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_study\dataset\credit-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_study\dataset\credit-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()

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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
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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
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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
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1,39.08,4,0,0,0,0,3,1,1,0,1,0,480,0,1
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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
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1,26.17,2,0,0,4,3,0,1,1,0,0,0,276,1,1
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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
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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
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1,23.58,11.5,1,1,5,1,3,1,1,0,0,0,20,16,1
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0,39.5,1.625,0,0,0,0,1.5,1,1,0,1,0,0,316,1
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1,64.08,0.165,0,0,13,7,0,0,0,1,1,0,232,100,-1
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1,46,4,0,0,4,3,0,0,1,0,1,0,100,960,-1
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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
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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

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