SVM

Author: lawlite19

SVM/SVM_scikit-learn.py

@@ -0,0 +1,71 @@
+import numpy as np
+from scipy import io as spio
+from matplotlib import pyplot as plt
+from sklearn import svm
+
+def SVM():
+    '''data1——线性分类'''
+    data1 = spio.loadmat('data1.mat')
+    X = data1['X']
+    y = data1['y']
+    y = np.ravel(y)
+    plot_data(X,y)
+    
+    model = svm.SVC(C=1.0,kernel='linear').fit(X,y) # 指定核函数为线性核函数
+    plot_decisionBoundary(X, y, model)  # 画决策边界
+    '''data2——非线性分类'''
+    data2 = spio.loadmat('data2.mat')
+    X = data2['X']
+    y = data2['y']
+    y = np.ravel(y)
+    plt = plot_data(X,y)
+    plt.show()
+    
+    model = svm.SVC(gamma=100).fit(X,y)     # gamma为核函数的系数，值越大拟合的越好
+    plot_decisionBoundary(X, y, model,class_='notLinear')   # 画决策边界
+    
+    
+    
+# 作图
+def plot_data(X,y):
+    plt.figure(figsize=(10,8))
+    pos = np.where(y==1)    # 找到y=1的位置
+    neg = np.where(y==0)    # 找到y=0的位置
+    p1, = plt.plot(np.ravel(X[pos,0]),np.ravel(X[pos,1]),'ro',markersize=8)
+    p2, = plt.plot(np.ravel(X[neg,0]),np.ravel(X[neg,1]),'g^',markersize=8)
+    plt.xlabel("X1")
+    plt.ylabel("X2")
+    plt.legend([p1,p2],["y==1","y==0"])
+    return plt
+    
+# 画决策边界
+def plot_decisionBoundary(X,y,model,class_='linear'):
+    plt = plot_data(X, y)
+    
+    # 线性边界        
+    if class_=='linear':
+        w = model.coef_
+        b = model.intercept_
+        xp = np.linspace(np.min(X[:,0]),np.max(X[:,1]),100)
+        yp = -(w[0,0]*xp+b)/w[0,1]
+        plt.plot(xp,yp,'b-',linewidth=2.0)
+        plt.show()
+    else:  # 非线性边界
+        x_1 = np.transpose(np.linspace(np.min(X[:,0]),np.max(X[:,0]),100).reshape(1,-1))
+        x_2 = np.transpose(np.linspace(np.min(X[:,1]),np.max(X[:,1]),100).reshape(1,-1))
+        X1,X2 = np.meshgrid(x_1,x_2)
+        vals = np.zeros(X1.shape)
+        for i in range(X1.shape[1]):
+            this_X = np.hstack((X1[:,i].reshape(-1,1),X2[:,i].reshape(-1,1)))
+            vals[:,i] = model.predict(this_X)
+        
+        plt.contour(X1,X2,vals,[0,1],color='blue')
+        plt.show()
+    
+
+
+if __name__ == "__main__":
+    SVM()
+    
+    
+    

SVM/data.txt

@@ -0,0 +1,118 @@
+0.051267,0.69956,1
+-0.092742,0.68494,1
+-0.21371,0.69225,1
+-0.375,0.50219,1
+-0.51325,0.46564,1
+-0.52477,0.2098,1
+-0.39804,0.034357,1
+-0.30588,-0.19225,1
+0.016705,-0.40424,1
+0.13191,-0.51389,1
+0.38537,-0.56506,1
+0.52938,-0.5212,1
+0.63882,-0.24342,1
+0.73675,-0.18494,1
+0.54666,0.48757,1
+0.322,0.5826,1
+0.16647,0.53874,1
+-0.046659,0.81652,1
+-0.17339,0.69956,1
+-0.47869,0.63377,1
+-0.60541,0.59722,1
+-0.62846,0.33406,1
+-0.59389,0.005117,1
+-0.42108,-0.27266,1
+-0.11578,-0.39693,1
+0.20104,-0.60161,1
+0.46601,-0.53582,1
+0.67339,-0.53582,1
+-0.13882,0.54605,1
+-0.29435,0.77997,1
+-0.26555,0.96272,1
+-0.16187,0.8019,1
+-0.17339,0.64839,1
+-0.28283,0.47295,1
+-0.36348,0.31213,1
+-0.30012,0.027047,1
+-0.23675,-0.21418,1
+-0.06394,-0.18494,1
+0.062788,-0.16301,1
+0.22984,-0.41155,1
+0.2932,-0.2288,1
+0.48329,-0.18494,1
+0.64459,-0.14108,1
+0.46025,0.012427,1
+0.6273,0.15863,1
+0.57546,0.26827,1
+0.72523,0.44371,1
+0.22408,0.52412,1
+0.44297,0.67032,1
+0.322,0.69225,1
+0.13767,0.57529,1
+-0.0063364,0.39985,1
+-0.092742,0.55336,1
+-0.20795,0.35599,1
+-0.20795,0.17325,1
+-0.43836,0.21711,1
+-0.21947,-0.016813,1
+-0.13882,-0.27266,1
+0.18376,0.93348,0
+0.22408,0.77997,0
+0.29896,0.61915,0
+0.50634,0.75804,0
+0.61578,0.7288,0
+0.60426,0.59722,0
+0.76555,0.50219,0
+0.92684,0.3633,0
+0.82316,0.27558,0
+0.96141,0.085526,0
+0.93836,0.012427,0
+0.86348,-0.082602,0
+0.89804,-0.20687,0
+0.85196,-0.36769,0
+0.82892,-0.5212,0
+0.79435,-0.55775,0
+0.59274,-0.7405,0
+0.51786,-0.5943,0
+0.46601,-0.41886,0
+0.35081,-0.57968,0
+0.28744,-0.76974,0
+0.085829,-0.75512,0
+0.14919,-0.57968,0
+-0.13306,-0.4481,0
+-0.40956,-0.41155,0
+-0.39228,-0.25804,0
+-0.74366,-0.25804,0
+-0.69758,0.041667,0
+-0.75518,0.2902,0
+-0.69758,0.68494,0
+-0.4038,0.70687,0
+-0.38076,0.91886,0
+-0.50749,0.90424,0
+-0.54781,0.70687,0
+0.10311,0.77997,0
+0.057028,0.91886,0
+-0.10426,0.99196,0
+-0.081221,1.1089,0
+0.28744,1.087,0
+0.39689,0.82383,0
+0.63882,0.88962,0
+0.82316,0.66301,0
+0.67339,0.64108,0
+1.0709,0.10015,0
+-0.046659,-0.57968,0
+-0.23675,-0.63816,0
+-0.15035,-0.36769,0
+-0.49021,-0.3019,0
+-0.46717,-0.13377,0
+-0.28859,-0.060673,0
+-0.61118,-0.067982,0
+-0.66302,-0.21418,0
+-0.59965,-0.41886,0
+-0.72638,-0.082602,0
+-0.83007,0.31213,0
+-0.72062,0.53874,0
+-0.59389,0.49488,0
+-0.48445,0.99927,0
+-0.0063364,0.99927,0
+0.63265,-0.030612,0

SVM/data1.mat

@@ -636,6 +636,18 @@ def predict(Theta1,Theta2,X):
 - 归一化后训练集预测准确度     
 ![enter description here][23]
 
+--------------------
+
+## 四、SVM支持向量机
+
+### 1、代价函数
+- 在逻辑回归中，我们的代价为：![\cos t({h_\theta }(x),y) = \left\{ {\begin{array}{c}    { - \log ({h_\theta }(x))} \\    { - \log (1 - {h_\theta }(x))}  \end{array} \begin{array}{c}    {y = 1} \\    {y = 0}  \end{array} } \right.](http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=%5Ccos%20t%28%7Bh_%5Ctheta%20%7D%28x%29%2Cy%29%20%3D%20%5Cleft%5C%7B%20%7B%5Cbegin%7Barray%7D%7Bc%7D%20%20%20%20%7B%20-%20%5Clog%20%28%7Bh_%5Ctheta%20%7D%28x%29%29%7D%20%5C%5C%20%20%20%20%7B%20-%20%5Clog%20%281%20-%20%7Bh_%5Ctheta%20%7D%28x%29%29%7D%20%20%5Cend%7Barray%7D%20%5Cbegin%7Barray%7D%7Bc%7D%20%20%20%20%7By%20%3D%201%7D%20%5C%5C%20%20%20%20%7By%20%3D%200%7D%20%20%5Cend%7Barray%7D%20%7D%20%5Cright.)，其中：![{h_\theta }({\text{z}}) = \frac{1}{{1 + {e^{ - z}}}}](http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=%7Bh_%5Ctheta%20%7D%28%7B%5Ctext%7Bz%7D%7D%29%20%3D%20%5Cfrac%7B1%7D%7B%7B1%20%2B%20%7Be%5E%7B%20-%20z%7D%7D%7D%7D)，![{h_\theta }({\text{z}}) = \frac{1}{{1 + {e^{ - z}}}}](http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=%7Bh_%5Ctheta%20%7D%28%7B%5Ctext%7Bz%7D%7D%29%20%3D%20%5Cfrac%7B1%7D%7B%7B1%20%2B%20%7Be%5E%7B%20-%20z%7D%7D%7D%7D)
+- 如图所示，如果`y=1`，`cost`代价函数如图所示    
+![enter description here][24]
+我们想让![{\theta ^T}x >  > 0](http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=%7B%5Ctheta%20%5ET%7Dx%20%3E%20%20%3E%200)，即`z>>0`，这样的话`cost`代价函数才会趋于最小（这是我们想要的），所以用途中**红色**的函数![\cos {t_1}(z)](http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=%5Ccos%20%7Bt_1%7D%28z%29)代替逻辑回归中的cost
+- 当`y=0`时同样，用![\cos {t_0}(z)](http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=%5Ccos%20%7Bt_0%7D%28z%29)代替
+![enter description here][25]
+
 
   [1]: ./images/LinearRegression_01.png "LinearRegression_01.png"
   [2]: ./images/LogisticRegression_01.png "LogisticRegression_01.png"
@@ -659,4 +671,6 @@ def predict(Theta1,Theta2,X):
   [20]: ./images/NeuralNetwork_06.png "NeuralNetwork_06.png"
   [21]: ./images/NeuralNetwork_07.png "NeuralNetwork_07.png"
   [22]: ./images/NeuralNetwork_08.png "NeuralNetwork_08.png"
-  [23]: ./images/NeuralNetwork_09.png "NeuralNetwork_09.png"
+  [23]: ./images/NeuralNetwork_09.png "NeuralNetwork_09.png"
+  [24]: ./images/SVM_01.png "SVM_01.png"
+  [25]: ./images/SVM_02.png "SVM_02.png"