第2章 k-最近邻分类

2.1 利用距离分类（Classifying with distance measurements）

K最近邻（kNN，k-NearestNeighbor）分类算法是数据挖掘分类技术中最简单的方法之一。K最近邻是指$k$k个最近邻居，即每个样本都由它最邻近的$k$k个邻居中的多数派决定，$k$k通常小于20。

优点：高准确率，对异常值不敏感，对数据无须假设

缺点：计算复杂，消耗大量内存

适用范围：数值，标称值

KNN步骤：

1. 收集数据
   
2. 准备：数值型数据，结构化数据为宜
   
3. 分析：任意方法
   
4. 训练：KNN无需训练
   
5. 测试：计算错误率
   
6. 使用
   

2.1.1. 准备：Python导入数据

import numpy as np
import operator

def createDataSet():
    group = np.array([[1.0, 1.1], [1.0, 1.0], [0.0, 0.0], [0.0, 0.1]])
    labels = ['A', 'A', 'B', 'B']
    return group, labels

group, labels = createDataSet()
print(group)
print(labels)

[[1.  1.1]
 [1.  1. ]
 [0.  0. ]
 [0.  0.1]]
['A', 'A', 'B', 'B']

2.1.2 k-NN分类算法

# Listing 2.1 k-Nearest Neighbors algorithm

def classify0(inX, dataSet, labels, k):
    dataSetSize = dataSet.shape[0]
    
    # distance calculation
    diffMat = np.tile(inX, (dataSetSize, 1)) - dataSet
    sqDiffMat = diffMat ** 2
    sqDistances = sqDiffMat.sum(axis=1)
    distances = sqDistances ** 0.5
    sortedDistIndicies = distances.argsort()
    
    # voting with lowest k distances
    classCount = {}
    for i in range(k):
        voteIlabel = labels[sortedDistIndicies[i]]
        classCount[voteIlabel] = classCount.get(voteIlabel, 0) + 1
        
    # sort dictionary
    sortedClassCount = sorted(classCount.items(), key=operator.itemgetter(1), reverse=True)
    
    return sortedClassCount[0][0]
    

输入参数：
inX - 待预测样本
group - 训练样本
labels - 标签
k - k

欧氏距离（矢量$\bf{xA}$xA和$\bf{xB}$xB的欧氏距离）：

$d=\sqrt{(xA_0-xB_0)^2+(xA_1-xB_1)^2}$d=(xA0​−xB0​)2+(xA1​−xB1​)2​

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

'B'

2.1.3 测试分类器

2.2 例：利用KNN改善约会网站的匹配（Example: improving matches from a dating site with kNN.ipynb）

1. 收集数据：文本文件
   
2. 准备：解析文本
   
3. 分析：Matplotlib二维可视化
   
4. 训练：KNN无需训练
   
5. 测试：计算错误率
   
6. 使用
   

2.2.1 准备：解析文本中的数据

文本（TestSet.txt）：

• 包含1000条样本

• 每条样本包含3个特征

  1.每年飞行里程

  2.玩游戏时间比例

  3.每周消费的冰淇淋

# Listing 2.2 Text record to NumPy parsing code

def file2Matrix(filename):
    
    with open(filename) as fr:
        returnMat = []
        classLabelVector = []

        # parse line to a list
        for line in fr.readlines():
            line = line.strip()
            listFromLine = line.split("\t")
            returnMat.append([float(item) for item in listFromLine[0 : 3]])
            classLabelVector.append(int(listFromLine[-1]))
    
    returnMat = np.array(returnMat)
    
    return returnMat, classLabelVector

datingDataMat, datingLabels = file2Matrix("datingTestSet2.txt")
print(datingDataMat)
print(type(datingDataMat))
print(datingLabels[0 : 20])

[[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]]
<class 'numpy.ndarray'>
[3, 2, 1, 1, 1, 1, 3, 3, 1, 3, 1, 1, 2, 1, 1, 1, 1, 1, 2, 3]

2.2.2 分析：利用Matplotlib创建散点图

import matplotlib.pyplot as plt
%matplotlib inline

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 * np.array(datingLabels), 15.0 * np.array(datingLabels))
plt.show()

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

2.2.3 准备：数值归一化

# Listing 2.3 Data-normalizing code

def autoNorm(dataSet):
    minVals = dataSet.min(0)
    maxVals = dataSet.max(0)
    ranges = maxVals - minVals
    normDataSet = np.zeros(dataSet.shape)
    m = dataSet.shape[0]
    normDataSet = dataSet - np.tile(minVals, (m, 1))
    # element-wise division
    normDataSet = normDataSet / np.tile(ranges, (m, 1))
    
    return normDataSet, ranges, minVals

normMat, ranges, minVals = autoNorm(datingDataMat)
print(normMat)
print(ranges)
print(minVals)

[[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]]
[9.1273000e+04 2.0919349e+01 1.6943610e+00]
[0.       0.       0.001156]

2.2.4 测试：测试分类器

# Listing 2.4 Classifier testing code for dating site

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 :, :],
                                     datingLabels[numTestVecs :],
                                     3)
        print("the classifier came back with: {}, the real answer is: {}"
              .format(classifierResult, datingLabels[i]))
        if (classifierResult != datingLabels[i]):
            errorCount += 1
            
    print("the total error rate is: {}".format(errorCount / numTestVecs))
    

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: 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: 0.05

2.2.5 使用

# Listing 2.5 Dating site predictor function

def classifyPerson():
    resultList = ["not at all", "in small doses", "in large doses"]
    percentTats = float(input("percentage of time spend 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("datingTestSet2.txt")
    normMat, ranges, minVals = autoNorm(datingDataMat)
    inArr = (np.array([ffMiles, percentTats, iceCream]) - minVals) / ranges
    classifierResult = classify0(inArr, normMat, datingLabels, 3)
    print("You will probably like this person: {}".format(resultList[classifierResult - 1]))

classifyPerson()

percentage of time spend playing video games?10
frequent flier miles earned per year?200000
liters of ice cream consumed per year?3
You will probably like this person: not at all

2.3 例：手写识别系统（Example: a handwriting recognition system）

1. 收集数据：文本文件
   
2. 准备：编写函数classify0()，将图片转为列表
   
3. 分析：
   
4. 训练：KNN无需训练
   
5. 测试：计算错误率
   
6. 使用：
   

2.3.1 准备：将图片转换为测试向量

def img2vector(filename):
    returnVect = []
    with open(filename) as fr:
        for i in range(32):
            lineStr = fr.readline()
            returnVect.extend([int(bit) for bit in lineStr[0 : 32]])
            
    returnVect = np.array(returnVect, ndmin=2)
    return returnVect

testVector = img2vector("./testDigits/0_13.txt")
print(testVector[0, 0 : 31])
testVector = img2vector("./testDigits/0_13.txt")
print(testVector[0, 32 : 63])

[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]
[0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0]

2.3.2 测试

# Listing 2.6 Handwritten digits testing code

import os

def handwritingClassTest():
    
    hwLabels = []
    # get contents of directory
    trainingFileList = os.listdir("./trainingDigits/")
    m = len(trainingFileList)
    trainingMat = np.zeros((m, 1024))
    
    for i in range(m):
        # process class num from filename
        fileNameStr = trainingFileList[i]
        fileStr = fileNameStr.split(".")[0]
        classNumStr = int(fileStr.split("_")[0])
        hwLabels.append(classNumStr)
        
        trainingMat[i, :] = img2vector("./trainingDigits/{}".format(fileNameStr))
        
    errorCount = 0.0
    
    testFileList = os.listdir("./testDigits/")
    mTest = len(testFileList)
    for i in range(mTest):
        fileNameStr = testFileList[i]
        fileStr = fileNameStr.split(".")[0]
        classNumStr = int(fileStr.split("_")[0])
        vectorUnderTest = img2vector("./trainingDigits/{}".format(fileNameStr))
        classifierResult = classify0(vectorUnderTest, trainingMat, hwLabels, 3)
        print("the classifier came back with: {}, the real answer is: {}"
              .format(classifierResult, classNumStr))
        
        if (classifierResult != classNumStr):
            errorCount += 1.0
            
    print("the total number of errors is: {}".format(errorCount))
    print("the total error rate is: {}".format(errorCount / 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: 6, 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
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
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
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
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
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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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
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the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
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the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
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the classifier came back with: 3, the real answer is: 3
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the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
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the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
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the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
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the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
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the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
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the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 3, the real answer is: 3
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
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the classifier came back with: 4, the real answer is: 4
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the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
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the classifier came back with: 4, the real answer is: 4
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the classifier came back with: 9, the real answer is: 4
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the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
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the classifier came back with: 4, the real answer is: 4
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the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 6, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
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the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 4, the real answer is: 4
the classifier came back with: 9, the real answer is: 5
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the classifier came back with: 5, the real answer is: 5
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the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
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the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
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the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 9, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 9, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 9, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 5, the real answer is: 5
the classifier came back with: 6, the real answer is: 6
the classifier came back with: 6, the real answer is: 6
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the classifier came back with: 6, the real answer is: 6
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the classifier came back with: 6, the real answer is: 6
the classifier came back with: 6, the real answer is: 6
the classifier came back with: 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: 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: 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: 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: 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: 1, 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: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 7, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the classifier came back with: 9, the real answer is: 9
the total number of errors is: 13.0
the total error rate is: 0.013742071881606765

2.4 总结

k-NN是一种基于实例的简单高效分类算法。当数据集规模很大时，需要消耗大量内存和计算。此外，k-NN无法给出训练数据的内在结构。