Python机器学习k-近邻算法怎么实现
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K-近邻算法概述
简单地说, k-近邻算法采用测量不同特征值之间的距离方法进行分类。
k-近邻算法
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。
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, 知道样本集中每一数据与所属分类的对应关系。
输入没有标签的新数据后, 将新数据的每个特征与样本集中数据对应的特征进行比较, 然后算法提取样本集中特征最相似数据 (最近邻)的分类标签。
一般来说, 只选择样本数据集中前 k个最相似的数据, 这就是k-近邻算法中k的出处, 通常 k 是不大于 20 的整数。
最后, 选择 k个最相似数据中出现次数最多的分类, 作为新数据的分类。
k-近邻算法的一般流程
收集数据: 可以使用任何方法。
准备数据: 距离计算所需要的数值, 最好是结构化的数据格式。
分析数据: 可以使用任何方法。
训练算法: 此步骤不适用于 k-近邻算法。
测试算法: 计算错误率。
使用算法: 首先需要输入样本数据和结构化的输出结果, 然后运行 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。
from numpy import * import operator
def createDataSet(): group = array([[1.0,1.1],[1.0,1.0],[0,0],[0,0.1]]) labels = ['A','A','B','B'] return group, labels
group, labels = createDataSet()
group
array([[1. , 1.1], [1. , 1. ], [0. , 0. ], [0. , 0.1]])
labels
['A', 'A', 'B', 'B']
a = tile([3,3],(4,1)) a
array([[3, 3], [3, 3], [3, 3], [3, 3]])
实施KNN算法
其伪代码如下:
对末知类别属性的数据集中的每个点依次执行以下操作:
计算已知类别数据集中的点与当前点之间的距离;
按照距离递增次序排序;
选取与当前点距离最小的k个点;
确定前k个点所在类别的出现频率;
返回前k个点出现频率最高的类别作为当前点的预测分类。
def classify0(inX, dataSet, labels, k):
dataSetSize = dataSet.shape[0]
diffMat = tile(inX,(dataSetSize,1)) - dataSet
sqDiffMat = diffMat**2
sqDistances = sqDiffMat.sum(axis=1)
distances = sqDistances**0.5
sortedDistIndicies = distances.argsort()
classCount = {}
for i in range(k):
voteIlabel = labels[sortedDistIndicies[i]]
classCount[voteIlabel] = classCount.get(voteIlabel,0) + 1
sortedClassCount = sorted(classCount.items(),key = operator.itemgetter(1), reverse=True)
return sortedClassCount[0][0]classify0([0,0],group,labels,3)
'B'
示例：手写识别系统
数据集如下图：
示例: 使用k-近邻算法的手写识别系统
收集数据: 提供文本文件。
准备数据: 编写函数 classify0(), 将图像格式转换为分类器使用的list格式。
分析数据: 在Python命令提示符中检查数据, 确保它符合要求。
训练算法: 此步骤不适用于 k-近邻算法。
测试算法: 编写函数使用提供的部分数据集作为测试样本, 测试样本与非测试样本 的区别在于测试样本是已经完成分类的数据, 如果预测分类与实际类别不同, 则标记 为一个错误。
使用算法：本例没有完成此步骤，若你感兴趣可以构建完整的应用程序，从图像中提 取数字, 并完成数字识别, 美国的邮件分栋系统就是一个实际运行的类似系统。
图像转换为向量
def img2vector(filename): returnVect = zeros((1,1024)) fr = open(filename) for i in range(32): lineStr = fr.readline() for j in range(32): returnVect[0,32*i+j] = int(lineStr[j]) return returnVect
testVector = img2vector('digits/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.])
from os import listdir
def handwritingClassTest():
hwLables = []
trainingFileList = listdir('digits/trainingDigits')
m = len(trainingFileList)
trainingMat = zeros((m,1024))
for i in range(m):
fileNameStr = trainingFileList[i]
fileStr = fileNameStr.split('.')[0]
classNumStr = int(fileStr.split('_')[0])
hwLables.append(classNumStr)
trainingMat[i,:] = img2vector('digits/trainingDigits/%s' % fileNameStr)
testFileList = listdir('digits/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('digits/testDigits/%s' % fileNameStr)
classifierResult = classify0(vectorUnderTest, trainingMat,hwLables,3)
print("the classifier came back width: %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()
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classifier came back width: 6, the real answer is: 6 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 1, the real answer is: 8 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 7, the real answer is: 1 the classifier came back width: 7, the real answer is: 9 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 1, the real answer is: 9 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 6, the real answer is: 5 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 9, the real answer is: 3 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 7, the real answer is: 7 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 9, the real answer is: 9 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 6, the real answer is: 6 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 3, the real answer is: 3 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 1, the real answer is: 1 the classifier came back width: 2, the real answer is: 2 the classifier came back width: 8, the real answer is: 8 the classifier came back width: 4, the real answer is: 4 the classifier came back width: 0, the real answer is: 0 the classifier came back width: 5, the real answer is: 5 the classifier came back width: 8, the real answer is: 8 the total number of errors is :10 the total error rate is:0.010571
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