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‎LogisticRegression/LogisticRegression.py‎

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@@ -58,7 +58,7 @@ def plot_data(X,y):
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# 映射为多项式
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def mapFeature(X1,X2):
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degree = 3; # 映射的最高次方
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degree = 2; # 映射的最高次方
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out = np.ones((X1.shape[0],1)) # 映射后的结果数组（取代X）
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'''
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这里以degree=2为例，映射为1,x1,x2,x1^2,x1,x2,x2^2
@@ -75,7 +75,7 @@ def costFunction(initial_theta,X,y,inital_lambda):
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J = 0
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h = sigmoid(np.dot(X,initial_theta)) # 计算h(z)
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theta1 = initial_theta.copy() # 因为正则化j=1从1开始，不包含0，所以赋值一份，前theta(0)值为0
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theta1 = initial_theta.copy() # 因为正则化j=1从1开始，不包含0，所以复制一份，前theta(0)值为0
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theta1[0] = 0
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temp = np.dot(np.transpose(theta1),theta1)

‎images/LogisticRegression_04.png‎

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‎images/LogisticRegression_05.png‎

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‎images/LogisticRegression_06.png‎

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‎images/LogisticRegression_07.png‎

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‎readme.md‎

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@@ -137,7 +137,7 @@ from sklearn.preprocessing import StandardScaler #引入缩放的包
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- 目的是为了防止过拟合
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- 在代价函数中加上一项![\frac{\lambda }{{2m}}\sum\limits_{j = 1}^m {\theta _j^2} ](http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=%5Cfrac%7B%5Clambda%20%7D%7B%7B2m%7D%7D%5Csum%5Climits_%7Bj%20%3D%201%7D%5Em%20%7B%5Ctheta%20_j%5E2%7D%20)，所以最终的代价函数为：
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![J(\theta ) = - \frac{1}{m}\sum\limits_{i = 1}^m {[{y^{(i)}}\log ({h_\theta }({x^{(i)}}) + (1 - } {y^{(i)}})\log (1 - {h_\theta }({x^{(i)}})] + \frac{\lambda }{{2m}}\sum\limits_{j = 1}^m {\theta _j^2} ](http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=J%28%5Ctheta%20%29%20%3D%20%20-%20%5Cfrac%7B1%7D%7Bm%7D%5Csum%5Climits_%7Bi%20%3D%201%7D%5Em%20%7B%5B%7By%5E%7B%28i%29%7D%7D%5Clog%20%28%7Bh_%5Ctheta%20%7D%28%7Bx%5E%7B%28i%29%7D%7D%29%20%2B%20%281%20-%20%7D%20%7By%5E%7B%28i%29%7D%7D%29%5Clog%20%281%20-%20%7Bh_%5Ctheta%20%7D%28%7Bx%5E%7B%28i%29%7D%7D%29%5D%20%2B%20%5Cfrac%7B%5Clambda%20%7D%7B%7B2m%7D%7D%5Csum%5Climits_%7Bj%20%3D%201%7D%5Em%20%7B%5Ctheta%20_j%5E2%7D%20)
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- 注意j是重1开始的，因为theta(0)为一个常数项，X中最前面一列会加上1列，所以乘积还是theta(0),feature没有关系，没有必要正则化
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- 注意j是重1开始的，因为theta(0)为一个常数项，X中最前面一列会加上1列1，所以乘积还是theta(0),feature没有关系，没有必要正则化
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- 正则化后的代价：
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```
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# 代价函数
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return out
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```
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### 6、使用`scipy`的优化方法
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- 梯度下降使用`scipy`中`optimize`中的`fmin_bfgs`函数
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- 调用scipy中的优化算法fmin_bfgs（拟牛顿法Broyden-Fletcher-Goldfarb-Shanno
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- costFunction是自己实现的一个求代价的函数，
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- initial_theta表示初始化的值,
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- fprime指定costFunction的梯度
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- args是其余测参数，以元组的形式传入，最后会将最小化costFunction的theta返回
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```
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result = optimize.fmin_bfgs(costFunction, initial_theta, fprime=gradient, args=(X,y,initial_lambda))
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```
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### 7、运行结果
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- data1决策边界和准确度
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![enter description here][5]
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![enter description here][6]
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- data2决策边界和准确度
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![enter description here][7]
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![enter description here][8]
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[1]: ./images/LinearRegression_01.png "LinearRegression_01.png"
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[2]: ./images/LogisticRegression_01.png "LogisticRegression_01.png"
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[3]: ./images/LogisticRegression_02.png "LogisticRegression_02.png"
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[4]: ./images/LogisticRegression_03.jpg "LogisticRegression_03.jpg"
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[4]: ./images/LogisticRegression_03.jpg "LogisticRegression_03.jpg"
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[5]: ./images/LogisticRegression_04.png "LogisticRegression_04.png"
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[6]: ./images/LogisticRegression_05.png "LogisticRegression_05.png"
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[7]: ./images/LogisticRegression_06.png "LogisticRegression_06.png"
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[8]: ./images/LogisticRegression_07.png "LogisticRegression_07.png"

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