Python機器學習實戰(zhàn)之k-近鄰算法的實現(xiàn)
K-近鄰算法概述
簡單地說, k-近鄰算法采用測量不同特征值之間的距離方法進行分類。
k-近鄰算法
- 優(yōu)點:精度高、對異常值不敏感、無數(shù)據(jù)輸入假定。
- 缺點: 計算復雜度高、空間復雜度高。
適用數(shù)據(jù)范圍: 數(shù)值型和標稱型。
工作原理
- 存在一個樣本數(shù)據(jù)集合, 也稱作訓練樣本集, 并且樣本集中每個數(shù)據(jù)都存在標簽, 知道樣本集中每一數(shù)據(jù)與所屬分類的對應關系。
- 輸入沒有標簽的新數(shù)據(jù)后, 將新數(shù)據(jù)的每個特征與樣本集中數(shù)據(jù)對應的特征進行比較, 然后算法提取樣本集中特征最相似數(shù)據(jù) (最近鄰)的分類標簽。
- 一般來說, 只選擇樣本數(shù)據(jù)集中前 k個最相似的數(shù)據(jù), 這就是k-近鄰算法中k的出處, 通常 k 是不大于 20 的整數(shù)。
- 最后, 選擇 k個最相似數(shù)據(jù)中出現(xiàn)次數(shù)最多的分類, 作為新數(shù)據(jù)的分類。
k-近鄰算法的一般流程
- 收集數(shù)據(jù): 可以使用任何方法。
- 準備數(shù)據(jù): 距離計算所需要的數(shù)值, 最好是結(jié)構(gòu)化的數(shù)據(jù)格式。
- 分析數(shù)據(jù): 可以使用任何方法。
- 訓練算法: 此步驟不適用于 k-近鄰算法。
- 測試算法: 計算錯誤率。
- 使用算法: 首先需要輸入樣本數(shù)據(jù)和結(jié)構(gòu)化的輸出結(jié)果, 然后運行 k-近鄰算法判定輸 入數(shù)據(jù)分別屬于哪個分類, 最后應用對計算出的分類執(zhí)行后續(xù)的處理。
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]])
實施KNN算法
其偽代碼如下:
對末知類別屬性的數(shù)據(jù)集中的每個點依次執(zhí)行以下操作:
- 計算已知類別數(shù)據(jù)集中的點與當前點之間的距離;
- 按照距離遞增次序排序;
- 選取與當前點距離最小的k個點;
- 確定前k個點所在類別的出現(xiàn)頻率;
- 返回前k個點出現(xiàn)頻率最高的類別作為當前點的預測分類。
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:手寫識別系統(tǒng)
數(shù)據(jù)集如下圖:
示例: 使用k-近鄰算法的手寫識別系統(tǒng)
- 收集數(shù)據(jù): 提供文本文件。
- 準備數(shù)據(jù): 編寫函數(shù) classify0(), 將圖像格式轉(zhuǎn)換為分類器使用的list格式。
- 分析數(shù)據(jù): 在Python命令提示符中檢查數(shù)據(jù), 確保它符合要求。
- 訓練算法: 此步驟不適用于 k-近鄰算法。
- 測試算法: 編寫函數(shù)使用提供的部分數(shù)據(jù)集作為測試樣本, 測試樣本與非測試樣本 的區(qū)別在于測試樣本是已經(jīng)完成分類的數(shù)據(jù), 如果預測分類與實際類別不同, 則標記 為一個錯誤。
- 使用算法:本例沒有完成此步驟,若你感興趣可以構(gòu)建完整的應用程序,從圖像中提 取數(shù)字, 并完成數(shù)字識別, 美國的郵件分棟系統(tǒng)就是一個實際運行的類似系統(tǒng)。
圖像轉(zhuǎn)換為向量?
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: 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: 8, the real answer is: 8 the classifier came back width: 3, 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: 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: 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: 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: 3, 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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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