Ajout du perceptron multi-couches

02-intro_rna/01-perceptron.py

@@ -42,7 +42,7 @@ t_debut = time.time()
 # Init des plots
 fig = plt.figure(figsize=(15, 5))
 fig.suptitle("Classificateur par perceptron")
-donnees_ax = fig.add_subplot(2,3,(1,4)) # Observations : x1 et cibles : y1
+donnees_ax = fig.add_subplot(2,4,(1,5)) # Observations : x1 et cibles : y1
 # f_activ_ax = fig.add_subplot(2,3,2) 
 # df_activ_ax = fig.add_subplot(2,3,5)
 
@@ -113,23 +113,39 @@ def sigmoid(_x):
 def echelon(_x): # Heaviside
     return (_x >= 0).astype(_x.dtype)
 
+def relu(_x):
+    return np.maximum(0, _x)
+
+def tanh(_x):
+    return  np.tanh(_x)
+
+def derivation(f, _x, eps=0.000001):
+    return (f(_x + eps) - f(_x))/eps
+
 def derivation(f, _x, eps=0.000001):
     return (f(_x + eps) - f(_x))/eps
 
 # Fonctions d'activation
-f_activ_ax = fig.add_subplot(2,3,2) 
+f_activ_ax = fig.add_subplot(2,4,2) 
 f_activ_ax.set_title("Fonctions d'activation")
 f_activ_x = np.linspace(-5, 5, 200)
-f_activ_ax.set(xlim=(-5,5), ylim=(0, 1.25))
+f_activ_ax.set(xlim=(-5,5), ylim=(-1.25, 1.25))
 f_activ_ax.plot(f_activ_x, sigmoid(f_activ_x), "g-", label="Sigmoïde")
 f_activ_ax.plot(f_activ_x, echelon(f_activ_x), "b-", label="Échelon")
+f_activ_ax.plot(f_activ_x, tanh(f_activ_x), "r-", label="Tanh")
+f_activ_ax.plot(f_activ_x, relu(f_activ_x), "m-", label="ReLU")
+f_activ_ax.text(-4,1, "f (x)", va='center', ha='center')
 f_activ_ax.legend()
 
 # Dérivée
-df_activ_ax = fig.add_subplot(2,3,5)
+df_activ_ax = fig.add_subplot(2,4,6)
+df_activ_ax.set(xlim=(-5,5), ylim=(0, 1.1))
 df_activ_ax.plot(f_activ_x, derivation(sigmoid, f_activ_x), "g-", label="f'(Sigmoïde)")
 df_activ_ax.plot(f_activ_x, derivation(echelon, f_activ_x), "b-", label="f'(Échelon)")
-df_activ_ax.legend()
+df_activ_ax.plot(f_activ_x, derivation(tanh, f_activ_x), "r-", label="f'(Tanh)")
+df_activ_ax.plot(f_activ_x, derivation(relu, f_activ_x), "m-", label="f'(ReLU)")
+df_activ_ax.text(-4,1, "f '(x)", va='center', ha='center')
+# df_activ_ax.legend()
 
 ###############################################################################
 # Perceptron multi-couches (pmc)
@@ -142,22 +158,36 @@ x1_mg, x2_mg = np.meshgrid(np.linspace(-0.2, 1.2, 100), np.linspace(-0.2, 1.2, 1
 
 z1_pmc_xor = pmc_xor(x1_mg, x2_mg, activation=echelon)
 z2_pmc_xor = pmc_xor(x1_mg, x2_mg, activation=sigmoid)
+z3_pmc_xor = pmc_xor(x1_mg, x2_mg, activation=tanh)
+z4_pmc_xor = pmc_xor(x1_mg, x2_mg, activation=relu)
 
-pmc_xor_echelon_ax = fig.add_subplot(2,3,3)
-pmc_xor_echelon_ax.set_title("Xor (perceptron multi-couches) - Activation par Échelon")
+pmc_xor_echelon_ax = fig.add_subplot(2,4,3)
+pmc_xor_echelon_ax.set_title("Xor PMC par Échelon")
 pmc_xor_echelon_ax.contourf(x1_mg, x2_mg, z1_pmc_xor)
 pmc_xor_echelon_ax.plot([0, 1], [0, 1], "rs", markersize=15)
 pmc_xor_echelon_ax.plot([0, 1], [1, 0], "g^", markersize=15)
 pmc_xor_echelon_ax.grid(True)
 
-pmc_xor_sigmoid_ax = fig.add_subplot(2,3,6)
-# pmc_xor_sigmoid_ax.set_title("Xor (perceptron multi-couches) - Activation par Sigmoïde)")
+pmc_xor_sigmoid_ax = fig.add_subplot(2,4,4)
+pmc_xor_sigmoid_ax.set_title("Xor PMC par Sigmoïde")
 pmc_xor_sigmoid_ax.contourf(x1_mg, x2_mg, z2_pmc_xor)
 pmc_xor_sigmoid_ax.plot([0, 1], [0, 1], "rs", markersize=15)
 pmc_xor_sigmoid_ax.plot([0, 1], [1, 0], "g^", markersize=15)
 pmc_xor_sigmoid_ax.grid(True)
-pmc_xor_sigmoid_ax.set_xlabel("Xor (perceptron multi-couches) - Activation par Sigmoïde", fontsize=12)
 
+pmc_xor_tanh_ax = fig.add_subplot(2,4,7)
+pmc_xor_tanh_ax.contourf(x1_mg, x2_mg, z3_pmc_xor)
+pmc_xor_tanh_ax.plot([0, 1], [0, 1], "rs", markersize=15)
+pmc_xor_tanh_ax.plot([0, 1], [1, 0], "g^", markersize=15)
+pmc_xor_tanh_ax.grid(True)
+pmc_xor_tanh_ax.set_xlabel("Xor PMC par Tanh", fontsize=12)
+
+pmc_xor_relu_ax = fig.add_subplot(2,4,8)
+pmc_xor_relu_ax.contourf(x1_mg, x2_mg, z4_pmc_xor)
+pmc_xor_relu_ax.plot([0, 1], [0, 1], "rs", markersize=15)
+pmc_xor_relu_ax.plot([0, 1], [1, 0], "g^", markersize=15)
+pmc_xor_relu_ax.grid(True)
+pmc_xor_relu_ax.set_xlabel("Xor PMC par ReLU", fontsize=12)
 
 plt.show()