k-近邻算法（KNN）

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#机器学习 #KNN

KNN算法

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KNN算法

原理：存在一个样本数据集合，每个数据都有标签，且与所属的分类一一对应。输入没有标签的数据，其特征与样本集中数据的特征进行比较，通常计算特征的距离值，找出距离最近的前k个样本数据，查看这些数据对应的分类标签，把输入的数据归为次数最多的分类。

优点：

  • 精度高、对异常值不敏感、无数据输入假定。

缺点：

  • 计算复杂度高、空间复杂度高。
  • 整个训练过程需要将所有的训练样本极其输出label存储起来，因此，空间成本很大。
  • 测试过程中，每个测试样本都需要与所有的训练样本进行比较，运行时间成本很大。
  • 采用距离比较的方式，分类准确率不高。

K-近邻算法的一般流程

  1. 收集数据：可以使用任何方法
  2. 准备数据：距离计算所有需要的数值，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：此步骤不适合k-近邻算法
  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话的数出结果，然后运行k-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。

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()
print(group)
print(labels)

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

实施kNN分类算法

操作步骤：

  1. 计算已知类别数据集中的点与当前点之间的距离
  2. 按照距离递增次序排序
  3. 选取与当前点距离最小的k个点
  4. 确定前k个点所在类别的出现频率
  5. 返回前k个点出现频率最高的类别作为当前点的预测分类
def classify0(inX,dataSet,labels, k):   # inX是测试集，dataSet是训练集，labels是训练样本标签，k是取的最近邻个数
    dataSetSize = dataSet.shape[0]
    diffMat = tile(inX, (dataSetSize, 1)) - dataSet
    print('diffMat:',diffMat)
    sqDiffMat = diffMat**2
    sqDistances = sqDiffMat.sum(axis=1)
    print('sqDistances:',sqDistances)
    distances = sqDistances**0.5
    print('distances:',distances)
    sortedDistIndices = distances.argsort()   # argsort() 对元素从小到大排列，并返回索引值
    print('sortedDistIndices:',sortedDistIndices[1])
    classCount={}
    for i in range(k):
        voteIlabel = labels[sortedDistIndices[i]]
        print('voteIlabel:',voteIlabel)
        classCount[voteIlabel] = classCount.get(voteIlabel,0) + 1
    sortedClassCount = sorted(classCount.items(),key=operator.itemgetter(1),reverse=True)
    print('sortedClassCount:',sortedClassCount)
    return sortedClassCount[0][0]

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

diffMat: [[-1.  -1.1]
 [-1.  -1. ]
 [ 0.   0. ]
 [ 0.  -0.1]]
sqDistances: [2.21 2.   0.   0.01]
distances: [1.48660687 1.41421356 0.         0.1       ]
sortedDistIndices: 3
voteIlabel: B
voteIlabel: B
voteIlabel: A
sortedClassCount: [('B', 2), ('A', 1)]





'B'

使用k-近邻算法改进约会网站的配对效果

# 导入程序所需要的模块
import numpy as np
import operator

# 将文本记录转换为Numpy的解析程序
def file2matrix(filename):
    fr = open(filename)
    arrayOLines = fr.readlines()
    numberOfLines = len(arrayOLines)
    returnMat = np.zeros((numberOfLines,3))   # 初始化特征矩阵
    classLabelVector = []
    index = 0
    for line in arrayOLines:
        line = line.strip()
        listFromLine = line.split('\t')   # 按'\t'对字符串进行分割，listFromLine 是列表
        returnMat[index,:] = listFromLine[0:3]
        classLabelVector.append(int(listFromLine[-1]))
        index += 1
    return returnMat,classLabelVector

datingDataMat,datingLabels = file2matrix('datingTestSet2.txt')
print(datingDataMat,datingLabels)

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

分析数据：使用Matplotlib创建散点图

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

玩视频游戏所耗时间百分比

准备数据：归一化数值

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

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]])

定义KNN算法

def classify0(inX,dataSet,labels, k):
    dataSetSize = dataSet.shape[0]
    diffMat = np.tile(inX, (dataSetSize, 1)) - dataSet
#     print('diffMat:',diffMat)
    sqDiffMat = diffMat**2
    sqDistances = sqDiffMat.sum(axis=1)
#     print('sqDistances:',sqDistances)
    distances = sqDistances**0.5
#     print('distances:',distances)
    sortedDistIndices = distances.argsort()   # argsort() 对元素从小到大排列，并返回索引值
#     print('sortedDistIndices:',sortedDistIndices[1])
    classCount={}
    for i in range(k):
        voteIlabel = labels[sortedDistIndices[i]]
#         print('voteIlabel:',voteIlabel)
        classCount[voteIlabel] = classCount.get(voteIlabel,0) + 1
    sortedClassCount = sorted(classCount.items(),key=operator.itemgetter(1),reverse=True)
#     print('sortedClassCount:',sortedClassCount)
    return sortedClassCount[0][0]

测试算法：作为完整程序验证分类器

def datingClassTest():
    hoRatio = 0.10      #整个数据集的10%用来测试
    datingDataMat, datingLabels = file2matrix('datingTestSet2.txt')       #导入数据集
    normMat, ranges, minVals = autoNorm(datingDataMat)    # 所有特征归一化
    m = normMat.shape[0]    # 样本个数
    numTestVecs = int(m*hoRatio)    # 测试样本个数
    errorCount = 0.0
    for i in range(numTestVecs):
        classifierResult = classify0(normMat[i, :], normMat[numTestVecs:m, :], datingLabels[numTestVecs:m], 3)
        print("the classifier came back with: %d, the real answer is: %d" % (classifierResult, datingLabels[i]))
        if (classifierResult != datingLabels[i]): errorCount += 1.0
    print("the total error rate is: %f" % (errorCount / float(numTestVecs)))    # 打印错误率
    print(errorCount)    # 打印错误个数
    
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: 0.050000
5.0

使用算法：构建完整可用系统

def classifyPerson():
    resultList = ['not at all','in small do','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('datingTestSet2.txt')
    normMat, ranges,minVals = autoNorm(datingDataMat)
    inArr = array([ffMiles,percentTats,iceCream])
    classifierResult = classify0((inArr - minVals)/ranges,normMat,datingLabels,3)
    print('You will probably like this person:',resultList[classifierResult - 1])
    

classifyPerson()

percentage of time spent playing video games?65
frequent flier miles earned per year23333
liters of ice cream consumed per year?5
You will probably like this person: in large doses

手写识别系统

  1. 收集数据：提供文件
  2. 准备数据：编写函数img2vector()，将图像格式转换为分类器使用的向量格式
  3. 分析数据：在python命令提示符中检查数据，确保它符合要求
  4. 训练算法：knn不适用于此
  5. 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
  6. 使用算法：编写程序

准备数据：将图像转换为测试向量

# 导入程序所需要的模块
import numpy as np
import operator
from os import listdir   # os.listdir() 返回指定的文件夹包含的文件或文件夹的名字的列表

def img2vector(filename):
    returnVect = zeros((1,1024))  # 创建1*1024的向量，赋值0初始化
    fr = open(filename)
    for i in range(32):
        lineStr = fr.readline()
        for j in range(32):
            returnVect[0,32*i+j] = int(lineStr[j])
    return returnVect

testVector = img2vector('testDigits/0_13.txt')
testVector[0,0:31]

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

定义K近邻算法

def classify0(inX, dataSet, labels, k):    # inX是测试集，dataSet是训练集，lebels是训练样本标签，k是取的最近邻个数
    dataSetSize = dataSet.shape[0]    # 训练样本个数
    diffMat = np.tile(inX, (dataSetSize, 1)) - dataSet    # np.tile: 重复n次
    sqDiffMat = diffMat**2
    sqDistances = sqDiffMat.sum(axis=1)
    distances = sqDistances**0.5    # distance是inX与dataSet的欧氏距离
    sortedDistIndicies = distances.argsort()    # 返回排序从小到达的索引位置
    classCount = {}   # 字典存储k近邻不同label出现的次数
    for i in range(k):
        voteIlabel = labels[sortedDistIndicies[i]]
        classCount[voteIlabel] = classCount.get(voteIlabel, 0) + 1    # 对应label加1，classCount中若无此key，则默认为0
    sortedClassCount = sorted(classCount.items(), key=operator.itemgetter(1), reverse=True)    # operator.itemgetter 获取对象的哪个维度的数据
    return sortedClassCount[0][0]    # 返回k近邻中所属类别最多的哪一类

测试算法：使用k-近邻算法识别手写数字

def handwritingClassTest():
    # 训练样本
    hwLabels = []
    trainingFileList = listdir('trainingDigits')  # 导入训练集
    m = len(trainingFileList)
    trainingMat = zeros((m,1024))
    for i in range(m):
        fileNameStr = trainingFileList[i]  # fileNameStr 得到的是每个文件名称，例如"0_0.txt"
        fileStr = fileNameStr.split(',')[0]  #去掉“.txt”，剩下“0_0”
        classNumStr = int(fileStr.split('_')[0])  # 按下划线‘_' 划分“0_0”,取第一个元素为类别标签
        hwLabels.append(classNumStr)  # 顺序添加图片的标签
        trainingMat[i,:] = img2vector('trainingDigits/%s' % fileNameStr)
    # 测试样本
    testFileList = listdir('testDigits')
    errorCount = 0.0
    mTest = len(testFileList)
    for i in range(mTest):
        fileNameStr = testFileList[i]
        fileStr = fileNameStr.split(',')[0]
        classNumStr = int(fileStr.split('_')[0])
        vectorUnderTest = img2vector('testDigits/%s' % fileNameStr)
        classifierResult = classify0(vectorUnderTest, trainingMat,hwLabels,3)
        print('the classifier came back with: %d , the real answer is :%d' % (classifierResult,classNumStr))
        if (classifierResult != classNumStr) :
            errorCount += 1.0
    print('\nthe total number of errors is: %d' % errorCount)
    print('\nthe total error rate is : %f' %(errorCount/float(mTest)))

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
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: 7 , 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
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 9 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 3 , the real answer is :3
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 4 , the real answer is :4
the classifier came back with: 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
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the classifier came back with: 6 , 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
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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
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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
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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
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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
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the classifier came back with: 6 , the real answer is :6
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the classifier came back with: 6 , the real answer is :6
the classifier came back with: 6 , the real answer is :6
the classifier came back with: 6 , the real answer is :6
the classifier came back with: 6 , the real answer is :6
the classifier came back with: 6 , the real answer is :6
the classifier came back with: 6 , the real answer is :6
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
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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
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the classifier came back with: 6 , the real answer is :6
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the classifier came back with: 6 , the real answer is :6
the classifier came back with: 6 , the real answer is :6
the classifier came back with: 6 , the real answer is :6
the classifier came back with: 6 , the real answer is :6
the classifier came back with: 6 , the real answer is :6
the classifier came back with: 6 , the real answer is :6
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 is: 10

the total error rate is : 0.010571
分类算法：K-近邻(KNN)算法及其优化
kkchenjj的博客
07-14 1397
K-近邻算法(K-Nearest Neighbors, KNN)是一种基于实例的学习方法，用于分类和回归。
机器学习——K-近邻算法
fishsmans的博客
09-27 658
机器学习——K-近邻算法 简单地说，k-近邻算法采用测量不同特征值之间的距离方法进行分类 一、K-近邻算法 K近邻（K-Nearest Neighbor, KNN）是一种最经典和最简单的有监督学习方法之一。K-近邻算法是最简单的分类器，没有显式的学习过程或训练过程，是懒惰学习（Lazy Learning）。当对数据的分布只有很少或者没有任何先验知识时，K 近邻算法是一个不错的选择。 ​ K近邻算法既能够用来解决分类问题，也能够用来解决回归问题。该方法有着非常简单的原理：当对测试样本进行分类时，首先通过扫描训
机器学习实战——k-近邻算法
Digger的博客
10-14 616
k-近邻算法 算法流程 1.收集数据 2.计算目标数据与样本数据的距离 3.将计算得到的距离进行递增排序 4.选取与目标数据距离最小的k个样本数据 5.统计前k个样本数据分类出现的频率 5.前k个样本数据值对应的分类出现频率最高的类别则为目标数据的类别 距离计算方法 使用欧式距离公式，计算两个向量点xA和xB之间的距离： 代码实现 from numpy import * import operator # 运算符模块 # 导入数据 def createDataSet(): group = a
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文章目录 系列文章目录 前言 一、k近邻算法是什么？ 二、使用步骤 1.引入库 2.读入数据 总结 前言 随着人工智能的不断发展，机器学习这门技术也越来越重要，很多人都开启了学习机器学习，本文就介绍了机器学习的基础内容——k近邻算法及python的实现。 提示：以下是本篇文章正文内容，下面案例可供参考 一、k近邻算法是什么？ K最近邻（k—Nearest Neighborhood，KNN）分类算法，是1967年由Cover T和Hart P提出的一种...
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JeffreyLiannnn的博客
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k-近邻算法概述 简单来说，k-近邻算法采用测量不同特征值之间的距离方法进行分类 优点：精度高、对异常值不敏感、无数据输入假定 缺点：计算复杂度高、空间复杂度高 适用数据范围：数值型和标称型 k-近邻算法工作原理：存在一个样本数据集合，也称作训练样本集，并且样本集中每个数据都存在标签，即我们知道样本集中每一个数据与所属分类的对应关系。输入没有标签的新数据后，将新数据的每个特征与样本集中数据对应的特征进行比较，然后算法提取样本集中特征最相似数据的分类标签。一般来说只取前k个最相似的数据，通常k是不大于20的整
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K-近邻算法（KNN）详解机器学习（一）：K-近邻算法（KNN）概述K-近邻算法的具体应用K-近邻算法的具体代码使用K-邻近算法实现手写识别系统插入链接与图片如何插入一段漂亮的代码片生成一个适合你的列表创建一个表格设定内容居中、居左、居右SmartyPants创建一个自定义列表如何创建一个注脚注释也是必不可少的KaTeX数学公式新的甘特图功能，丰富你的文章UML 图表FLowchart流程图导出与导入导出导入 机器学习（一）： K-近邻算法（KNN）概述 K-近邻算法采用测量不同特征值之间的距离方法进行分类
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内容概要：本文深入剖析了k-近邻(KNN)算法的核心原理及其在数据挖掘中的应用实践。首先，文章详细解释了KNN的数学模型，包括分类决策函数、回归预测函数以及常用的距离度量公式如欧氏距离和曼哈顿距离。接着，通过...
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KNN 概述 k-近邻（kNN, k-NearestNeighbor）算法是一种基本分类与回归方法，我们这里只讨论分类问题中的 k-近邻算法。 一句话总结：近朱者赤近墨者黑！ k 近邻算法的输入为实例的特征向量，对应于特征空间的点；输出为实例的类别，可以取多类。k 近邻算法假设给定一个训练数据集，其中的实例类别已定。分类时，对新的实例，根据其 k 个最近邻的训练实例的类别，通过多数表决等方式进行预测。因此，k近邻算法不具有显式的学习过程。 k 近邻算法实际上利用训练数据集对特征向量空间进行划分，并作为其分类
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