KNN算法python实现

KNN算法python实现

算法概述

算法优缺点

• 优点：精度高、对异常值不敏感、无数据输入假定。
• 缺点：计算复杂度高、空间复杂度高。
• 适用数据范围：数值型和标称型。

算法流程

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

算法准备

使用python导入数据

from numpy import *
import operator

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

group, labels = createDataSet()

group

array([[1. , 1.1],
       [1. , 1. ],
       [0. , 0. ],
       [0. , 0.1]])

labels

['A', 'A', 'B', 'B']

实施KNN分类算法

对未知类别属性的数据集中的每个点依次执行以下操作：

• 计算已知类别数据集中的点与当前点之间的距离；
• 按照距离递增次序排序；
• 选取与当前点距离最小的走个点；
• 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。

# 各近邻算法
def classify0(inX, dataSet, labels, k):
    dataSetSize = dataSet.shape[0]
    diffMat = tile(inX, (dataSetSize, 1)) - dataSet # tile函数作用见下面的例子
    sqDiffMat = diffMat ** 2
    sqDistances = sqDiffMat.sum(axis = 1)
    distances = sqDistances**0.5
    sortedDistIndicies = distances.argsort() # argsort返回数组从小到大的索引值
    classCount = {}
    
    for i in range(k):
        votellabel = labels[sortedDistIndicies[i]]
        classCount[votellabel] = classCount.get(votellabel, 0) + 1
        
    sortedClassCount = sorted(classCount.items(), key = operator.itemgetter(1), reverse = True)
    return sortedClassCount[0][0]

classifyO ()函数有4个输人参数:用于分类的输人向量是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

tile([1,2],2)

array([1, 2, 1, 2])

输出[1,2,1,2]

tile([1,2],(2,2))

array([[1, 2, 1, 2],
       [1, 2, 1, 2]])

重复顺序为： [1,2] => [[1,2] , [1,2]] => [[1,2,1,2] , [1,2,1,2]]

tile([1,2],(2,2,3))

array([[[1, 2, 1, 2, 1, 2],
        [1, 2, 1, 2, 1, 2]],

       [[1, 2, 1, 2, 1, 2],
        [1, 2, 1, 2, 1, 2]]])

重复顺序为： [1,2] => [[1,2] , [1,2]] => [[[1,2],[1,2]] , [[1,2],[1,2]]] => [[[1,2,1,2,1,2],[1,2,1,2,1,2]] , [[1,2,1,2,1,2],[1,2,1,2,1,2]]]

# sortedDistIndicies = ((((tile([0, 0], (4, 1)) - group) ** 2).sum(axis = 1))**0.5).argsort()
classify0([0, 0], group, labels, 3)

'B'

示例：使用k-近邻算法改进约会网站的配对效果

• 收集数据：提供文本文件。
• 准备数据: 使用Pyhton解析文本文件。
• 分析数据：使用Matplotlib画二维扩散图。
• 训练算法：此步驟不适用于k近邻算法。
• 测试算法：使用海伦提供的部分数据作为测试样本。
  测试样本和非测试样本的区别在于：测试样本是已经完成分类的数据，如果预测分类
  与实际类别不同，则标记为一个错误。
• 使用算法：产生简单的命令行程序，然后海伦可以输入一些特征数据以判断对方是否为自己喜欢的类型。

收集数据

数据存放在data/datingTestSet2.txt中，数据共1000行， 特征为3：

• 每年获得的飞行常客里程数
• 玩视频游戏所耗时间百分比
• 每周消费的冰淇淋公升数

# 读取数据
def file2matrix(filenam):
    data = open(filename)
    lines = data.readlines()
    numberOfLines = len(lines)
    returnMat = zeros((numberOfLines, 3))
    classLabelVector = []
    index = 0
    for line in lines:
        line = line.strip()
        listFromLine = line.split('\t')
        returnMat[index, :] = listFromLine[0:3]
        classLabelVector.append(int(listFromLine[-1]))
        index += 1
    return returnMat, classLabelVector

filename = 'data/datingTestSet2.txt'
datingDataMat, datingLabels = file2matrix(filename)

datingDataMat

array([[4.0920000e+04, 8.3269760e+00, 9.5395200e-01],
       [1.4488000e+04, 7.1534690e+00, 1.6739040e+00],
       [2.6052000e+04, 1.4418710e+00, 8.0512400e-01],
       ...,
       [2.6575000e+04, 1.0650102e+01, 8.6662700e-01],
       [4.8111000e+04, 9.1345280e+00, 7.2804500e-01],
       [4.3757000e+04, 7.8826010e+00, 1.3324460e+00]])

datingLabels[:20]

[3, 2, 1, 1, 1, 1, 3, 3, 1, 3, 1, 1, 2, 1, 1, 1, 1, 1, 2, 3]

分析数据

%matplotlib inline
import matplotlib
import matplotlib.pyplot as plt

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

fig = plt.figure()
ax = fig.add_subplot(111)
ax.scatter(datingDataMat[:, 1], datingDataMat[:, 2], 15.0 * array(datingLabels), 15.0 * array(datingLabels))
plt.show()

fig = plt.figure()
ax = fig.add_subplot(111)
ax.scatter(datingDataMat[:, 0], datingDataMat[:, 1], 15.0 * array(datingLabels), 15.0 * array(datingLabels))
plt.show()

归一化数据

在计算距离的时候，数字差值较大的属性对计算结果的影响最大，导致对每个特征不公平，所以在计算之前要对数据归一化。

这里使用最大-最小归一化

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

# 归一化特征值
def autoNorm(dataSet):
    minVals = dataSet.min(0)
    maxVals = dataSet.max(0)
    ranges = maxVals - minVals
    normDataSet = zeros(shape(dataSet))
    m = dataSet.shape[0]
    normDataSet = dataSet - tile(minVals, (m, 1))
    normDataSet = normDataSet / tile(ranges, (m, 1))
    return normDataSet, ranges, minVals

dataSet = group
dataSet

array([[1. , 1.1],
       [1. , 1. ],
       [0. , 0. ],
       [0. , 0.1]])

minVals = dataSet.min(0);
minVals

array([0., 0.])

maxVals = dataSet.max(0);
maxVals

array([1. , 1.1])

ranges = maxVals - minVals;
ranges

array([1. , 1.1])

normDataSet = zeros(shape(dataSet))
normDataSet

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

m = dataSet.shape[0]
normDataSet = dataSet - tile(minVals, (m, 1))
normDataSet

array([[1. , 1.1],
       [1. , 1. ],
       [0. , 0. ],
       [0. , 0.1]])

normDataSet = normDataSet / tile(ranges, (m, 1))
normDataSet

array([[1.        , 1.        ],
       [1.        , 0.90909091],
       [0.        , 0.        ],
       [0.        , 0.09090909]])

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]])

ranges

array([9.1273000e+04, 2.0919349e+01, 1.6943610e+00])

minVals

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

测试算法

def datingClassTest(filename):
    hoRatio = 0.10
    datingDataMat, datingLabels = file2matrix(filename)
    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: {0}, the real answer is: {1}".format(classifierResult, datingLabels[i]))
        if(classifierResult != datingLabels[i]): errorCount += 1.0
    print("the total error rate is: %f" % (errorCount / float(numTestVecs)))

datingClassTest(filename)

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: 3, 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

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('data/datingTestSet2.txt')
    normMat, ranges, minVals = autoNorm(datingDataMat)
    inArr =array([ffMiles, percentTats, iceCream])
    classifierResult = classify0((inArr-minVals)/ranges, normMat,datingLabels, 3 )
    # print(classifierResult)
    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:1000
liters of ice cream consumed per year:0.1
2
you will probably like this person: in small doses

示例：手写识别系统

• 收集数据：提供文本文件。
• 准备数据：编写函数classify0() ,将图像格式转换为分类器使用的制格式。
• 分析数据：在python命令提示符中检查数据，确保它符合要求。
• 训练算法：此步驟不适用于各近邻算法。
• 测试算法：编写函数使用提供的部分数据集作为测试样本，测试样本与非测试样本的区别在于测试样本是已经完成分类的数据，如果预测分类与实际类别不同，则标记为一个错误。
• 使用算法：本例没有完成此步驟，若你感兴趣可以构建完整的应用程序，从图像中提取数字，并完成数字识别，美国的邮件分拣系统就是一个实际运行的类似系统。

收集数据

数据存放在data/trainingDigits/和data/testDigits/中，训练数据大约2000个，测试数据大约900个， 把32 * 32的二进制图像矩阵转换为1 * 1024的向量：

分析准备数据

# img2vector函数，将图像转换为向量
def img2vector(filename):
    returnVect = zeros((1, 1024))
    data = open(filename)
    for i in range(32):
        lineStr = data.readline()
        for j in range(32):
            returnVect[0, 32*i + j] = int(lineStr[j])
    return returnVect

filename = 'data/trainingDigits/0_13.txt'
testVector = img2vector(filename)

testVector[0, 0:31]

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

测试算法

import os

def handWritingClassTest():
    hwLabels = []
    trainingFileList = os.listdir('data/trainingDigits/')
    m = len(trainingFileList)
    trainingMat = zeros((m, 1024))
    for i in range(m):
        fileNameStr = trainingFileList[i]
        filename = 'data/trainingDigits/{}'.format(fileNameStr)
        fileStr = fileNameStr.split('.')[0]
        classNumStr = int(fileStr.split('_')[0]) # 标签
        hwLabels.append(classNumStr)
        trainingMat[i, :] = img2vector(filename)
    testFileList = os.listdir('data/testDigits/')
    errorCount = 0
    mTest = len(testFileList)
    for i in range(mTest):
        fileNameStr = testFileList[i]
        filename = 'data/testDigits/{}'.format(fileNameStr)
        fileStr = fileNameStr.split('.')[0]
        classNumStr = int(fileStr.split('_')[0]) # 标签
        vectorUnderTest = img2vector(filename)
        classifierResult = classify0(vectorUnderTest, trainingMat, hwLabels, 3 )
        print("the classifier came back with: {0}, the real answer is: {1}".format(classifierResult, classNumStr))
        if(classifierResult != classNumStr): errorCount += 1.0
            
    print("the total number of errors id: %d" % errorCount)
    print("the 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
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
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
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
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
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: 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: 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: 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: 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
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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
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
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
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
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
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
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
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
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
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: 7, the real answer is: 7
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: 7, the real answer is: 7
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: 7, the real answer is: 7
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: 7, the real answer is: 7
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: 7, the real answer is: 7
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: 7, the real answer is: 7
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: 7, the real answer is: 7
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: 7, the real answer is: 7
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: 7, the real answer is: 7
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: 7, the real answer is: 7
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: 7, the real answer is: 7
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: 7, the real answer is: 7
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: 7, the real answer is: 7
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: 7, the real answer is: 7
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: 7, the real answer is: 7
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: 7, the real answer is: 7
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: 7, the real answer is: 7
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: 7, the real answer is: 7
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: 7, the real answer is: 7
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: 7, the real answer is: 7
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: 7, the real answer is: 7
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: 7, the real answer is: 7
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: 7, the real answer is: 7
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: 7, the real answer is: 7
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: 7, the real answer is: 7
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: 7, the real answer is: 7
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: 7, the real answer is: 7
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: 7, the real answer is: 7
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: 7, the real answer is: 7
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: 7, the real answer is: 7
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: 7, the real answer is: 7
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: 7, the real answer is: 7
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: 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: 6, 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: 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: 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: 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: 8, the real answer is: 8
the classifier came back with: 3, 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: 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: 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: 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: 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: 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: 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: 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: 8, the real answer is: 8
the classifier came back with: 1, 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 1, 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: 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 total number of errors id: 10
the total error rate is: 0.010571