is: 1
the classifier came back with 2, the real answer is: 2
the classifier came back with 1, the real answer is: 1
the classifier came back with 2, the real answer is: 2
the classifier came back with 2, the real answer is: 2
the classifier came back with 2, the real answer is: 2
the classifier came back with 2, the real answer is: 2
the classifier came back with 2, the real answer is: 2
the classifier came back with 3, the real answer is: 3
the classifier came back with 2, the real answer is: 2
the classifier came back with 3, the real answer is: 3
the classifier came back with 1, the real answer is: 1
the classifier came back with 2, the real answer is: 2
the classifier came back with 3, the real answer is: 3
the classifier came back with 2, the real answer is: 2
the classifier came back with 2, the real answer is: 2
the classifier came back with 3, the real answer is: 1
the classifier came back with 3, the real answer is: 3
the classifier came back with 1, the real answer is: 1
the classifier came back with 1, the real answer is: 1
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 1, the real answer is: 1
the classifier came back with 2, the real answer is: 2
the classifier came back with 3, the real answer is: 3
the classifier came back with 3, the real answer is: 1
the classifier came back with 3, the real answer is: 3
the classifier came back with 1, the real answer is: 1
the classifier came back with 2, the real answer is: 2
the classifier came back with 2, the real answer is: 2
the classifier came back with 1, the real answer is: 1
the classifier came back with 1, the real answer is: 1
the classifier came back with 3, the real answer is: 3
the classifier came back with 2, the real answer is: 3
the classifier came back with 1, the real answer is: 1
the classifier came back with 2, the real answer is: 2
the classifier came back with 1, the real answer is: 1
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 2, the real answer is: 2
the classifier came back with 1, the real answer is: 1
the classifier came back with 3, the real answer is: 1
the total error rate is: 0.050000

使用算法: 构建完整可用系统

1
2
3
4
5
6
7
8
9
10
def classifyPerson():
    resultList = ['not at all', 'in small doses', 'in large doses']
    percentTats = float(raw_input("percentage of time spent playing video games?"))
    ffMiles = float(raw_input("frequent flier miles earned per year?"))
    iceCream = float(raw_input("liters of ice cream consumed per year?"))
    datingDataMat, datingLabels = file2matrix('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]
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

手写识别系统

准备数据

1
2
3
4
5
6
7
8
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
1
2
testVector = img2vector('testDigits/0_13.txt')
testVector[0, 0:31]
array([ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
        0.,  1.,  1.,  1.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
        0.,  0.,  0.,  0.,  0.])

测试算法: 使用KNN算法识别手写数字

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
from os import listdir
def handWritingClassTest():
    hwLabels = []
    trainingFileList = listdir('trainingDigits')
    m = len(trainingFileList)
    trainingMat = np.zeros((m, 1024))
    for i in range(m):
        fileNameStr = trainingFileList[i]
        fileStr = fileNameStr.split('.')[0]
        classNumber = int(fileStr.split('_')[0])
        hwLabels.append(classNumber)
        trainingMat[i, :] = img2vector('trainingDigits/%s' % fileNameStr)
    testFileList = listdir('testDigits')
    errorCount = 0.0
    mTest = len(testFileList)
    for i in xrange(mTest):
        fileNameStr = testFileList[i]
        fileStr = fileNameStr.split('.')[0]
        classNumber = int(fileStr.split('_')[0])
        vectorUnderTest = img2vector('testDigits/%s' % fileNameStr)
        classifierResult = classify0(vectorUnderTest, trainingMat, hwLabels, 10)
        print "the classifier came back with %d, the real answer is: %d" % (classifierResult, classNumber)
        if classifierResult!=classNumber: errorCount += 1
    print "\nthe total number of errors is: %d" % errorCount
    print "\nthe total error rate is: %f" % (errorCount/float(mTest))
1
handWritingClassTest()
the classifier came back with 3, the real answer is: 3
the classifier came back with 2, the real answer is: 2
the classifier came back with 1, the real answer is: 1
the classifier came back with 6, the real answer is: 6
the classifier came back with 4, the real answer is: 4
the classifier came back with 2, the real answer is: 2
the classifier came back with 3, the real answer is: 3
the classifier came back with 8, the real answer is: 8
the classifier came back with 2, the real answer is: 2
the classifier came back with 8, the real answer is: 8
the classifier came back with 9, the real answer is: 9
the classifier came back with 4, the real answer is: 4
the classifier came back with 3, the real answer is: 3
the classifier came back with 1, the real answer is: 1
the classifier came back with 3, the real answer is: 3
the classifier came back with 1, the real answer is: 1
the classifier came back with 8, the real answer is: 8
the classifier came back with 1, the real answer is: 1
the classifier came back with 8, the real answer is: 8
the classifier came back with 1, the real answer is: 1
the classifier came back with 8, the real answer is: 8
the classifier came back with 5, the real answer is: 5
the classifier came back with 6, the real answer is: 6
the classifier came back with 5, the real answer is: 5
the classifier came back with 4, the real answer is: 4
the classifier came back with 5, the real answer is: 5
the classifier came back with 7, the real answer is: 7
the classifier came back with 1, the real answer is: 1
the classifier came back with 4, the real answer is: 4
the classifier came back with 8, the real answer is: 8
the classifier came back with 7, the real answer is: 7
the classifier came back with 3, the real answer is: 3
the classifier came back with 9, the real answer is: 9
the classifier came back with 1, the real answer is: 1
the classifier came back with 0, the real answer is: 0
the classifier came back with 5, the real answer is: 5
the classifier came back with 6, the real answer is: 6
the classifier came back with 3, the real answer is: 3
the classifier came back with 2, the real answer is: 2
the classifier came back with 4, the real answer is: 4
the classifier came back with 3, the real answer is: 3
the classifier came back with 5, the real answer is: 5
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: 5
the classifier came back with 3, the real answer is: 3
the classifier came back with 0, the real answer is: 0
the classifier came back with 2, the real answer is: 2
the classifier came back with 3, the real answer is: 8
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 7, the real answer is: 7
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 7, the real answer is: 7
the classifier came back with 6, the real answer is: 6
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 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: 9
the classifier came back with 8, the real answer is: 8
the classifier came back with 2, the real answer is: 2
the classifier came back with 4, the real answer is: 4
the classifier came back with 3, the real answer is: 3
the classifier came back with 1, the real answer is: 1
the classifier came back with 7, the real answer is: 7
the classifier came back with 9, the real answer is: 9
the classifier came back with 7, the real answer is: 7
the classifier came back with 1, the real answer is: 1
the classifier came back with 1, the real answer is: 1
the classifier came back with 3, the real answer is: 3
the classifier came back with 8, the real answer is: 8
the classifier came back with 4, the real answer is: 4
the classifier came back with 1, the real answer is: 8
the classifier came back with 2, the real answer is: 2
the classifier came back with 1, the real answer is: 1
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 6, the real answer is: 6
the classifier came back with 1, the real answer is: 1
the classifier came back with 9, the real answer is: 9
the classifier came back with 5, the real answer is: 5
the classifier came back with 0, the real answer is: 0
the classifier came back with 8, the real answer is: 8
the classifier came back with 9, the real answer is: 9
the classifier came back with 5, the real answer is: 5
the classifier came back with 1, the real answer is: 1
the classifier came back with 5, the real answer is: 5
the classifier came back with 7, the real answer is: 7
the classifier came back with 1, the real answer is: 1
the classifier came back with 6, the real answer is: 6
the classifier came back with 7, the real answer is: 7
the classifier came back with 3, the real answer is: 3
the classifier came back with 1, the real answer is: 1
the classifier came back with 0, the real answer is: 0
the classifier came back with 1, the real answer is: 9
the classifier came back with 1, the real answer is: 1
the classifier came back with 6, the real answer is: 6
the classifier came back with 2, the real answer is: 2
the classifier came back with 1, the real answer is: 1
the classifier came back with 1, the real answer is: 8
the classifier came back with 7, the real answer is: 7
the classifier came back with 2, the real answer is: 2
the classifier came back with 4, the real answer is: 4
the classifier came back with 0, the real answer is: 0
the classifier came back with 4, the real answer is: 4
the classifier came back with 2, the real answer is: 2
the classifier came back with 1, the real answer is: 1
the classifier came back with 1, the real answer is: 1
the classifier came back with 2, the real answer is: 2
the classifier came back with 8, the real answer is: 8
the classifier came back with 9, the real answer is: 9
the classifier came back with 8, the real answer is: 8
the classifier came back with 7, the real answer is: 7
the classifier came back with 5, the real answer is: 5
the classifier came back with 8, the real answer is: 8
the classifier came back with 4, the real answer is: 4
the classifier came back with 3, the real answer is: 3
the classifier came back with 8, the real answer is: 8
the classifier came back with 3, the real answer is: 3
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 4, the real answer is: 4
the classifier came back with 2, the real answer is: 2
the classifier came back with 7, the real answer is: 7
the classifier came back with 0, the real answer is: 0
the classifier came back with 5, the real answer is: 5
the classifier came back with 0, the real answer is: 0
the classifier came back with 6, the real answer is: 6
the classifier came back with 5, the real answer is: 5
the classifier came back with 2, the real answer is: 2
the classifier came back with 7, the real answer is: 7
the classifier came back with 2, the real answer is: 2
the classifier came back with 6, the real answer is: 6
the classifier came back with 3, the real answer is: 3
the classifier came back with 2, the real answer is: 2
the classifier came back with 1, the real answer is: 1
the classifier came back with 1, the real answer is: 1
the classifier came back with 7, the real answer is: 7
the classifier came back with 9, the real answer is: 9
the classifier came back with 5, the real answer is: 5
the classifier came back with 0, the real answer is: 0
the classifier came back with 8, the real answer is: 8
the classifier came back with 7, the real answer is: 7
the classifier came back with 7, the real answer is: 7
the classifier came back with 0, the real answer is: 0
the classifier came back with 7, the real answer is: 7
the classifier came back with 7, the real answer is: 7
the classifier came back with 9, the real answer is: 9
the classifier came back with 6, the real answer is: 6
the classifier came back with 3, the real answer is: 3
the classifier came back with 8, the real answer is: 8
the classifier came back with 6, the real answer is: 6
the classifier came back with 3, the real answer is: 3
the classifier came back with 0, the real answer is: 0
the classifier came back with 3, the real answer is: 3
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 1, the real answer is: 1
the classifier came back with 7, the real answer is: 7
the classifier came back with 8, the real answer is: 8
the classifier came back with 0, the real answer is: 0
the classifier came back with 8, the real answer is: 8
the classifier came back with 8, the real answer is: 8
the classifier came back with 9, the real answer is: 9
the classifier came back with 0, the real answer is: 0
the classifier came back with 8, the real answer is: 8
the classifier came back with 7, the real answer is: 7
the classifier came back with 5, the real answer is: 5
the classifier came back with 9, the real answer is: 9
the classifier came back with 7, the real answer is: 7
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 7, the real answer is: 7
the classifier came back with 9, the real answer is: 9
the classifier came back with 4, the real answer is: 4
the classifier came back with 5, the real answer is: 5
the classifier came back with 1, the real answer is: 1
the classifier came back with 2, the real answer is: 2
the classifier came back with 4, the real answer is: 4
the classifier came back with 8, the real answer is: 8
the classifier came back with 6, the real answer is: 6
the classifier came back with 1, the real answer is: 1
the classifier came back with 8, the real answer is: 8
the classifier came back with 9, the real answer is: 9
the classifier came back with 0, the real answer is: 0
the classifier came back with 3, the real answer is: 3
the classifier came back with 8, the real answer is: 8
the classifier came back with 9, the real answer is: 9
the classifier came back with 3, the real answer is: 3
the classifier came back with 7, the real answer is: 7
the classifier came back with 1, the real answer is: 1
the classifier came back with 6, the real answer is: 6
the classifier came back with 2, the real answer is: 2
the classifier came back with 7, the real answer is: 7
the classifier came back with 0, the real answer is: 0
the classifier came back with 5, the real answer is: 5
the classifier came back with 0, the real answer is: 0
the classifier came back with 2, the real answer is: 2
the classifier came back with 1, the real answer is: 1
the classifier came back with 7, the real answer is: 7
the classifier came back with 0, the real answer is: 0
the classifier came back with 8, the real answer is: 8
the classifier came back with 5, the real answer is: 5
the classifier came back with 6, the real answer is: 6
the classifier came back with 3, the real answer is: 3
the classifier came back with 7, the real answer is: 7
the classifier came back with 9, the real answer is: 9
the classifier came back with 1, the real answer is: 1
the classifier came back with 7, the real answer is: 7
the classifier came back with 2, the real answer is: 2
the classifier came back with 0, the real answer is: 0
the classifier came back with 7, the real answer is: 7
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 7, the real answer is: 7
the classifier came back with 4, the real answer is: 4
the classifier came back with 3, the real answer is: 3
the classifier came back with 9, the real answer is: 9
the classifier came back with 7, the real answer is: 7
the classifier came back with 0, the real answer is: 0
the classifier came back with 2, the real answer is: 2
the classifier came back with 4, the real answer is: 4
the classifier came back with 2, the real answer is: 2
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 0, the real answer is: 0
the classifier came back with 9, the real answer is: 9
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: 5
the classifier came back with 9, the real answer is: 9
the classifier came back with 4, the real answer is: 4
the classifier came back with 8, the real answer is: 8
the classifier came back with 1, the real answer is: 1
the classifier came back with 2, the real answer is: 2
the classifier came back with 8, the real answer is: 8
the classifier came back with 8, the real answer is: 8
the classifier came back with 3, the real answer is: 3
the classifier came back with 7, the real answer is: 7
the classifier came back with 6, the real answer is: 6
the classifier came back with 7, the real answer is: 7
the classifier came back with 8, the real answer is: 8
the classifier came back with 6, the real answer is: 6
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: 4
the classifier came back with 5, the real answer is: 5
the classifier came back with 0, the real answer is: 4
the classifier came back with 6, the real answer is: 6
the classifier came back with 5, the real answer is: 5
the classifier came back with 7, the real answer is: 7
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 1, the real answer is: 1
the classifier came back with 9, the real answer is: 9
the classifier came back with 6, the real answer is: 6
the classifier came back with 9, the real answer is: 9
the classifier came back with 2, the real answer is: 2
the classifier came back with 7, the real answer is: 7
the classifier came back with 7, the real answer is: 7
the classifier came back with 5, the real answer is: 5
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 5, the real answer is: 5
the classifier came back with 2, the real answer is: 2
the classifier came back with 9, the real answer is: 2
the classifier came back with 1, the real answer is: 1
the classifier came back with 1, the real answer is: 1
the classifier came back with 1, the real answer is: 1
the classifier came back with 0, the real answer is: 0
the classifier came back with 7, the real answer is: 7
the classifier came back with 4, the real answer is: 4
the classifier came back with 0, the real answer is: 0
the classifier came back with 4, the real answer is: 4
the classifier came back with 2, the real answer is: 2
the classifier came back with 0, the real answer is: 0
the classifier came back with 9, the real answer is: 9
the classifier came back with 5, the real answer is: 5
the classifier came back with 6, the real answer is: 6
the classifier came back with 0, the real answer is: 0
the classifier came back with 2, the real answer is: 2
the classifier came back with 5, the real answer is: 5
the classifier came back with 6, the real answer is: 6
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 7, the real answer is: 7
the classifier came back with 1, the real answer is: 1
the classifier came back with 4, the real answer is: 4
the classifier came back with 3, the real answer is: 3
the classifier came back with 1, the real answer is: 1
the classifier came back with 6, the real answer is: 6
the classifier came back with 2, the real answer is: 2
the classifier came back with 9, the real answer is: 9
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 4, the real answer is: 4
the classifier came back with 1, the real answer is: 1
the classifier came back with 9, the real answer is: 9
the classifier came back with 4, the real answer is: 4
the classifier came back with 7, the real answer is: 7
the classifier came back with 9, the real answer is: 5
the classifier came back with 4, the real answer is: 4
the classifier came back with 8, the real answer is: 8
the classifier came back with 3, the real answer is: 3
the classifier came back with 1, the real answer is: 1
the classifier came back with 9, the real answer is: 4
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 9, the real answer is: 9
the classifier came back with 7, the real answer is: 7
the classifier came back with 6, the real answer is: 6
the classifier came back with 3, the real answer is: 3
the classifier came back with 2, the real answer is: 2
the classifier came back with 4, the real answer is: 4
the classifier came back with 6, the real answer is: 6
the classifier came back with 7, the real answer is: 7
the classifier came back with 2, the real answer is: 2
the classifier came back with 1, the real answer is: 1
the classifier came back with 2, the real answer is: 2
the classifier came back with 7, the real answer is: 7
the classifier came back with 8, the real answer is: 8
the classifier came back with 5, the real answer is: 5
the classifier came back with 2, the real answer is: 2
the classifier came back with 7, the real answer is: 7
the classifier came back with 5, the real answer is: 5
the classifier came back with 9, the real answer is: 9
the classifier came back with 4, the real answer is: 4
the classifier came back with 9, the real answer is: 9
the classifier came back with 8, the real answer is: 8
the classifier came back with 2, the real answer is: 2
the classifier came back with 6, the real answer is: 6
the classifier came back with 7, the real answer is: 7
the classifier came back with 5, the real answer is: 5
the classifier came back with 3, the real answer is: 3
the classifier came back with 6, the real answer is: 6
the classifier came back with 3, the real answer is: 3
the classifier came back with 6, the real answer is: 6
the classifier came back with 5, the real answer is: 5
the classifier came back with 7, the real answer is: 7
the classifier came back with 4, the real answer is: 4
the classifier came back with 5, the real answer is: 5
the classifier came back with 8, the real answer is: 8
the classifier came back with 0, the real answer is: 0
the classifier came back with 1, the real answer is: 1
the classifier came back with 0, the real answer is: 0
the classifier came back with 6, the real answer is: 6
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 5, the real answer is: 5
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 8, the real answer is: 8
the classifier came back with 4, the real answer is: 4
the classifier came back with 1, the real answer is: 1
the classifier came back with 5, the real answer is: 5
the classifier came back with 2, the real answer is: 2
the classifier came back with 1, the real answer is: 1
the classifier came back with 0, the real answer is: 0
the classifier came back with 2, the real answer is: 2
the classifier came back with 2, the real answer is: 2
the classifier came back with 4, the real answer is: 4
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 1, the real answer is: 1
the classifier came back with 7, the real answer is: 7
the classifier came back with 6, the real answer is: 6
the classifier came back with 1, the real answer is: 1
the classifier came back with 1, the real answer is: 1
the classifier came back with 1, the real answer is: 1
the classifier came back with 1, the real answer is: 1
the classifier came back with 3, the real answer is: 3
the classifier came back with 8, the real answer is: 8
the classifier came back with 0, the real answer is: 0
the classifier came back with 4, the real answer is: 4
the classifier came back with 2, the real answer is: 2
the classifier came back with 3, the real answer is: 3
the classifier came back with 6, the real answer is: 6
the classifier came back with 2, the real answer is: 2
the classifier came back with 5, the real answer is: 5
the classifier came back with 8, the real answer is: 8
the classifier came back with 4, the real answer is: 4
the classifier came back with 5, the real answer is: 5
the classifier came back with 4, the real answer is: 4
the classifier came back with 5, the real answer is: 5
the classifier came back with 8, the real answer is: 8
the classifier came back with 1, the real answer is: 1
the classifier came back with 5, the real answer is: 5
the classifier came back with 9, the real answer is: 9
the classifier came back with 3, the real answer is: 3
the classifier came back with 2, the real answer is: 2
the classifier came back with 0, the real answer is: 0
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 0, the real answer is: 0
the classifier came back with 4, the real answer is: 4
the classifier came back with 9, the real answer is: 9
the classifier came back with 7, the real answer is: 7
the classifier came back with 3, the real answer is: 3
the classifier came back with 0, the real answer is: 0
the classifier came back with 8, the real answer is: 8
the classifier came back with 9, the real answer is: 9
the classifier came back with 0, the real answer is: 0
the classifier came back with 1, the real answer is: 1
the classifier came back with 7, the real answer is: 7
the classifier came back with 1, the real answer is: 1
the classifier came back with 1, the real answer is: 8
the classifier came back with 1, the real answer is: 1
the classifier came back with 5, the real answer is: 5
the classifier came back with 6, the real answer is: 6
the classifier came back with 2, the real answer is: 2
the classifier came back with 8, the real answer is: 8
the classifier came back with 2, the real answer is: 2
the classifier came back with 5, the real answer is: 5
the classifier came back with 7, the real answer is: 7
the classifier came back with 0, the real answer is: 0
the classifier came back with 7, the real answer is: 7
the classifier came back with 7, the real answer is: 7
the classifier came back with 0, the real answer is: 0
the classifier came back with 7, the real answer is: 7
the classifier came back with 7, the real answer is: 7
the classifier came back with 5, the real answer is: 5
the classifier came back with 8, the real answer is: 8
the classifier came back with 4, the real answer is: 4
the classifier came back with 9, the real answer is: 9
the classifier came back with 3, the real answer is: 3
the classifier came back with 9, the real answer is: 9
the classifier came back with 6, the real answer is: 6
the classifier came back with 5, the real answer is: 5
the classifier came back with 6, the real answer is: 6
the classifier came back with 4, the real answer is: 4
the classifier came back with 2, the real answer is: 2
the classifier came back with 5, the real answer is: 5
the classifier came back with 0, the real answer is: 0
the classifier came back with 6, the real answer is: 6
the classifier came back with 8, the real answer is: 8
the classifier came back with 8, the real answer is: 8
the classifier came back with 3, the real answer is: 3
the classifier came back with 0, the real answer is: 0
the classifier came back with 3, the real answer is: 3
the classifier came back with 2, the real answer is: 2
the classifier came back with 2, the real answer is: 2
the classifier came back with 2, the real answer is: 2
the classifier came back with 3, the real answer is: 3
the classifier came back with 8, the real answer is: 3
the classifier came back with 8, the real answer is: 8
the classifier came back with 2, the real answer is: 2
the classifier came back with 4, the real answer is: 4
the classifier came back with 8, the real answer is: 8
the classifier came back with 8, the real answer is: 8
the classifier came back with 7, the real answer is: 7
the classifier came back with 2, the real answer is: 2
the classifier came back with 6, the real answer is: 6
the classifier came back with 7, the real answer is: 7
the classifier came back with 8, the real answer is: 8
the classifier came back with 5, the real answer is: 5
the classifier came back with 7, the real answer is: 7
the classifier came back with 2, the real answer is: 2
the classifier came back with 2, the real answer is: 2
the classifier came back with 3, the real answer is: 3
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 7, the real answer is: 7
the classifier came back with 2, the real answer is: 2
the classifier came back with 7, the real answer is: 7
the classifier came back with 8, the real answer is: 8
the classifier came back with 0, the real answer is: 0
the classifier came back with 4, the real answer is: 4
the classifier came back with 3, the real answer is: 3
the classifier came back with 1, the real answer is: 8
the classifier came back with 2, the real answer is: 2
the classifier came back with 3, the real answer is: 3
the classifier came back with 7, the real answer is: 1
the classifier came back with 2, the real answer is: 2
the classifier came back with 7, the real answer is: 7
the classifier came back with 2, the real answer is: 2
the classifier came back with 5, the real answer is: 5
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 5, the real answer is: 5
the classifier came back with 3, the real answer is: 3
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 9, the real answer is: 9
the classifier came back with 8, the real answer is: 8
the classifier came back with 2, the real answer is: 2
the classifier came back with 6, the real answer is: 6
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 2, the real answer is: 2
the classifier came back with 1, the real answer is: 1
the classifier came back with 5, the real answer is: 5
the classifier came back with 4, the real answer is: 4
the classifier came back with 5, the real answer is: 5
the classifier came back with 3, the real answer is: 3
the classifier came back with 9, the real answer is: 9
the classifier came back with 0, the real answer is: 0
the classifier came back with 1, the real answer is: 1
the classifier came back with 2, the real answer is: 2
the classifier came back with 4, the real answer is: 4
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 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: 9
the classifier came back with 8, the real answer is: 8
the classifier came back with 5, the real answer is: 5
the classifier came back with 8, the real answer is: 8
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 1, the real answer is: 1
the classifier came back with 4, the real answer is: 4
the classifier came back with 1, the real answer is: 1
the classifier came back with 9, the real answer is: 9
the classifier came back with 6, the real answer is: 6
the classifier came back with 0, the real answer is: 0
the classifier came back with 7, the real answer is: 7
the classifier came back with 5, the real answer is: 5
the classifier came back with 3, the real answer is: 3
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 1, the real answer is: 1
the classifier came back with 9, the real answer is: 9
the classifier came back with 7, the real answer is: 7
the classifier came back with 4, the real answer is: 4
the classifier came back with 9, the real answer is: 9
the classifier came back with 5, the real answer is: 5
the classifier came back with 1, the real answer is: 1
the classifier came back with 5, the real answer is: 5
the classifier came back with 0, the real answer is: 0
the classifier came back with 1, the real answer is: 1
the classifier came back with 6, the real answer is: 6
the classifier came back with 8, the real answer is: 8
the classifier came back with 2, the real answer is: 2
the classifier came back with 9, the real answer is: 9
the classifier came back with 7, the real answer is: 7
the classifier came back with 6, the real answer is: 6
the classifier came back with 2, the real answer is: 2
the classifier came back with 9, the real answer is: 9
the classifier came back with 4, the real answer is: 4
the classifier came back with 2, the real answer is: 2
the classifier came back with 5, the real answer is: 5
the classifier came back with 4, the real answer is: 4
the classifier came back with 3, 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 6, the real answer is: 6
the classifier came back with 1, the real answer is: 1
the classifier came back with 6, the real answer is: 6
the classifier came back with 2, the real answer is: 2
the classifier came back with 9, the real answer is: 9
the classifier came back with 2, the real answer is: 2
the classifier came back with 6, the real answer is: 6
the classifier came back with 7, the real answer is: 7
the classifier came back with 8, the real answer is: 8
the classifier came back with 7, the real answer is: 7
the classifier came back with 7, the real answer is: 7
the classifier came back with 3, the real answer is: 3
the classifier came back with 1, the real answer is: 1
the classifier came back with 5, the real answer is: 5
the classifier came back with 1, the real answer is: 1
the classifier came back with 5, the real answer is: 5
the classifier came back with 0, the real answer is: 0
the classifier came back with 9, the real answer is: 3
the classifier came back with 2, the real answer is: 2
the classifier came back with 6, the real answer is: 6
the classifier came back with 0, the real answer is: 0
the classifier came back with 5, the real answer is: 5
the classifier came back with 0, the real answer is: 0
the classifier came back with 7, the real answer is: 7
the classifier came back with 3, the real answer is: 3
the classifier came back with 7, the real answer is: 7
the classifier came back with 1, the real answer is: 1
the classifier came back with 5, the real answer is: 5
the classifier came back with 7, the real answer is: 7
the classifier came back with 5, the real answer is: 5
the classifier came back with 0, the real answer is: 0
the classifier came back with 4, the real answer is: 4
the classifier came back with 8, the real answer is: 8
the classifier came back with 6, the real answer is: 6
the classifier came back with 0, the real answer is: 0
the classifier came back with 5, the real answer is: 5
the classifier came back with 1, the real answer is: 1
the classifier came back with 0, the real answer is: 0
the classifier came back with 7, the real answer is: 7
the classifier came back with 7, the real answer is: 7
the classifier came back with 4, the real answer is: 4
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 2, the real answer is: 2
the classifier came back with 5, the real answer is: 5
the classifier came back with 1, the real answer is: 1
the classifier came back with 7, the real answer is: 7
the classifier came back with 9, the real answer is: 9
the classifier came back with 1, the real answer is: 1
the classifier came back with 5, the real answer is: 5
the classifier came back with 4, the real answer is: 4
the classifier came back with 7, the real answer is: 7
the classifier came back with 4, the real answer is: 4
the classifier came back with 1, the real answer is: 1
the classifier came back with 9, the real answer is: 9
the classifier came back with 3, the real answer is: 3
the classifier came back with 6, the real answer is: 6
the classifier came back with 7, the real answer is: 7
the classifier came back with 5, the real answer is: 5
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 2, the real answer is: 2
the classifier came back with 0, the real answer is: 0
the classifier came back with 7, the real answer is: 9
the classifier came back with 7, the real answer is: 7
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: 4
the classifier came back with 2, the real answer is: 2
the classifier came back with 0, the real answer is: 0
the classifier came back with 7, the real answer is: 7
the classifier came back with 7, the real answer is: 7
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 8, the real answer is: 8
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: 3
the classifier came back with 2, the real answer is: 2
the classifier came back with 6, the real answer is: 8
the classifier came back with 3, the real answer is: 3
the classifier came back with 6, the real answer is: 6
the classifier came back with 3, the real answer is: 3
the classifier came back with 1, the real answer is: 1
the classifier came back with 4, the real answer is: 4
the classifier came back with 1, the real answer is: 8
the classifier came back with 2, the real answer is: 2
the classifier came back with 7, the real answer is: 7
the classifier came back with 5, the real answer is: 5
the classifier came back with 9, the real answer is: 9
the classifier came back with 1, the real answer is: 1
the classifier came back with 1, the real answer is: 1
the classifier came back with 8, the real answer is: 8
the classifier came back with 6, the real answer is: 6
the classifier came back with 5, the real answer is: 5
the classifier came back with 6, the real answer is: 6
the classifier came back with 2, the real answer is: 2
the classifier came back with 1, the real answer is: 1
the classifier came back with 5, the real answer is: 5
the classifier came back with 7, the real answer is: 7
the classifier came back with 0, the real answer is: 0
the classifier came back with 8, the real answer is: 8
the classifier came back with 6, the real answer is: 6
the classifier came back with 4, the real answer is: 4
the classifier came back with 7, the real answer is: 7
the classifier came back with 6, the real answer is: 6
the classifier came back with 8, the real answer is: 8
the classifier came back with 7, the real answer is: 7
the classifier came back with 9, the real answer is: 9
the classifier came back with 8, the real answer is: 8
the classifier came back with 5, the real answer is: 5
the classifier came back with 8, the real answer is: 8
the classifier came back with 3, the real answer is: 3
the classifier came back with 6, the real answer is: 6
the classifier came back with 8, the real answer is: 8
the classifier came back with 8, the real answer is: 8
the classifier came back with 8, the real answer is: 8
the classifier came back with 0, the real answer is: 0
the classifier came back with 2, the real answer is: 2
the classifier came back with 9, the real answer is: 9
the classifier came back with 2, the real answer is: 2
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 7, the real answer is: 7
the classifier came back with 3, the real answer is: 3
the classifier came back with 6, the real answer is: 6
the classifier came back with 9, the real answer is: 9
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 0, the real answer is: 0
the classifier came back with 6, the real answer is: 6
the classifier came back with 1, the real answer is: 1
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 8, the real answer is: 8
the classifier came back with 3, the real answer is: 3
the classifier came back with 7, the real answer is: 7
the classifier came back with 1, the real answer is: 1
the classifier came back with 4, the real answer is: 4
the classifier came back with 8, the real answer is: 8
the classifier came back with 7, the real answer is: 7
the classifier came back with 1, the real answer is: 1
the classifier came back with 4, the real answer is: 4
the classifier came back with 1, the real answer is: 1
the classifier came back with 6, the real answer is: 6
the classifier came back with 9, the real answer is: 9
the classifier came back with 1, the real answer is: 1
the classifier came back with 8, the real answer is: 8
the classifier came back with 6, the real answer is: 6
the classifier came back with 4, the real answer is: 4
the classifier came back with 2, the real answer is: 2
the classifier came back with 5, the real answer is: 5
the classifier came back with 8, the real answer is: 8
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 0, the real answer is: 0
the classifier came back with 3, the real answer is: 3
the classifier came back with 1, the real answer is: 1
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 2, the real answer is: 2
the classifier came back with 9, the real answer is: 9
the classifier came back with 6, the real answer is: 6
the classifier came back with 5, the real answer is: 5
the classifier came back with 4, the real answer is: 4
the classifier came back with 1, the real answer is: 1
the classifier came back with 4, the real answer is: 4
the classifier came back with 6, 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 0, the real answer is: 0
the classifier came back with 4, the real answer is: 4
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 3, the real answer is: 3
the classifier came back with 8, the real answer is: 8
the classifier came back with 6, the real answer is: 6
the classifier came back with 0, the real answer is: 0
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 4, the real answer is: 4
the classifier came back with 7, the real answer is: 7
the classifier came back with 2, the real answer is: 2
the classifier came back with 4, the real answer is: 4
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 7, the real answer is: 7
the classifier came back with 2, the real answer is: 2
the classifier came back with 0, the real answer is: 0
the classifier came back with 5, the real answer is: 5
the classifier came back with 0, the real answer is: 0
the classifier came back with 8, the real answer is: 8
the classifier came back with 1, the real answer is: 1
the classifier came back with 9, the real answer is: 9
the classifier came back with 1, the real answer is: 1
the classifier came back with 5, the real answer is: 5
the classifier came back with 6, the real answer is: 6
the classifier came back with 5, the real answer is: 5
the classifier came back with 4, the real answer is: 4
the classifier came back with 9, the real answer is: 9
the classifier came back with 7, the real answer is: 7
the classifier came back with 3, the real answer is: 3
the classifier came back with 5, the real answer is: 5
the classifier came back with 0, the real answer is: 0
the classifier came back with 8, the real answer is: 8
the classifier came back with 8, the real answer is: 8
the classifier came back with 8, the real answer is: 8
the classifier came back with 1, the real answer is: 1
the classifier came back with 5, the real answer is: 5
the classifier came back with 0, the real answer is: 0
the classifier came back with 1, the real answer is: 1
the classifier came back with 7, the real answer is: 7
the classifier came back with 3, the real answer is: 3
the classifier came back with 9, the real answer is: 9
the classifier came back with 5, the real answer is: 5
the classifier came back with 6, the real answer is: 6
the classifier came back with 2, the real answer is: 2
the classifier came back with 0, the real answer is: 0
the classifier came back with 4, the real answer is: 4
the classifier came back with 5, the real answer is: 5
the classifier came back with 2, the real answer is: 2
the classifier came back with 4, the real answer is: 4
the classifier came back with 2, the real answer is: 2
the classifier came back with 6, the real answer is: 6
the classifier came back with 1, the real answer is: 1
the classifier came back with 0, the real answer is: 0
the classifier came back with 7, the real answer is: 7
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 5, the real answer is: 5
the classifier came back with 9, the real answer is: 9
the classifier came back with 4, the real answer is: 4
the classifier came back with 9, the real answer is: 9
the classifier came back with 4, the real answer is: 4
the classifier came back with 5, the real answer is: 5
the classifier came back with 6, the real answer is: 6
the classifier came back with 9, the real answer is: 9
the classifier came back with 8, the real answer is: 8
the classifier came back with 9, the real answer is: 9
the classifier came back with 0, the real answer is: 0
the classifier came back with 7, the real answer is: 7
the classifier came back with 5, the real answer is: 5
the classifier came back with 1, the real answer is: 1
the classifier came back with 4, the real answer is: 4
the classifier came back with 2, the real answer is: 2
the classifier came back with 0, the real answer is: 0
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 2, the real answer is: 2
the classifier came back with 3, the real answer is: 3
the classifier came back with 8, the real answer is: 8
the classifier came back with 6, the real answer is: 6
the classifier came back with 9, the real answer is: 9
the classifier came back with 4, the real answer is: 4
the classifier came back with 8, the real answer is: 8
the classifier came back with 9, the real answer is: 9
the classifier came back with 1, the real answer is: 1
the classifier came back with 8, the real answer is: 8
the classifier came back with 9, the real answer is: 9
the classifier came back with 1, the real answer is: 1
the classifier came back with 4, the real answer is: 4
the classifier came back with 6, the real answer is: 6
the classifier came back with 9, the real answer is: 9
the classifier came back with 4, the real answer is: 4
the classifier came back with 3, the real answer is: 3
the classifier came back with 2, the real answer is: 2
the classifier came back with 4, the real answer is: 4
the classifier came back with 9, the real answer is: 9
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 0, the real answer is: 0
the classifier came back with 5, the real answer is: 5
the classifier came back with 7, the real answer is: 7
the classifier came back with 1, the real answer is: 1
the classifier came back with 2, the real answer is: 2
the classifier came back with 0, the real answer is: 0
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 0, the real answer is: 0
the classifier came back with 5, the real answer is: 5
the classifier came back with 1, the real answer is: 1
the classifier came back with 9, the real answer is: 9
the classifier came back with 1, the real answer is: 1
the classifier came back with 3, the real answer is: 3
the classifier came back with 2, the real answer is: 2
the classifier came back with 6, the real answer is: 6
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 5, the real answer is: 5
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 9, the real answer is: 9
the classifier came back with 9, the real answer is: 9
the classifier came back with 5, the real answer is: 5
the classifier came back with 2, the real answer is: 2
the classifier came back with 8, the real answer is: 8
the classifier came back with 4, the real answer is: 4
the classifier came back with 7, the real answer is: 7
the classifier came back with 4, the real answer is: 4
the classifier came back with 7, the real answer is: 7
the classifier came back with 2, the real answer is: 3
the classifier came back with 8, the real answer is: 8
the classifier came back with 1, the real answer is: 1
the classifier came back with 8, the real answer is: 8
the classifier came back with 3, the real answer is: 3
the classifier came back with 8, the real answer is: 8
the classifier came back with 6, the real answer is: 6
the classifier came back with 5, the real answer is: 5
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 6, the real answer is: 6
the classifier came back with 2, the real answer is: 2
the classifier came back with 6, the real answer is: 6
the classifier came back with 3, the real answer is: 3
the classifier came back with 5, the real answer is: 5
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 1, the real answer is: 1
the classifier came back with 4, the real answer is: 4
the classifier came back with 7, the real answer is: 7
the classifier came back with 0, the real answer is: 0
the classifier came back with 1, the real answer is: 1
the classifier came back with 4, the real answer is: 4
the classifier came back with 1, the real answer is: 1
the classifier came back with 6, the real answer is: 6
the classifier came back with 9, the real answer is: 9
the classifier came back with 1, the real answer is: 1
the classifier came back with 2, the real answer is: 2
the classifier came back with 8, the real answer is: 8
the classifier came back with 1, the real answer is: 1
the classifier came back with 0, the real answer is: 0
the classifier came back with 8, the real answer is: 8
the classifier came back with 5, the real answer is: 5
the classifier came back with 2, 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 7, the real answer is: 7
the classifier came back with 2, the real answer is: 2
the classifier came back with 5, the real answer is: 5
the classifier came back with 0, the real answer is: 0
the classifier came back with 2, the real answer is: 2
the classifier came back with 2, the real answer is: 2
the classifier came back with 4, the real answer is: 4
the classifier came back with 8, the real answer is: 8
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 9, the real answer is: 9
the classifier came back with 8, the real answer is: 8
the classifier came back with 4, the real answer is: 4
the classifier came back with 2, the real answer is: 2
the classifier came back with 1, the real answer is: 1
the classifier came back with 2, the real answer is: 2
the classifier came back with 6, the real answer is: 6
the classifier came back with 7, the real answer is: 7
the classifier came back with 1, the real answer is: 1
the classifier came back with 5, the real answer is: 5
the classifier came back with 9, the real answer is: 9
the classifier came back with 3, the real answer is: 3
the classifier came back with 9, the real answer is: 9
the classifier came back with 7, the real answer is: 7
the classifier came back with 6, the real answer is: 6
the classifier came back with 0, the real answer is: 0
the classifier came back with 4, the real answer is: 4
the classifier came back with 6, the real answer is: 6
the classifier came back with 0, the real answer is: 0
the classifier came back with 1, the real answer is: 1
the classifier came back with 5, the real answer is: 5
the classifier came back with 2, the real answer is: 2
the classifier came back with 9, the real answer is: 9
the classifier came back with 8, the real answer is: 8
the classifier came back with 0, the real answer is: 0
the classifier came back with 2, the real answer is: 2
the classifier came back with 1, the real answer is: 1
the classifier came back with 0, the real answer is: 0
the classifier came back with 4, the real answer is: 4
the classifier came back with 6, the real answer is: 6
the classifier came back with 7, the real answer is: 7
the classifier came back with 0, the real answer is: 0
the classifier came back with 8, the real answer is: 8
the classifier came back with 8, the real answer is: 8
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 7, the real answer is: 7
the classifier came back with 6, the real answer is: 6
the classifier came back with 0, the real answer is: 0
the classifier came back with 6, the real answer is: 6

the total number of errors is: 20

the total error rate is: 0.021142

1
2