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  • 深度学习之逻辑回归的实现 -- sigmoid

    1 什么是逻辑回归

    1.1逻辑回归与线性回归的区别：

    　　线性回归预测的是一个连续的值，不论是单变量还是多变量（比如多层感知器），他都返回的是一个连续的值，放在图中就是条连续的曲线，他常用来表示的数学方法是Y=aX+b；

    　　与之相对的，逻辑回归给出的值并不是连续的，而是 类似于“是” 和 “否” 的回答，这就类似于二元分类的问题。

    1.2逻辑回归实现（sigmoid）：

    　　在逻辑回归算法中，我们常使用的激活函数是Sigmoid函数，他能够将数据映射到 0 到 1 之间，并且通过映射判断，如果映射到的值在 1 ，就返回出一个正面的结果，与之相反，当映射的值为0时就返回一个负面的结果，这就是我们上面所提到的回答： “是”或“否”。那么，什么是Sigmoid函数呢？

    　　Sigmoid函数是一种在生物学中常见的S型函数，也称为S型生长曲线，他的值我们可以看做是恒在 0  到  1 之间的（因为这段区间使我们真正所关心的）。sigmoid的形式如下图所示：   

    　　深度学习网络本质上来说也是一种多层映射网络，当我们输入特征后，在通过如多层感知器的映射后，会一层层的映射到一个最终的形式。使用Sigmoid函数的意义就在于，他会在最后的映射中将结果映射成为0 到 1 之间的值，这时候我们就可以将映射后的值看做是神经网络给出的概率的结果。

    1.3逻辑回归的常用损失函数（交叉熵）：

    　　在线性回归中，我们常用 “mse” （平方差） 来进行损失的刻画，但是“mse”一般来进行惩罚的是损失与原有的数据集在同一个数量级的情况，假如说数量级特别的庞大，但是损失值比较小，那么所得到的损失就会很小，不利于我们的训练。针对这种情形，我们在逻辑回归中（同时在大多数的二分类问题中）使用更有效的方法————交叉熵，他会给我们展现出一种更大的损失。下面这个图就直观的显示出了L2（均方差）与logistic（交叉熵）之间关于在处理损失的差别。

    　

    　　在keras中，我们使用的函数是binary_crossentropy,下面会以一个例子的形式来使用交叉熵实现逻辑回归。

    2逻辑回归的简单实现

     　　这是一个关于信用卡是否存在欺诈行为的预测。

    　　 我们给出部分数据集，并查看是否为一个二分类问题

    data = pd.read_csv('tensorflow_studydatasetcredit-a.csv')

# 查看数据
print(data.head())
# 查看数据是否为二分类问题
print(data.iloc[:,-1].value_counts())

     　　然后，我们取出数据，并建立一个神经网络模型，这里采用两个隐藏层，使得训练时拟合程度更高一些。

    # 取出除了最后一列的所有数据
x = data.iloc[:, :-1]
# 取出数据并进行替换
y = data.iloc[:, -1].replace(-1,0)

# 模拟神经网络创建顺序模型,添加两个隐藏层
# 第一层是获取到的4个单元的隐藏层，数据集是15个数据的元组,使用relu激活
# 第二层是一个简单的数据处理层
# 第三层是输出层，使用Sigmoid进行激活，完成映射
model = tf.keras.Sequential(
    [tf.keras.layers.Dense(4,input_shape=(15,),activation='relu'),
    tf.keras.layers.Dense(4,activation='relu'),
    tf.keras.layers.Dense(1,activation='sigmoid')]
)

model.summary()

    　　查看一下我们创建的模型是否符合我们的需求

     　　再配置一个优化器，采用TensorFlow的梯度下降算法进行优化，使用交叉熵作为损失函数，并计算其正确率，开始训练我们的模型，再调用原始数据集中的前三个数据进行预测测试。

    model.summary()

# 配置优化器
# 使用梯度下降算法进行优化，使用交叉熵作为损失函数，并计算其正确率
model.compile(
    optimizer='adam',
    loss='binary_crossentropy',
    metrics=['acc']
)

# 训练模型
history = model.fit(x,y,epochs=100)

    　t_data = data.iloc[:3,:-1]
    　print(model.predict(t_data))

    　　结果显而易见

     　　这时候，我们也可以通过pandas进行对我们模型的训练过程进行可视化查看，方便我们能够更加准确的针对我们的模型训练做一些改进。

    # 查看我们在训练过程中的loss和acc的变化情况
# 散点图展示数据
plt.figure(1)

ax1 = plt.subplot(2,1,1)
ax2 = plt.subplot(2,1,2)
plt.sca(ax1)
plt.title('loss ')
plt.plot(history.epoch,history.history.get('loss'))
plt.sca(ax2)
plt.title('acc ')
plt.plot(history.epoch,history.history.get('acc'))
plt.show()

     　　在这里，我们就会明显的发现，当我们训练到18次的时候，loss的变化就趋于稳定状态了，二acc也是跟随着loss的稳定趋于更小的波动。

    ：：下面附上源码和数据

    '''
@Author: mountain
@Date: 2020-03-30 16:11:00
@Description: 逻辑回归 --预测信用卡是否存在欺诈行为
'''
import pandas as pd
import matplotlib.pyplot as plt
import tensorflow as tf


data = pd.read_csv('tensorflow_studydatasetcredit-a.csv')

# 查看数据
print(data.head())
# 查看数据是否为二分类问题
print(data.iloc[:,-1].value_counts())


# 取出除了最后一列的所有数据
x = data.iloc[:, :-1]
# 取出数据并进行替换
y = data.iloc[:, -1].replace(-1,0)

# 模拟神经网络创建顺序模型,添加两个隐藏层
# 第一层是获取到的4个单元的隐藏层，数据集是15个数据的元组,使用relu激活
# 第二层是一个简单的数据处理层
# 第三层是输出层，使用Sigmoid进行激活，完成映射
model = tf.keras.Sequential(
    [tf.keras.layers.Dense(4,input_shape=(15,),activation='relu'),
    tf.keras.layers.Dense(4,activation='relu'),
    tf.keras.layers.Dense(1,activation='sigmoid')]
)

model.summary()

# 配置优化器
# 使用梯度下降算法进行优化，使用交叉熵作为损失函数，并计算其正确率
model.compile(
    optimizer='adam',
    loss='binary_crossentropy',
    metrics=['acc']
)

# 训练模型
history = model.fit(x,y,epochs=100)

t_data = data.iloc[:3,:-1]
print(model.predict(t_data))


# 查看我们在训练过程中的loss和acc的变化情况
# 散点图展示数据
plt.figure(1)

ax1 = plt.subplot(2,1,1)
ax2 = plt.subplot(2,1,2)
plt.sca(ax1)
plt.title('loss ')
plt.plot(history.epoch,history.history.get('loss'))
plt.sca(ax2)
plt.title('acc ')
plt.plot(history.epoch,history.history.get('acc'))
plt.show()
    ljhg
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1,68.67,15,0,0,11,5,0,0,0,14,1,0,0,3376,-1
0,28,2,0,0,5,1,4.165,0,0,2,0,0,181,0,-1
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1,40.83,10,0,0,8,1,1.75,0,1,0,1,0,29,837,-1
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1,32.33,0.54,0,0,2,0,0.04,0,1,0,1,0,440,11177,-1
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0,56,12.5,0,0,5,1,8,0,1,0,0,0,24,2028,-1
1,49.83,13.585,0,0,5,1,8.5,0,1,0,0,0,0,0,-1
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0,25,12.5,0,0,12,0,3,0,1,0,0,2,20,0,-1
1,26.08,8.665,0,0,12,0,1.415,0,1,0,1,0,160,150,-1
1,18.42,9.25,0,0,8,0,1.21,0,0,4,1,0,60,540,-1
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0,47.67,0.29,0,0,0,2,15,0,0,20,1,0,0,15000,-1
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1,22.42,5.665,0,0,8,0,2.585,0,0,7,1,0,129,3257,-1
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0,40.58,5,0,0,0,0,5,0,0,7,1,0,0,3065,-1
1,28.67,1.04,0,0,0,0,2.5,0,0,5,0,0,300,1430,-1
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1,41.33,1,0,0,3,2,2.25,0,1,0,0,0,0,300,-1
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1,35.42,12,0,0,8,1,14,0,0,8,1,0,0,6590,-1
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1,18.92,9.25,1,1,0,0,1,0,0,4,0,0,80,500,-1
1,50.08,12.54,0,0,12,0,2.29,0,0,3,0,0,156,0,-1
0,65.42,11,0,0,11,5,20,0,0,7,0,0,22,0,-1
1,17.58,9,0,0,12,0,1.375,0,1,0,0,0,0,0,-1
1,18.83,9.54,0,0,12,0,0.085,0,1,0,1,0,100,0,-1
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1,47.42,3,0,0,10,0,13.875,0,0,2,0,0,519,1704,-1
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1,58.42,21,0,0,3,2,10,0,0,13,1,0,0,6700,-1
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0,28.33,5,0,0,9,0,11,0,1,0,0,0,70,0,-1
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0,45,8.5,0,0,2,1,14,0,0,1,0,0,88,2000,-1
1,19.67,0.21,0,0,8,1,0.29,0,0,11,1,0,80,99,-1
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0,41.42,5,0,0,8,1,5,0,0,6,0,0,470,0,-1
1,17.83,11,0,0,10,1,1,0,0,11,1,0,0,3000,-1
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0,18.17,10.25,0,0,0,1,1.085,1,1,0,1,0,320,13,1
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1,24.5,1.75,1,1,0,0,0.165,1,1,0,1,0,132,0,1
0,32.75,2.335,0,0,1,1,5.75,1,1,0,0,0,292,0,1
1,52.17,0,1,1,13,7,0,1,1,0,1,0,0,0,1
1,48.17,1.335,0,0,3,8,0.335,1,1,0,1,0,0,120,1
1,20.42,10.5,1,1,10,1,0,1,1,0,0,0,154,32,1
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1,32,6,0,0,1,0,1.25,1,1,0,1,0,272,0,1
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0,32.33,2.5,0,0,0,0,1.25,1,1,0,0,0,280,0,1
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1,19.17,5.415,0,0,3,1,0.29,1,1,0,1,0,80,484,1
1,18.17,10,1,1,8,1,0.165,1,1,0,1,0,340,0,1
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0,21.17,0.875,1,1,0,1,0.25,1,1,0,1,0,280,204,1
0,23.92,0.585,1,1,2,1,0.125,1,1,0,1,0,240,1,1
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1,16.5,1.25,0,0,8,0,0.25,1,0,1,1,0,108,98,1
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0,17.58,10,0,0,9,1,0.165,1,0,1,1,0,120,1,1
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0,18.83,0.415,1,1,0,0,0.165,1,0,1,1,0,200,1,1
1,21.75,1.75,1,1,4,3,0,1,1,0,1,0,160,0,1
0,23,0.75,0,0,6,0,0.5,1,1,0,0,2,320,0,1
1,18.25,10,0,0,9,0,1,1,0,1,1,0,120,1,1
0,25.42,0.54,0,0,9,0,0.165,1,0,1,1,0,272,444,1
0,35.75,2.415,0,0,9,0,0.125,1,0,2,1,0,220,1,1
1,16.08,0.335,0,0,13,7,0,1,0,1,1,0,160,126,1
1,31.92,3.125,0,0,13,7,3.04,1,0,2,0,0,200,4,1
0,69.17,9,0,0,13,7,4,1,0,1,1,0,70,6,1
0,32.92,2.5,0,0,12,0,1.75,1,0,2,0,0,720,0,1
0,16.33,2.75,0,0,12,0,0.665,1,0,1,1,0,80,21,1
0,22.17,12.125,0,0,0,0,3.335,1,0,2,0,0,180,173,1
1,57.58,2,0,0,13,7,6.5,1,0,1,1,0,0,10,1
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0,23.42,1,0,0,0,0,0.5,1,1,0,0,2,280,0,1
1,15.92,2.875,0,0,8,0,0.085,1,1,0,1,0,120,0,1
1,24.75,13.665,0,0,8,1,1.5,1,1,0,1,0,280,1,1
0,48.75,26.335,1,1,13,7,0,0,1,0,0,0,0,0,1
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0,18.58,10.29,0,0,13,7,0.415,1,1,0,1,0,80,0,1
0,27.75,1.29,0,0,5,1,0.25,1,1,0,0,2,140,0,1
1,31.75,3,1,1,4,3,0,1,1,0,1,0,160,20,1
1,24.83,4.5,0,0,9,0,1,1,1,0,0,0,360,6,1
0,19,1.75,1,1,0,0,2.335,1,1,0,0,0,112,6,1
1,16.33,0.21,0,0,12,0,0.125,1,1,0,1,0,200,1,1
1,18.58,10,0,0,1,0,0.415,1,1,0,1,0,80,42,1
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0,23,0.75,0,0,6,0,0.5,0,1,0,0,2,320,0,1
0,21.17,0.25,1,1,0,1,0.25,1,1,0,1,0,280,204,1
0,17.5,22,2,2,13,8,0,1,1,0,0,1,450,1e+005,-1
0,19.17,0,1,1,6,2,0,1,1,0,0,2,500,1,-1
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1,18.08,0.375,2,2,2,7,10,1,1,0,0,2,300,0,-1
1,33.67,0.375,0,0,2,0,0.375,1,1,0,1,0,300,44,-1
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0,33.67,1.25,0,0,9,0,1.165,1,1,0,1,0,120,0,1
1,29.5,1.085,1,1,10,0,1,1,1,0,1,0,280,13,1
0,30.17,1.085,1,1,0,0,0.04,1,1,0,1,0,170,179,1
0,34.83,2.5,1,1,9,0,3,1,1,0,1,2,200,0,1
1,33.25,2.5,1,1,0,0,2.5,1,1,0,0,0,0,2,1
0,34.08,2.5,0,0,0,0,1,1,1,0,1,0,460,16,1
1,25.25,12.5,0,0,1,0,1,1,1,0,0,0,180,1062,1
0,34.75,2.5,0,0,2,2,0.5,1,1,0,1,0,348,0,1
0,27.67,0.75,0,0,8,1,0.165,1,1,0,0,0,220,251,1
0,47.33,6.5,0,0,0,0,1,1,1,0,0,0,0,228,1
1,34.83,1.25,1,1,3,1,0.5,1,1,0,0,0,160,0,1
1,33.25,3,1,1,12,0,2,1,1,0,1,0,180,0,1
0,28,3,0,0,9,0,0.75,1,1,0,0,0,300,67,1
1,39.08,4,0,0,0,0,3,1,1,0,1,0,480,0,1
0,42.75,4.085,0,0,12,0,0.04,1,1,0,1,0,108,100,1
0,26.92,2.25,0,0,3,2,0.5,1,1,0,0,0,640,4000,1
0,33.75,2.75,0,0,3,2,0,1,1,0,1,0,180,0,1
0,38.92,1.75,0,0,5,0,0.5,1,1,0,0,0,300,2,1
0,62.75,7,0,0,11,5,0,1,1,0,1,0,0,12,1
0,26.75,4.5,1,1,0,2,2.5,1,1,0,1,0,200,1210,1
0,63.33,0.54,0,0,0,0,0.585,0,0,3,0,0,180,0,1
0,27.83,1.5,0,0,9,0,2.25,1,0,1,0,0,100,3,1
1,26.17,2,0,0,4,3,0,1,1,0,0,0,276,1,1
0,22.17,0.585,1,1,13,7,0,1,1,0,1,0,100,0,1
0,22.5,11.5,1,1,6,0,1.5,1,1,0,0,0,0,4000,1
0,30.75,1.585,0,0,1,0,0.585,1,1,0,0,2,0,0,1
0,36.67,2,0,0,3,0,0.25,1,1,0,0,0,221,0,1
1,16,0.165,0,0,12,0,1,1,0,2,0,0,320,1,1
0,41.17,1.335,0,0,1,0,0.165,1,1,0,1,0,168,0,1
1,19.5,0.165,0,0,8,0,0.04,1,1,0,0,0,380,0,1
0,32.42,3,0,0,1,0,0.165,1,1,0,0,0,120,0,1
1,36.75,4.71,0,0,13,7,0,1,1,0,1,0,160,0,1
1,30.25,5.5,0,0,5,0,5.5,1,1,0,0,2,100,0,1
0,23.08,2.5,0,0,13,7,0.085,1,1,0,0,0,100,4208,1
0,26.83,0.54,0,0,5,7,0,1,1,0,1,0,100,0,1
0,16.92,0.335,1,1,5,0,0.29,1,1,0,1,2,200,0,1
0,24.42,2,0,0,11,6,0.165,1,0,2,1,0,320,1300,1
0,42.83,1.25,0,0,6,0,13.875,1,0,1,0,0,352,112,1
1,22.75,6.165,0,0,12,0,0.165,1,1,0,1,0,220,1000,1
0,39.42,1.71,1,1,6,0,0.165,1,1,0,1,2,400,0,1
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1,33.08,1.625,0,0,1,0,0.54,1,1,0,0,0,0,0,1
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0,34,5.085,1,1,3,2,1.085,1,1,0,0,0,480,0,1
1,69.5,6,0,0,13,7,0,1,1,0,1,2,0,0,1
1,19.58,0.665,1,1,0,0,1,1,0,1,1,0,2000,2,1
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0,25.17,3,0,0,0,0,1.25,1,0,1,1,0,0,22,1
1,22.67,0.79,0,0,3,0,0.085,1,1,0,1,0,144,0,1
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1,22.25,1.25,1,1,13,7,3.25,1,1,0,1,0,280,0,1
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1,26.58,2.54,1,1,13,7,0,1,1,0,0,0,180,60,1
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0,29.42,1.25,0,0,9,0,1.75,1,1,0,1,0,200,0,1
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0,33.67,2.165,0,0,0,0,1.5,1,1,0,1,1,120,0,1
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1,27.67,2.04,0,0,9,0,0.25,1,1,0,0,0,180,50,1
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0,19.58,0.585,0,0,13,7,0,1,0,3,1,0,350,769,1
1,53.33,0.165,0,0,13,7,0,1,1,0,0,2,62,27,1
1,27.17,1.25,0,0,13,7,0,1,0,1,1,0,92,300,1
0,25.92,0.875,0,0,5,0,0.375,1,0,2,0,0,174,3,1
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1,17.67,0,1,1,4,7,0,1,1,0,1,0,86,0,1
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1,27.33,1.665,0,0,13,7,0,1,1,0,1,0,340,1,1
0,31.25,1.125,0,0,13,7,0,1,0,1,1,0,96,19,1
0,20,7,0,0,0,0,0.5,1,1,0,1,0,0,0,1
0,39.5,1.625,0,0,0,0,1.5,1,1,0,1,0,0,316,1
0,36.5,4.25,0,0,8,0,3.5,1,1,0,1,0,454,50,1
0,52.42,1.5,0,0,1,0,3.75,1,1,0,0,0,0,350,1
0,36.17,18.125,0,0,9,0,0.085,1,1,0,1,0,320,3552,1
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0,36.17,5.5,0,0,3,2,5,1,1,0,1,0,210,687,1
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1,36.58,0.29,0,0,13,7,0,1,0,10,1,0,200,18,1
1,23,1.835,0,0,4,3,0,1,0,1,1,0,200,53,1
1,27.58,3,0,0,6,0,2.79,1,0,1,0,0,280,10,1
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1,30.42,1.375,0,0,9,1,0.04,1,0,3,1,0,0,33,1
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1,21.92,11.665,0,0,5,1,0.085,1,1,0,1,0,320,5,1
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0,19.17,4,1,1,3,0,1,1,1,0,0,0,360,1000,1
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0,26.75,2,0,0,1,0,0.75,1,1,0,0,0,80,0,1
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0,34.67,1.08,0,0,6,0,1.165,1,1,0,1,2,28,0,1
0,74.83,19,1,1,13,7,0.04,1,0,2,1,0,0,351,1
0,28.17,0.125,1,1,5,0,0.085,1,1,0,1,0,216,2100,1
0,24.5,13.335,1,1,12,0,0.04,1,1,0,0,0,120,475,1
0,18.83,3.54,1,1,13,7,0,1,1,0,0,0,180,1,1
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1,25,0.875,0,0,10,1,1.04,0,1,0,0,0,160,5860,-1
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0,39,5,0,0,2,0,3.5,0,0,10,0,0,0,0,-1
1,64.08,0.165,0,0,13,7,0,0,0,1,1,0,232,100,-1
0,28.25,5.125,0,0,10,0,4.75,0,0,2,1,0,420,7,-1
1,28.75,3.75,0,0,0,0,1.085,0,0,1,0,0,371,0,-1
0,31.33,19.5,0,0,0,0,7,0,0,16,1,0,0,5000,-1
1,18.92,9,0,0,12,0,0.75,0,0,2,1,0,88,591,-1
1,24.75,3,0,0,8,1,1.835,0,0,19,1,0,0,500,-1
1,30.67,12,0,0,0,0,2,0,0,1,1,0,220,19,-1
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0,13.75,4,1,1,9,0,1.75,0,0,2,0,0,120,1000,-1
1,46,4,0,0,4,3,0,0,1,0,1,0,100,960,-1
1,44.33,0,0,0,0,0,2.5,0,1,0,1,0,0,0,-1
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1,60.92,5,0,0,12,0,4,0,0,4,1,0,0,99,-1
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1,28.17,0.375,0,0,8,0,0.585,0,0,4,1,0,80,0,-1
0,39.17,1.71,0,0,10,0,0.125,0,0,5,0,0,480,0,-1
1,30,5.29,0,0,11,6,2.25,0,0,5,0,0,99,500,-1
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1,22.5,8.5,0,0,8,0,1.75,0,0,10,1,0,80,990,1
1,28.58,1.665,0,0,8,0,2.415,0,1,0,0,0,440,0,1
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0,41.58,1.75,0,0,5,0,0.21,0,1,0,1,0,160,0,1
1,57.08,0.335,0,0,3,2,1,0,1,0,0,0,252,2197,1
1,55.75,7.08,0,0,5,1,6.75,0,0,3,0,0,100,50,1
0,43.25,25.21,0,0,8,1,0.21,0,0,1,1,0,760,90,1
1,25.33,2.085,0,0,0,1,2.75,0,1,0,0,0,360,1,1
1,24.58,0.67,0,0,12,1,1.75,0,1,0,1,0,400,0,1
0,43.17,2.25,0,0,3,2,0.75,0,1,0,1,0,560,0,1
0,40.92,0.835,0,0,13,7,0,0,1,0,1,0,130,1,1
0,31.83,2.5,0,0,12,0,7.5,0,1,0,0,0,523,0,1
1,33.92,1.585,1,1,13,7,0,0,1,0,1,0,320,0,1
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1,25,12.33,0,0,2,1,3.5,0,0,6,1,0,400,458,-1
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1,65.17,14,0,0,13,7,0,0,0,11,0,0,0,1400,-1
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1,28.08,15,1,1,11,5,0,0,1,0,1,0,0,13212,-1
0,73.42,17.75,0,0,13,7,0,0,1,0,0,0,0,0,-1
0,64.08,20,0,0,10,1,17.5,0,0,9,0,0,0,1000,-1
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0,27,0.75,0,0,0,1,4.25,0,0,3,0,0,312,150,-1
0,34.17,5.25,0,0,9,0,0.085,1,1,0,0,0,290,6,-1
0,38.67,0.21,0,0,5,0,0.085,0,1,0,0,0,280,0,-1
0,25.75,0.75,0,0,0,2,0.25,0,1,0,1,0,349,23,-1
1,46.08,3,0,0,0,0,2.375,0,0,8,0,0,396,4159,-1
1,21.5,6,0,0,12,0,2.5,0,0,3,1,0,80,918,-1
0,20.5,2.415,0,0,0,0,2,0,0,11,0,0,200,3000,-1
1,29.5,0.46,0,0,5,0,0.54,0,0,4,1,0,380,500,-1
0,29.83,1.25,1,1,5,0,0.25,1,1,0,1,0,224,0,1
0,20.08,0.25,0,0,8,0,0.125,1,1,0,1,0,200,0,1
0,23.42,0.585,0,0,0,1,0.085,0,1,0,1,0,180,0,1
1,29.58,1.75,1,1,5,0,1.25,1,1,0,0,0,280,0,1
0,16.17,0.04,0,0,0,0,0.04,1,1,0,1,0,0,0,-1
0,32.33,3.5,0,0,5,0,0.5,1,1,0,0,0,232,0,1
0,47.83,4.165,0,0,10,2,0.085,1,1,0,0,0,520,0,1
0,20,1.25,1,1,5,0,0.125,1,1,0,1,0,140,4,1
0,27.58,3.25,1,1,8,1,5.085,1,0,2,0,0,369,1,1
0,22,0.79,0,0,9,0,0.29,1,0,1,1,0,420,283,1
0,19.33,10.915,0,0,0,2,0.585,1,0,2,0,0,200,7,1
1,38.33,4.415,0,0,0,0,0.125,1,1,0,1,0,160,0,1
0,29.42,1.25,0,0,0,1,0.25,1,0,2,0,0,400,108,1
0,22.67,0.75,0,0,3,0,1.585,1,0,1,0,0,400,9,1
0,32.25,14,1,1,13,7,0,1,0,2,1,0,160,1,1
0,29.58,4.75,0,0,6,0,2,1,0,1,0,0,460,68,1
0,18.42,10.415,1,1,12,0,0.125,0,1,0,1,0,120,375,1
0,22.17,2.25,0,0,3,0,0.125,1,1,0,1,0,160,10,1
0,22.67,0.165,0,0,0,3,2.25,1,1,0,0,2,0,0,-1
0,18.83,0,0,0,8,0,0.665,1,1,0,1,0,160,1,1
0,21.58,0.79,1,1,2,0,0.665,1,1,0,1,0,160,0,1
0,23.75,12,0,0,0,0,2.085,1,1,0,1,2,80,0,1
0,36.08,2.54,0,0,13,7,0,1,1,0,1,0,0,1000,1
0,29.25,13,0,0,1,1,0.5,1,1,0,1,0,228,0,1
1,19.58,0.665,0,0,9,0,1.665,1,1,0,1,0,220,5,1
1,22.92,1.25,0,0,8,0,0.25,1,1,0,0,0,120,809,1
1,27.25,0.29,0,0,6,1,0.125,1,0,1,0,0,272,108,1
1,38.75,1.5,0,0,13,7,0,1,1,0,1,0,76,0,1
0,32.42,2.165,1,1,5,7,0,1,1,0,1,0,120,0,1
1,23.75,0.71,0,0,9,0,0.25,1,0,1,0,0,240,4,1
0,18.17,2.46,0,0,0,4,0.96,1,0,2,0,0,160,587,1
0,40.92,0.5,1,1,6,0,0.5,1,1,0,0,0,130,0,1
0,19.5,9.585,0,0,12,0,0.79,1,1,0,1,0,80,350,1
0,28.58,3.625,0,0,12,0,0.25,1,1,0,0,0,100,0,1
0,35.58,0.75,0,0,5,0,1.5,1,1,0,0,0,231,0,1
0,34.17,2.75,0,0,3,2,2.5,1,1,0,0,0,232,200,1
0,31.58,0.75,1,1,12,0,3.5,1,1,0,0,0,320,0,1
1,52.5,7,0,0,12,1,3,1,1,0,1,0,0,0,1
0,36.17,0.42,1,1,9,0,0.29,1,1,0,0,0,309,2,1
0,37.33,2.665,0,0,2,0,0.165,1,1,0,0,0,0,501,1
1,20.83,8.5,0,0,0,0,0.165,1,1,0,1,0,0,351,1
0,24.08,9,0,0,12,0,0.25,1,1,0,0,0,0,0,1
0,25.58,0.335,0,0,5,1,3.5,1,1,0,0,0,340,0,1
1,35.17,3.75,0,0,13,7,0,1,0,6,1,0,0,200,1
0,48.08,3.75,0,0,3,2,1,1,1,0,1,0,100,2,1
1,15.83,7.625,0,0,8,0,0.125,1,0,1,0,0,0,160,1
1,22.5,0.415,0,0,3,0,0.335,1,1,0,0,2,144,0,1
0,21.5,11.5,0,0,3,0,0.5,0,1,0,0,0,100,68,1
1,23.58,0.83,0,0,8,0,0.415,1,0,1,0,0,200,11,1
1,21.08,5,1,1,13,7,0,1,1,0,1,0,0,0,1
0,25.67,3.25,0,0,0,1,2.29,1,0,1,0,0,416,21,1
1,38.92,1.665,0,0,12,0,0.25,1,1,0,1,0,0,390,1
1,15.75,0.375,0,0,0,0,1,1,1,0,1,0,120,18,1
1,28.58,3.75,0,0,0,0,0.25,1,0,1,0,0,40,154,1
0,22.25,9,0,0,12,0,0.085,1,1,0,1,0,0,0,1
0,29.83,3.5,0,0,0,0,0.165,1,1,0,1,0,216,0,1
1,23.5,1.5,0,0,9,0,0.875,1,1,0,0,0,160,0,1
0,32.08,4,1,1,2,0,1.5,1,1,0,0,0,120,0,1
0,31.08,1.5,1,1,9,0,0.04,1,1,0,1,2,160,0,1
0,31.83,0.04,1,1,6,0,0.04,1,1,0,1,0,0,0,1
1,21.75,11.75,0,0,0,0,0.25,1,1,0,0,0,180,0,1
1,17.92,0.54,0,0,0,0,1.75,1,0,1,0,0,80,5,1
0,30.33,0.5,0,0,1,1,0.085,1,1,0,0,2,252,0,1
0,51.83,2.04,1,1,13,7,1.5,1,1,0,1,0,120,1,1
0,47.17,5.835,0,0,9,0,5.5,1,1,0,1,0,465,150,1
0,25.83,12.835,0,0,2,0,0.5,1,1,0,1,0,0,2,1
1,50.25,0.835,0,0,12,0,0.5,1,1,0,0,0,240,117,1
1,37.33,2.5,0,0,3,1,0.21,1,1,0,1,0,260,246,1
1,41.58,1.04,0,0,12,0,0.665,1,1,0,1,0,240,237,1
1,30.58,10.665,0,0,8,1,0.085,1,0,12,0,0,129,3,1
0,19.42,7.25,0,0,6,0,0.04,1,0,1,1,0,100,1,1
1,17.92,10.21,0,0,13,7,0,1,1,0,1,0,0,50,1
1,20.08,1.25,0,0,0,0,0,1,1,0,1,0,0,0,1
0,19.5,0.29,0,0,5,0,0.29,1,1,0,1,0,280,364,1
0,27.83,1,1,1,1,1,3,1,1,0,1,0,176,537,1
0,17.08,3.29,0,0,3,0,0.335,1,1,0,0,0,140,2,1
0,36.42,0.75,1,1,1,0,0.585,1,1,0,1,0,240,3,1
0,40.58,3.29,0,0,6,0,3.5,1,1,0,0,2,400,0,1
0,21.08,10.085,1,1,11,1,1.25,1,1,0,1,0,260,0,1
1,22.67,0.75,0,0,0,0,2,1,0,2,0,0,200,394,1
1,25.25,13.5,1,1,13,7,2,1,0,1,0,0,200,1,1
0,17.92,0.205,0,0,12,0,0.04,1,1,0,1,0,280,750,1
0,35,3.375,0,0,0,1,8.29,1,1,0,0,0,0,0,1
    credit-a.csv

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