update kernel func

face.rec.klda.homework.py

@@ -66,13 +66,15 @@ class KernelDiscriminantAnalysis(BaseEstimator, ClassifierMixin,
         self.N = 0 # 用于存放 Kernel LDA 最优化公式中的 N
         self.EigenVectors = None # 用于存放 Kernel LDA 最优化公式中的 M 对应的广义特征向量, 每一列为一个特征向量, 按照对应特征值大小排序
 
-    def Kernal(self,x,y,gamma):
+    ### Defining a kernel, can replace it with linear or others
+    def Kernel(self,x,y,gamma):
         return math.exp(-(x-y).T.dot(x-y)*gamma)
 
+    ### Computting kernel matrix,
+    ### input: X1(n_samples_1,n_feature) * X2(n_samples_2,n_feature)
+    ### Output: (n_samples_1,n_samples_2)
     def Kernal_matrix(self,x1,x2,gamma):
-        #print(x1.shape,x2.shape,gamma)
-        #print(self.Kernal([1,1],[2,2],gamma=gamma))
-        return np.fromfunction(np.vectorize(lambda i,j: self.Kernal(x1[int(i),:],x2[int(j),:],gamma=gamma)), (x1.shape[0],x2.shape[0]), dtype=np.float32)
+        return np.fromfunction(np.vectorize(lambda i,j: self.Kernel(x1[int(i),:],x2[int(j),:],gamma=gamma)), (x1.shape[0],x2.shape[0]), dtype=np.float32)
 
     def fit(self, X, y):
         """Fit KDA model.
@@ -105,14 +107,17 @@ class KernelDiscriminantAnalysis(BaseEstimator, ClassifierMixin,
         l.append(X1.shape[0])
 
         ### Computing M, based on M = (M0-M1) @ (M1-M1).T, M is symmetric
+        ### Alternatively, we can use sklearn.metrics.pairwise.rbf_kernel
+        ### Reason of using this function is that we can replace the RBF kernel by other kernels easily
         M0 = np.mean(self.Kernal_matrix(X,X0,gamma=self.gamma),axis=-1).reshape(-1,1)
         M1 = np.mean(self.Kernal_matrix(X,X1,gamma=self.gamma),axis=-1).reshape(-1,1)
         self.M = (M0-M1) @ (M0-M1).T
 
         ### Computing kernal matrix K0 and K1
+        ### Alternatively, we can use sklearn.metrics.pairwise.rbf_kernel
         self.K = []
-        self.K.append(rbf_kernel(X,X0,gamma=self.gamma))
-        self.K.append(rbf_kernel(X,X1,gamma=self.gamma))
+        self.K.append(self.Kernal_matrix(X,X0,gamma=self.gamma))
+        self.K.append(self.Kernal_matrix(X,X0,gamma=self.gamma))
         ### Computing N, N is symmetric
         for i in range(1):
             self.N += self.K[i] @ (np.eye(l[i]) - np.full((l[i],l[i]),1./l[i])) @ self.K[i].T