In [1]:
from numpy import * #科学计算包
import operator #运算符模块
def creatDataSet():
group = array([[1.0,1.1],[1.0,1.0],[0,0],[0,0.1]])
labels = ['A','A','B','B']
return group, labels
In [2]:
group, labels = creatDataSet()
group
Out[2]:
array([[ 1. , 1.1],
[ 1. , 1. ],
[ 0. , 0. ],
[ 0. , 0.1]])
In [3]:
labels
Out[3]:
['A', 'A', 'B', 'B']
k-近邻算法¶
In [4]:
def classify0(inX, dataSet, labels, k):
"""
inx[1,2,3]
DS=[[1,2,3],[1,2,0]]
inX: 用于分类的输入向量
dataSet: 输入的训练样本集
labels: 标签向量
k: 选择最近邻居的数目
注意：labels元素数目和dataSet行数相同；程序使用欧式距离公式.
预测数据所在分类可在输入下列命令
kNN.classify0([0,0], group, labels, 3)
"""
# -----------实现 classify0() 方法的第一种方式----------------------------------------------------------------------------------------------------------------------------
# 1. 距离计算
dataSetSize = dataSet.shape[0]
# tile生成和训练样本对应的矩阵，并与训练样本求差
"""
tile: 列-3表示复制的行数， 行-1／2表示对inx的重复的次数
In [8]: tile(inx, (3, 1))
Out[8]:
array([[1, 2, 3],
[1, 2, 3],
[1, 2, 3]])
In [9]: tile(inx, (3, 2))
Out[9]:
array([[1, 2, 3, 1, 2, 3],
[1, 2, 3, 1, 2, 3],
[1, 2, 3, 1, 2, 3]])
"""
diffMat = tile(inX, (dataSetSize, 1)) - dataSet
"""
欧氏距离： 点到点之间的距离
第一行： 同一个点 到 dataSet的第一个点的距离。
第二行： 同一个点 到 dataSet的第二个点的距离。
...
第N行： 同一个点 到 dataSet的第N个点的距离。
[[1,2,3],[1,2,3]]-[[1,2,3],[1,2,0]]
(A1-A2)^2+(B1-B2)^2+(c1-c2)^2
"""
# 取平方
sqDiffMat = diffMat ** 2
# 将矩阵的每一行相加
sqDistances = sqDiffMat.sum(axis=1)
# 开方
distances = sqDistances ** 0.5
# 根据距离排序从小到大的排序，返回对应的索引位置
# argsort() 是将x中的元素从小到大排列，提取其对应的index（索引），然后输出到y。
# 例如：y=array([3,0,2,1,4,5]) 则，x[3]=-1最小，所以y[0]=3,x[5]=9最大，所以y[5]=5。
# print 'distances=', distances
sortedDistIndicies = distances.argsort()
# print 'distances.argsort()=', sortedDistIndicies
# 2. 选择距离最小的k个点
classCount = {}
for i in range(k):
# 找到该样本的类型
voteIlabel = labels[sortedDistIndicies[i]]
# 在字典中将该类型加一
# 字典的get方法
# 如：list.get(k,d) 其中 get相当于一条if...else...语句,参数k在字典中，字典将返回list[k];如果参数k不在字典中则返回参数d,如果K在字典中则返回k对应的value值
# l = {5:2,3:4}
# print l.get(3,0)返回的值是4；
# Print l.get（1,0）返回值是0；
classCount[voteIlabel] = classCount.get(voteIlabel, 0) + 1
# 3. 排序并返回出现最多的那个类型
# 字典的 items() 方法，以列表返回可遍历的(键，值)元组数组。
# 例如：dict = {'Name': 'Zara', 'Age': 7} print "Value : %s" % dict.items() Value : [('Age', 7), ('Name', 'Zara')]
# sorted 中的第2个参数 key=operator.itemgetter(1) 这个参数的意思是先比较第几个元素
# 例如：a=[('b',2),('a',1),('c',0)] b=sorted(a,key=operator.itemgetter(1)) >>>b=[('c',0),('a',1),('b',2)] 可以看到排序是按照后边的0,1,2进行排序的，而不是a,b,c
# b=sorted(a,key=operator.itemgetter(0)) >>>b=[('a',1),('b',2),('c',0)] 这次比较的是前边的a,b,c而不是0,1,2
# b=sorted(a,key=opertator.itemgetter(1,0)) >>>b=[('c',0),('a',1),('b',2)] 这个是先比较第2个元素，然后对第一个元素进行排序，形成多级排序。
sortedClassCount = sorted(classCount.items(), key=operator.itemgetter(1), reverse=True)
return sortedClassCount[0][0]
# ------------------------------------------------------------------------------------------------------------------------------------------
# 实现 classify0() 方法的第二种方式
# """
# 1. 计算距离
# 欧氏距离： 点到点之间的距离
# 第一行： 同一个点 到 dataSet的第一个点的距离。
# 第二行： 同一个点 到 dataSet的第二个点的距离。
# ...
# 第N行： 同一个点 到 dataSet的第N个点的距离。
# [[1,2,3],[1,2,3]]-[[1,2,3],[1,2,0]]
# (A1-A2)^2+(B1-B2)^2+(c1-c2)^2
# inx - dataset 使用了numpy broadcasting，见 https://docs.scipy.org/doc/numpy-1.13.0/user/basics.broadcasting.html
# np.sum() 函数的使用见 https://docs.scipy.org/doc/numpy-1.13.0/reference/generated/numpy.sum.html
# """
# dist = np.sum((inx - dataset)**2, axis=1)**0.5
# """
# 2. k个最近的标签
# 对距离排序使用numpy中的argsort函数， 见 https://docs.scipy.org/doc/numpy-1.13.0/reference/generated/numpy.sort.html#numpy.sort
# 函数返回的是索引，因此取前k个索引使用[0 : k]
# 将这k个标签存在列表k_labels中
# """
# k_labels = [labels[index] for index in dist.argsort()[0 : k]]
# """
# 3. 出现次数最多的标签即为最终类别
# 使用collections.Counter可以统计各个标签的出现次数，most_common返回出现次数最多的标签tuple，例如[('lable1', 2)]，因此[0][0]可以取出标签值
# """
# label = Counter(k_labels).most_common(1)[0][0]
# return label
In [5]:
result = classify0([0,0], group, labels, 3)
result
Out[5]:
'B'
In [6]:
#sklearn实现KNN
import numpy as np
import matplotlib.pyplot as plt
from numpy import *
from matplotlib.colors import ListedColormap
from sklearn import neighbors, datasets
n_neighbors = 3
# 导入一些要玩的数据
# iris = datasets.load_iris()
# X = iris.data[:, :2] # 我们只采用前两个feature. 我们可以使用二维数据集避免这个丑陋的切片
# y = iris.target
# print 'X=', type(X), X
# print 'y=', type(y), y
X = array([[-1.0, -1.1], [-1.0, -1.0], [0, 0], [1.0, 1.1], [2.0, 2.0], [2.0, 2.1]])
y = array([0, 0, 0, 1, 1, 1])
# print 'X=', type(X), X
# print 'y=', type(y), y
h = .02 # 网格中的步长
# 创建彩色的地图
# cmap_light = ListedColormap(['#FFAAAA', '#AAFFAA', '#AAAAFF'])
# cmap_bold = ListedColormap(['#FF0000', '#00FF00', '#0000FF'])
cmap_light = ListedColormap(['#FFAAAA', '#AAFFAA'])
cmap_bold = ListedColormap(['#FF0000', '#00FF00'])
for weights in ['uniform', 'distance']:
# 我们创建了一个knn分类器的实例，并适合数据。
clf = neighbors.KNeighborsClassifier(n_neighbors, weights=weights)
clf.fit(X, y)
# 绘制决策边界。为此，我们将为每个分配一个颜色
# 来绘制网格中的点 [x_min, x_max]x[y_min, y_max].
x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1
y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1
xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
np.arange(y_min, y_max, h))
Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
# 将结果放入一个彩色图中
Z = Z.reshape(xx.shape)
plt.figure()
plt.pcolormesh(xx, yy, Z, cmap=cmap_light)
# 绘制训练点
plt.scatter(X[:, 0], X[:, 1], c=y, cmap=cmap_bold)
plt.xlim(xx.min(), xx.max())
plt.ylim(yy.min(), yy.max())
plt.title("3-Class classification (k = %i, weights = '%s')"
% (n_neighbors, weights))
plt.show()
案例1 优化约会网站的配对效果¶
In [7]:
def file2matrix(filename):
"""
Desc:
导入训练数据
parameters:
filename: 数据文件路径
return:
数据矩阵 returnMat 和对应的类别 classLabelVector
"""
fr = open(filename)
# 获得文件中的数据行的行数
numberOfLines = len(fr.readlines())
# 生成对应的空矩阵
# 例如：zeros(2，3)就是生成一个 2*3的矩阵，各个位置上全是 0
returnMat = zeros((numberOfLines, 3)) # prepare matrix to return
classLabelVector = [] # prepare labels return
fr = open(filename)
index = 0
for line in fr.readlines():
# str.strip([chars]) --返回移除字符串头尾指定的字符生成的新字符串
line = line.strip()
# 以 '\t' 切割字符串
listFromLine = line.split('\t')
# 每列的属性数据
returnMat[index, :] = listFromLine[0:3]
# 每列的类别数据，就是 label 标签数据
classLabelVector.append(int(listFromLine[-1]))
index += 1
# 返回数据矩阵returnMat和对应的类别classLabelVector
return returnMat, classLabelVector
In [8]:
datingDataMat, datingLabels = file2matrix('datingTestSet2.txt')
In [9]:
import matplotlib
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.add_subplot(111)
ax.scatter(datingDataMat[:, 1], datingDataMat[:, 2])
plt.show()
In [10]:
fig = plt.figure()
ax = fig.add_subplot(111)
ax.scatter(datingDataMat[:, 1], datingDataMat[:, 2], 15.0*array(datingLabels), 15.0*array(datingLabels))
plt.show()
In [11]:
fig = plt.figure()
ax = fig.add_subplot(111)
ax.scatter(datingDataMat[:, 0], datingDataMat[:, 1], 15.0*array(datingLabels), 15.0*array(datingLabels))
plt.show()
In [12]:
def autoNorm(dataSet):
"""
Desc:
归一化特征值，消除特征之间量级不同导致的影响
parameter:
dataSet: 数据集
return:
归一化后的数据集 normDataSet. ranges和minVals即最小值与范围，并没有用到
归一化公式：
Y = (X-Xmin)/(Xmax-Xmin)
其中的 min 和 max 分别是数据集中的最小特征值和最大特征值。该函数可以自动将数字特征值转化为0到1的区间。
"""
# 计算每种属性的最大值、最小值、范围
minVals = dataSet.min(0)
maxVals = dataSet.max(0)
# 极差
ranges = maxVals - minVals
# -------第一种实现方式---start-------------------------
normDataSet = zeros(shape(dataSet))
m = dataSet.shape[0]
# 生成与最小值之差组成的矩阵
normDataSet = dataSet - tile(minVals, (m, 1))
# 将最小值之差除以范围组成矩阵
normDataSet = normDataSet / tile(ranges, (m, 1)) # element wise divide
# -------第二种实现方式---end---------------------------------------------
# # -------第二种实现方式---start---------------------------------------
# norm_dataset = (dataset - minvalue) / ranges
# # -------第二种实现方式---end---------------------------------------------
return normDataSet, ranges, minVals
In [13]:
normMat, ranges, minVals = autoNorm(datingDataMat)
In [14]:
ranges
Out[14]:
array([ 9.12730000e+04, 2.09193490e+01, 1.69436100e+00])
In [15]:
minVals
Out[15]:
array([ 0. , 0. , 0.001156])
In [16]:
def datingClassTest():
"""
Desc:
对约会网站的测试方法
parameters:
none
return:
错误数
"""
# 设置测试数据的的一个比例（训练数据集比例=1-hoRatio）
hoRatio = 0.1 # 测试范围,一部分测试一部分作为样本
# 从文件中加载数据
datingDataMat, datingLabels = file2matrix('datingTestSet2.txt') # load data setfrom file
# 归一化数据
normMat, ranges, minVals = autoNorm(datingDataMat)
# m 表示数据的行数，即矩阵的第一维
m = normMat.shape[0]
# 设置测试的样本数量， numTestVecs:m表示训练样本的数量
numTestVecs = int(m * hoRatio)
print ('numTestVecs=', numTestVecs)
errorCount = 0.0
for i in range(numTestVecs):
# 对数据测试
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)))
print (errorCount)
In [17]:
datingClassTest()
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In [18]:
def classifyPerson():
resultList = ['not at all', 'in small doses', 'in large doses']
percentTats = float(input("percentage of time spent playing video games ?"))
ffMiles = float(input("frequent filer 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])
In [19]:
classifyPerson()
percentage of time spent playing video games ?100 frequent filer miles earned per year?10000 liters of ice cream consumed per year?22 You will probably like this person: in large doses
案例2 手写识别系统¶
In [20]:
def img2vector(filename):
"""
将图像数据转换为向量
:param filename: 图片文件 因为我们的输入数据的图片格式是 32 * 32的
:return: 一维矩阵
该函数将图像转换为向量：该函数创建 1 * 1024 的NumPy数组，然后打开给定的文件，
循环读出文件的前32行，并将每行的头32个字符值存储在NumPy数组中，最后返回数组。
"""
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
In [21]:
testVector = img2vector('./digits/testDigits/0_13.txt')
In [22]:
testVector[0, 0:31]
Out[22]:
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.])
In [23]:
testVector[0, 32:63]
Out[23]:
array([ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1.,
1., 1., 1., 1., 1., 1., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0.])
In [24]:
from os import listdir
def handwritingClassTest():
# 1. 导入训练数据
hwLabels = []
trainingFileList = listdir('./digits/trainingDigits') # load the training set
m = len(trainingFileList)
trainingMat = zeros((m, 1024))
# hwLabels存储0～9对应的index位置， trainingMat存放的每个位置对应的图片向量
for i in range(m):
fileNameStr = trainingFileList[i]
fileStr = fileNameStr.split('.')[0] # take off .txt
classNumStr = int(fileStr.split('_')[0])
hwLabels.append(classNumStr)
# 将 32*32的矩阵->1*1024的矩阵
trainingMat[i, :] = img2vector('./digits/trainingDigits/%s' % fileNameStr)
# 2. 导入测试数据
testFileList = listdir('./digits/testDigits') # iterate through the test set
errorCount = 0.0
mTest = len(testFileList)
for i in range(mTest):
fileNameStr = testFileList[i]
fileStr = fileNameStr.split('.')[0] # take off .txt
classNumStr = int(fileStr.split('_')[0])
vectorUnderTest = img2vector('./digits/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)))
In [25]:
handwritingClassTest()
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: 3, the real answer is: 3 the classifier came back with: 9, the real answer is: 9 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: 9, the real answer is: 9 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 0, the real answer is: 0 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: 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: 2, the real answer is: 2 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: 9, the real answer is: 9 the classifier came back with: 8, the real answer is: 8 the classifier came back with: 1, the real answer is: 8 the classifier came back with: 1, the real answer is: 1 the classifier came back with: 8, the real answer is: 8 the classifier came back with: 1, the real answer is: 1 the classifier came back with: 3, the real answer is: 8 the classifier came back with: 9, the real answer is: 9 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: 5, the real answer is: 5 the classifier came back with: 2, the real answer is: 2 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: 2, the real answer is: 2 the classifier came back with: 2, the real answer is: 2 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 3, the real answer is: 3 the classifier came back with: 0, the real answer is: 0 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 0, the real answer is: 0 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: 0, the real answer is: 0 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: 3, the real answer is: 3 the classifier came back with: 4, the real answer is: 4 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: 9, the real answer is: 9 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: 7, the real answer is: 7 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 0, the real answer is: 0 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 0, the real answer is: 0 the classifier came back with: 2, the real answer is: 2 the classifier came back with: 5, the real answer is: 5 the classifier came back with: 2, the real answer is: 2 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: 2, the real answer is: 2 the classifier came back with: 2, the real answer is: 2 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: 1, the real answer is: 1 the classifier came back with: 1, the real answer is: 1 the classifier came back with: 8, the real answer is: 8 the classifier came back with: 6, the real answer is: 6 the classifier came back with: 9, the real answer is: 9 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: 1, the real answer is: 1 the classifier came back with: 6, the real answer is: 6 the classifier came back with: 8, the real answer is: 8 the classifier came back with: 6, the real answer is: 6 the classifier came back with: 1, the real answer is: 1 the classifier came back with: 6, the real answer is: 6 the classifier came back with: 2, the real answer is: 2 the classifier came back with: 5, the real answer is: 5 the classifier came back with: 2, the real answer is: 2 the classifier came back with: 5, the real answer is: 5 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: 5, the real answer is: 5 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 7, the real answer is: 7 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: 9, the real answer is: 9 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 7, the real answer is: 9 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: 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: 3, the real answer is: 3 the classifier came back with: 9, 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: 3, the real answer is: 3 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 7, the real answer is: 7 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: 7, the real answer is: 7 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: 0, the real answer is: 0 the classifier came back with: 0, the real answer is: 0 the classifier came back with: 5, the real answer is: 5 the classifier came back with: 2, the real answer is: 2 the classifier came back with: 5, the real answer is: 5 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: 5, the real answer is: 5 the classifier came back with: 5, the real answer is: 5 the classifier came back with: 2, the real answer is: 2 the classifier came back with: 8, the real answer is: 8 the classifier came back with: 1, the real answer is: 1 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 8, the real answer is: 8 the classifier came back with: 6, the real answer is: 6 the classifier came back with: 1, the real answer is: 1 the classifier came back with: 8, the real answer is: 8 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: 8, the real answer is: 8 the classifier came back with: 6, the real answer is: 6 the classifier came back with: 1, the real answer is: 1 the classifier came back with: 8, the real answer is: 8 the classifier came back with: 9, 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with: 0, the real answer is: 0 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 4, the real answer is: 4 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: 3, the real answer is: 3 the classifier came back with: 4, the real answer is: 4 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: 7, the real answer is: 7 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 4, the real answer is: 4 the classifier came back with: 0, the real answer is: 0 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: 0, the real answer is: 0 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 0, the real answer is: 0 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: 2, the real answer is: 2 the classifier came back with: 2, the real answer is: 2 the classifier came back with: 5, the real answer is: 5 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: 9, the real answer is: 9 the classifier came back with: 8, the real answer is: 8 the classifier came back with: 1, the real answer is: 1 the classifier came back with: 8, the real answer is: 8 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: 6, the real answer is: 6 the classifier came back with: 6, the real answer is: 6 the classifier came back with: 1, the real answer is: 1 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: 2, the real answer is: 2 the classifier came back with: 5, the real answer is: 5 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: 5, the real answer is: 5 the classifier came back with: 5, the real answer is: 5 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 0, the real answer is: 0 the classifier came back with: 9, the real answer is: 9 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: 9, the real answer is: 9 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 4, the real answer is: 4 the classifier came back with: 7, the real answer is: 7 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: 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: 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: 8, the real answer is: 8 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: 0, the real answer is: 0 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 0, the real answer is: 0 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 0, the real answer is: 0 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: 5, the real answer is: 5 the classifier came back with: 5, the real answer is: 5 the classifier came back with: 6, the real answer is: 6 the classifier came back with: 1, the real answer is: 1 the classifier came back with: 8, the real answer is: 8 the classifier came back with: 6, the real answer is: 6 the classifier came back with: 8, the real answer is: 8 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: 8, the real answer is: 8 the classifier came back with: 6, the real answer is: 6 the classifier came back with: 8, the real answer is: 8 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: 8, the real answer is: 8 the classifier came back with: 6, the real answer is: 6 the classifier came back with: 1, the real answer is: 1 the classifier came back with: 6, the real answer is: 6 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: 1 the classifier came back with: 6, the real answer is: 6 the classifier came back with: 1, the real answer is: 8 the classifier came back with: 6, the real answer is: 6 the classifier came back with: 1, the real answer is: 1 the classifier came back with: 5, the real answer is: 5 the classifier came back with: 2, the real answer is: 2 the classifier came back with: 5, the real answer is: 5 the classifier came back with: 2, the real answer is: 2 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 0, the real answer is: 0 the classifier came back with: 9, the real answer is: 9 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: 9 the classifier came back with: 7, the real answer is: 7 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: 3, the real answer is: 3 the classifier came back with: 8, the real answer is: 8 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: 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: 3, the real answer is: 3 the classifier came back with: 8, the real answer is: 8 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: 0, the real answer is: 0 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 0, the real answer is: 0 the classifier came back with: 7, the real answer is: 7 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: 5, the real answer is: 5 the classifier came back with: 2, the real answer is: 2 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: 8, the real answer is: 8 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: 8, the real answer is: 8 the classifier came back with: 6, the real answer is: 6 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: 6 the classifier came back with: 1, the real answer is: 1 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: 1 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: 2, the real answer is: 2 the classifier came back with: 5, the real answer is: 5 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: 7, the real answer is: 7 the classifier came back with: 9, the real answer is: 9 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: 4, the real answer is: 4 the classifier came back with: 4, the real answer is: 4 the classifier came back with: 3, the real answer is: 3 the classifier came back with: 8, the real answer is: 8 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: 3, the real answer is: 3 the classifier came back with: 8, the real answer is: 8 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: 6, the real answer is: 6 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: 7, the real answer is: 7 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: 9, the real answer is: 9 the classifier came back with: 5, the real answer is: 5 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: 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: 1 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: 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: 1 the classifier came back with: 6, the real answer is: 6 the classifier came back with: 1, the real answer is: 1 the classifier came back with: 6, the real answer is: 6 the classifier came back with: 8, the real answer is: 8 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: 8, the real answer is: 8 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: 8, the real answer is: 8 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: 5, the real answer is: 5 the classifier came back with: 0, the real answer is: 0 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 0, the real answer is: 0 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 4, the real answer is: 4 the classifier came back with: 4, the real answer is: 4 the classifier came back with: 6, the real answer is: 6 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: 3, the real answer is: 3 the classifier came back with: 8, the real answer is: 8 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: 8, the real answer is: 8 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: 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: 7, the real answer is: 7 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: 0, the real answer is: 0 the classifier came back with: 0, the real answer is: 0 the classifier came back with: 7, the real answer is: 7 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: 2, the real answer is: 2 the classifier came back with: 2, the real answer is: 2 the classifier came back with: 5, the real answer is: 5 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: 8, the real answer is: 8 the classifier came back with: 6, the real answer is: 6 the classifier came back with: 8, the real answer is: 8 the classifier came back with: 1, the real answer is: 1 the classifier came back with: 8, the real answer is: 8 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: 1, the real answer is: 1 the classifier came back with: 8, the real answer is: 8 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: 8, the real answer is: 8 the classifier came back with: 6, the real answer is: 6 the classifier came back with: 1, the real answer is: 1 the classifier came back with: 6, the real answer is: 6 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: 1 the classifier came back with: 1, the real answer is: 1 the classifier came back with: 6, the real answer is: 6 the classifier came back with: 1, the real answer is: 8 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: 5, the real answer is: 5 the classifier came back with: 5, the real answer is: 5 the classifier came back with: 2, the real answer is: 2 the classifier came back with: 4, the real answer is: 4 the classifier came back with: 0, the real answer is: 0 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 0, the real answer is: 0 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 7, the real answer is: 7 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: 3, the real answer is: 3 the classifier came back with: 3, the real answer is: 3 the classifier came back with: 8, the real answer is: 8 the classifier came back with: 4, the real answer is: 4 the classifier came back with: 3, the real answer is: 3 the classifier came back with: 8, the real answer is: 8 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: 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: 3, the real answer is: 3 the classifier came back with: 6, the real answer is: 6 the classifier came back with: 3, the real answer is: 3 the classifier came back with: 0, the real answer is: 0 the classifier came back with: 7, the real answer is: 7 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: 7 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 0, the real answer is: 0 the classifier came back with: 4, the real answer is: 4 the classifier came back with: 2, the real answer is: 2 the classifier came back with: 5, the real answer is: 5 the classifier came back with: 2, the real answer is: 2 the classifier came back with: 5, the real answer is: 5 the classifier came back with: 2, the real answer is: 2 the classifier came back with: 6, the real answer is: 6 the classifier came back with: 1, the real answer is: 1 the classifier came back with: 8, the real answer is: 8 the classifier came back with: 6, the real answer is: 6 the classifier came back with: 8, the real answer is: 8 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: 8, the real answer is: 8 the classifier came back with: 6, the real answer is: 6 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: 7, the real answer is: 1 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: 6, the real answer is: 6 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: 1 the classifier came back with: 6, the real answer is: 6 the classifier came back with: 8, the real answer is: 8 the classifier came back with: 6, the real answer is: 6 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: 5, the real answer is: 5 the classifier came back with: 5, the real answer is: 5 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: 4, the real answer is: 4 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 0, the real answer is: 0 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 0, the real answer is: 0 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 3, the real answer is: 3 the classifier came back with: 6, the real answer is: 6 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: 3, the real answer is: 3 the classifier came back with: 8, the real answer is: 8 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: 3, the real answer is: 3 the classifier came back with: 3, the real answer is: 3 the classifier came back with: 6, the real answer is: 6 the classifier came back with: 4, the real answer is: 4 the classifier came back with: 3, the real answer is: 3 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: 0, the real answer is: 0 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 4, the real answer is: 4 the classifier came back with: 2, the real answer is: 2 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: 2, the real answer is: 2 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: 8, the real answer is: 8 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: 8, the real answer is: 8 the classifier came back with: 8, the real answer is: 8 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: 0, the real answer is: 0 the classifier came back with: 8, the real answer is: 8 the classifier came back with: 1, the real answer is: 1 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: 1 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: 2, the real answer is: 2 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: 2, the real answer is: 2 the classifier came back with: 4, the real answer is: 4 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 0, the real answer is: 0 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 4, the real answer is: 4 the classifier came back with: 3, the real answer is: 3 the classifier came back with: 6, the real answer is: 6 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: 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: 3, the real answer is: 3 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: 9, the real answer is: 9 the classifier came back with: 0, the real answer is: 0 the classifier came back with: 9, the real answer is: 9 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: 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: 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: 1 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: 1, the real answer is: 1 the classifier came back with: 1, the real answer is: 1 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: 6, the real answer is: 6 the classifier came back with: 6, the real answer is: 6 the classifier came back with: 8, the real answer is: 8 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: 8, the real answer is: 8 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: 5, the real answer is: 5 the classifier came back with: 5, the real answer is: 5 the classifier came back with: 4, the real answer is: 4 the classifier came back with: 0, the real answer is: 0 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: 7 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 6, the real answer is: 6 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: 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: 3, the real answer is: 3 the classifier came back with: 4, the real answer is: 4 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: 0, the real answer is: 0 the classifier came back with: 7, the real answer is: 7 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: 0, the real answer is: 0 the classifier came back with: 9, the real answer is: 9 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: 2, the real answer is: 2 the classifier came back with: 2, the real answer is: 2 the classifier came back with: 5, the real answer is: 5 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: 8, the real answer is: 8 the classifier came back with: 6, the real answer is: 6 the classifier came back with: 8, the real answer is: 8 the classifier came back with: 1, the real answer is: 1 the classifier came back with: 8, the real answer is: 8 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: 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: 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: 6, the real answer is: 6 the classifier came back with: 1, the real answer is: 1 the classifier came back with: 6, the real answer is: 6 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: 1 the classifier came back with: 1, the real answer is: 1 the classifier came back with: 6, the real answer is: 6 the classifier came back with: 8, the real answer is: 8 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: 5, the real answer is: 5 the classifier came back with: 5, the real answer is: 5 the classifier came back with: 2, the real answer is: 2 the classifier came back with: 5, the real answer is: 5 the classifier came back with: 4, the real answer is: 4 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: 0, the real answer is: 0 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 0, the real answer is: 0 the classifier came back with: 6, the real answer is: 6 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: 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: 3, the real answer is: 3 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: 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: 9, the real answer is: 9 the classifier came back with: 4, the real answer is: 4 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: 4, the real answer is: 4 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 3, the real answer is: 3 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 7, the real answer is: 7 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: 6, 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: 2, the real answer is: 2 the classifier came back with: 5, the real answer is: 5 the classifier came back with: 5, the real answer is: 5 the classifier came back with: 6, the real answer is: 6 the classifier came back with: 1, the real answer is: 1 the classifier came back with: 8, the real answer is: 8 the classifier came back with: 1, the real answer is: 1 the classifier came 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: 1, the real answer is: 1 the classifier came back with: 1, the real answer is: 1 the classifier came back with: 6, the real answer is: 6 the classifier came back with: 5, the real answer is: 5 the classifier came back with: 2, the real answer is: 2 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: 3, the real answer is: 5 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: 7, the real answer is: 7 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 3, the real answer is: 3 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 4, the real answer is: 4 the classifier came back with: 0, the real answer is: 0 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: 0, the real answer is: 0 the classifier came back with: 4, the real answer is: 4 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: 5, the real answer is: 5 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: 4, the real answer is: 4 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: 1, the real answer is: 1 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 0, the real answer is: 0 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: 0, the real answer is: 0 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 0, the real answer is: 0 the classifier came back with: 7, the real answer is: 7 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: 3, the real answer is: 3 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 2, the real answer is: 2 the classifier came back with: 5, the real answer is: 5 the classifier came back with: 2, the real answer is: 2 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: 2, the real answer is: 2 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: 8, the real answer is: 8 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 6, the real answer is: 6 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: 8, the real answer is: 8 the classifier came back with: 6, the real answer is: 6 the classifier came back with: 1, the real answer is: 1 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 7, the real answer is: 7 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: 6, the real answer is: 6 the classifier came back with: 8, the real answer is: 8 the classifier came back with: 6, the real answer is: 6 the classifier came back with: 1, the real answer is: 1 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 8, the real answer is: 8 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: 2, the real answer is: 2 the classifier came back with: 5, the real answer is: 5 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: 5, the real answer is: 5 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 3, the real answer is: 3 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 7, the real answer is: 7 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: 4, the real answer is: 4 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 4, the real answer is: 4 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: 3, the real answer is: 3 the classifier came back with: 4, the real answer is: 4 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: 5, the real answer is: 5 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: 3, the real answer is: 3 the classifier came back with: 5, the real answer is: 5 the classifier came back with: 4, the real answer is: 4 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: 7, the real answer is: 7 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 7, the real answer is: 7 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: 7, the real answer is: 7 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: 4, the real answer is: 4 the classifier came back with: 0, the real answer is: 0 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 3, the real answer is: 3 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 5, the real answer is: 5 the classifier came back with: 2, the real answer is: 2 the classifier came back with: 5, the real answer is: 5 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: 5, the real answer is: 5 the classifier came back with: 5, the real answer is: 5 the classifier came back with: 5, the real answer is: 5 the classifier came back with: 5, the real answer is: 5 the classifier came back with: 6, the real answer is: 8 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: 6, the real answer is: 6 the classifier came back with: 8, the real answer is: 8 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: 6, the real answer is: 6 the classifier came back with: 8, the real answer is: 8 the classifier came back with: 1, the real answer is: 1 the classifier came back with: 6, the real answer is: 6 the classifier came back with: 8, the real answer is: 8 the classifier came back with: 1, the real answer is: 1 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: 2, the real answer is: 2 the classifier came back with: 5, the real answer is: 5 the classifier came back with: 2, the real answer is: 2 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: 2, the real answer is: 2 the classifier came back with: 3, the real answer is: 3 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 0, the real answer is: 0 the classifier came back with: 4, the real answer is: 4 the classifier came back with: 0, the real answer is: 0 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 0, the real answer is: 0 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 1, the real answer is: 1 the classifier came back with: 4, the real answer is: 4 the classifier came back with: 3, the real answer is: 3 the classifier came back with: 5, the real answer is: 5 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: 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: 5, the real answer is: 5 the classifier came back with: 1, the real answer is: 1 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 4, the real answer is: 4 the classifier came back with: 0, the real answer is: 0 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: 0, the real answer is: 0 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 3, the real answer is: 3 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: 2, the real answer is: 2 the classifier came back with: 2, the real answer is: 2 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: 1, the real answer is: 1 the classifier came back with: 1, the real answer is: 1 the classifier came back with: 8, the real answer is: 8 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: 6, the real answer is: 6 the classifier came back with: 1, the real answer is: 1 the classifier came back with: 8, the real answer is: 8 the classifier came back with: 1, the real answer is: 1 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: 2, the real answer is: 2 the classifier came back with: 2, the real answer is: 2 the classifier came back with: 5, the real answer is: 5 the classifier came back with: 5, the real answer is: 5 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 3, the real answer is: 3 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 9, the real answer is: 9 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: 4, the real answer is: 4 the classifier came back with: 9, the real answer is: 9 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 7, the real answer is: 7 the classifier came back with: 1, the real answer is: 1 the classifier came back with: 5, the real answer is: 5 the classifier came back with: 4, the real answer is: 4 the classifier came back with: 3, the real answer is: 3 the classifier came back with: 3, the real answer is: 3 the total number of errors is: 11 the total error rate is: 0.011628
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