1 #######################数据结构部分#############################################

2 importnumpy as np3 importmatplotlib.pyplot as plt4

5 #%matplotlib inline

6

7 classNode(object):8 def __init__(self, inbound_nodes =[]):9 self.inbound_nodes =inbound_nodes10 self.value =None11 self.outbound_nodes =[]12

13 self.gradients ={}14

15 for node ininbound_nodes:16 node.outbound_nodes.append(self)17

18 defforward(self):19 raiseNotImplementedError20

21 defbackward(self):22 raiseNotImplementedError23

24

25 classInput(Node):26 def __init__(self):27 Node.__init__(self)28

29 defforward(self):30 pass

31

32 defbackward(self):33 self.gradients ={self : 0}34 for n inself.outbound_nodes:35 self.gradients[self] +=n.gradients[self]36

37 ##################################################################################

38 classLinear(Node):39 def __init__(self, X, W, b):40 Node.__init__(self, [X, W, b])41

42 defforward(self):43 X =self.inbound_nodes[0].value44 W = self.inbound_nodes[1].value45 b = self.inbound_nodes[2].value46 self.value = np.dot(X, W) +b47

48 defbackward(self):49 self.gradients = {n: np.zeros_like(n.value) for n inself.inbound_nodes }50 for n inself.outbound_nodes:51 grad_cost =n.gradients[self]52 self.gradients[self.inbound_nodes[0]] += np.dot(grad_cost, self.inbound_nodes[1].value.T)53 self.gradients[self.inbound_nodes[1]] +=np.dot(self.inbound_nodes[0].value.T, grad_cost)54 self.gradients[self.inbound_nodes[2]] += np.sum(grad_cost, axis = 0, keepdims =False)55

56 ###################################################################################

57 classSigmoid(Node):58 def __init__(self, node):59 Node.__init__(self, [node])60

61 def_sigmoid(self, x):62 return 1. / (1. + np.exp(-x)) #exp() 方法返回x的指数,e的x次幂

63

64 defforward(self):65 input_value =self.inbound_nodes[0].value66 self.value =self._sigmoid(input_value)67

68 defbackward(self):69 self.gradients = {n: np.zeros_like(n.value) for n inself.inbound_nodes}70 for n inself.outbound_nodes:71 grad_cost =n.gradients[self]72 sigmoid =self.value73 self.gradients[self.inbound_nodes[0]] += sigmoid * (1 - sigmoid) *grad_cost74

75

76 classMSE(Node):77 def __init__(self, y, a):78 Node.__init__(self, [y, a])79

80

81 defforward(self):82 y = self.inbound_nodes[0].value.reshape(-1, 1)83 a = self.inbound_nodes[1].value.reshape(-1, 1)84

85 self.m =self.inbound_nodes[0].value.shape[0]86 self.diff = y -a87 self.value = np.mean(self.diff**2)88

89

90 defbackward(self):91 self.gradients[self.inbound_nodes[0]] = (2 / self.m) *self.diff92 self.gradients[self.inbound_nodes[1]] = (-2 / self.m) *self.diff93

94

95

96 ##########################计算图部分#############################################

97 deftopological_sort(feed_dict):98 input_nodes = [n for n infeed_dict.keys()]99 G ={}100 nodes = [n for n ininput_nodes]101 while len(nodes) >0:102 n =nodes.pop(0)103 if n not inG:104 G[n] = {'in' : set(), 'out': set()}105 for m inn.outbound_nodes:106 if m not inG:107 G[m] = {'in' : set(), 'out': set()}108 G[n]['out'].add(m)109 G[m]['in'].add(n)110 nodes.append(m)111

112 L =[]113 S =set(input_nodes)114 while len(S) >0 :115 n =S.pop()116 ifisinstance(n, Input):117 n.value =feed_dict[n]118 L.append(n)119 for m inn.outbound_nodes:120 G[n]['out'].remove(m)121 G[m]['in'].remove(n)122 if len(G[m]['in']) ==0 :123 S.add(m)124 returnL125

126

127

128 #######################使用方法##############################################

129 #首先由图的定义执行顺序

130 #graph = topological_sort(feed_dict)

131 defforward_and_backward(graph):132 for n ingraph :133 n.forward()134

135 for n in graph[:: -1]:136 n.backward()137

138 #对各个模块进行正向计算和反向求导

139 #forward_and_backward(graph)

140

141 #########################介绍梯度下降################

142 def sgd_update(trainables, learning_rate = 1e-2):143 for t intrainables :144 t.value = t.value - learning_rate *t.gradients[t]145

146 ###########使用这个模型#################################

147 from sklearn.utils importresample148 from sklearn importdatasets149

150 #%matplotlib inline

151

152 data =datasets.load_iris()153 X_ =data.data154 y_ =data.target155 y_[y_ == 2] = 1 #0 for virginica, 1 for not virginica

156 print(X_.shape, y_.shape) #out (150,4) (150,)

157

158 ########################用写的模块来定义这个神经网络#########################

159

160 np.random.seed(0)161 n_features = X_.shape[1]162 n_class = 1

163 n_hidden = 3

164

165 X, y =Input(), Input()166 W1, b1 =Input(), Input()167 W2, b2 =Input(), Input()168

169 l1 =Linear(X, W1, b1)170 s1 =Sigmoid(l1)171 l2 =Linear(s1, W2, b2)172 t1 =Sigmoid(l2)173 cost =MSE(y, t1)174

175

176 ###########训练模型###########################################

177 #随即初始化参数值

178 W1_0 = np.random.random(X_.shape[1] * n_hidden).reshape([X_.shape[1], n_hidden])179 W2_0 = np.random.random(n_hidden *n_class).reshape([n_hidden, n_class])180 b1_0 =np.random.random(n_hidden)181 b2_0 =np.random.random(n_class)182

183 #将输入值带入算子

184 feed_dict ={185 X: X_, y: y_,186 W1:W1_0, b1: b1_0,187 W2:W2_0, b2: b2_0188 }189

190 #训练参数

191 #这里训练100轮(eprochs),每轮抽4个样本(batch_size),训练150/4次(steps_per_eproch),学习率 0.1

192 epochs = 100

193 m =X_.shape[0]194 batch_size = 4

195 steps_per_eproch = m //batch_size196 lr = 0.1

197

198 graph =topological_sort(feed_dict)199 trainables =[W1, b1,W2, b2]200

201 l_Mat_W1 =[W1_0]202 l_Mat_W2 =[W2_0]203

204 l_loss =[]205 for i inrange(epochs):206 loss =0207 for j inrange(steps_per_eproch):208 X_batch, y_batch = resample(X_, y_, n_samples =batch_size)209 X.value =X_batch210 y.value =y_batch211

212 forward_and_backward(graph)213 sgd_update(trainables, lr)214 loss += graph[-1].value215

216 l_loss.append(loss)217 if i % 10 ==9:218 print("Eproch %d, Loss = %1.5f" %(i, loss))219

220

221 #图形化显示

222 plt.plot(l_loss)223 plt.title("Cross Entropy value")224 plt.xlabel("Eproch")225 plt.ylabel("Loss")226 plt.show()227

228

229 ##########最后用模型预测所有的数据的情况

230 X.value =X_231 y.value =y_232 for n ingraph:233 n.forward()234

235

236 plt.plot(graph[-2].value.ravel())237 plt.title("predict for all 150 Iris data")238 plt.xlabel("Sample ID")239 plt.ylabel("Probability for not a virginica")240 plt.show()