1、加載必要的庫，生成數據集

import math import random import matplotlib.pyplot as plt import numpy as np class moon_data_class(object):def __init__(self,N,d,r,w):self.N=Nself.w=wself.d=dself.r=rdef sgn(self,x):if(x>0):return 1;else:return -1;def sig(self,x):return 1.0/(1+np.exp(x))def dbmoon(self):N1 = 10*self.NN = self.Nr = self.rw2 = self.w/2d = self.ddone = Truedata = np.empty(0)while done:#generate Rectangular datatmp_x = 2*(r+w2)*(np.random.random([N1, 1])-0.5)tmp_y = (r+w2)*np.random.random([N1, 1])tmp = np.concatenate((tmp_x, tmp_y), axis=1)tmp_ds = np.sqrt(tmp_x*tmp_x + tmp_y*tmp_y)#generate double moon data ---upperidx = np.logical_and(tmp_ds > (r-w2), tmp_ds < (r+w2))idx = (idx.nonzero())[0]if data.shape[0] == 0:data = tmp.take(idx, axis=0)else:data = np.concatenate((data, tmp.take(idx, axis=0)), axis=0)if data.shape[0] >= N:done = False#print (data)db_moon = data[0:N, :]#print (db_moon)#generate double moon data ----downdata_t = np.empty([N, 2])data_t[:, 0] = data[0:N, 0] + rdata_t[:, 1] = -data[0:N, 1] - ddb_moon = np.concatenate((db_moon, data_t), axis=0)return db_moon

2、定義激活函數

def rand(a,b):return (b-a)* random.random()+adef sigmoid(x):#return np.tanh(-2.0*x)return 1.0/(1.0+math.exp(-x)) def sigmoid_derivate(x):#return -2.0*(1.0-np.tanh(-2.0*x)*np.tanh(-2.0*x))return x*(1-x) #sigmoid函數的導數 def make_matrix(m,n, fill = 0.0):mat=[]for i in range(m):mat.append([fill]*n)

3、定義神經網絡

class BP_NET(object):def __init__(self):self.input_n = 0self.hidden_n = 0self.output_n = 0self.input_cells = []self.bias_input_n = []self.bias_output = []self.hidden_cells = []self.output_cells = []self.input_weights = []self.output_weights = []self.input_correction = []self.output_correction = []def setup(self, ni,nh,no):self.input_n = ni+1#輸入層+偏置項self.hidden_n = nhself.output_n = noself.input_cells = [1.0]*self.input_nself.hidden_cells = [1.0]*self.hidden_nself.output_cells = [1.0]*self.output_nself.input_weights = make_matrix(self.input_n,self.hidden_n)self.output_weights = make_matrix(self.hidden_n,self.output_n)for i in range(self.input_n):for h in range(self.hidden_n):self.input_weights[i][h] = rand(-0.2,0.2)for h in range(self.hidden_n):for o in range(self.output_n):self.output_weights[h][o] = rand(-2.0,2.0)self.input_correction = make_matrix(self.input_n , self.hidden_n)self.output_correction = make_matrix(self.hidden_n,self.output_n)def predict(self,inputs):for i in range(self.input_n-1):self.input_cells[i] = inputs[i]for j in range(self.hidden_n):total = 0.0for i in range(self.input_n):total += self.input_cells[i] * self.input_weights[i][j]self.hidden_cells[j] = sigmoid(total)for k in range(self.output_n):total = 0.0for j in range(self.hidden_n):total+= self.hidden_cells[j]*self.output_weights[j][k]# + self.bias_output[k]self.output_cells[k] = sigmoid(total)return self.output_cells[:]def back_propagate(self, case,label,learn,correct):#計算得到輸出output_cellsself.predict(case)output_deltas = [0.0]*self.output_nerror = 0.0#計算誤差 = 期望輸出-實際輸出for o in range(self.output_n):error = label[o] - self.output_cells[o] #正確結果和預測結果的誤差：0,1，-1output_deltas[o]= sigmoid_derivate(self.output_cells[o])*error#誤差穩定在0~1內hidden_deltas = [0.0] * self.hidden_nfor j in range(self.hidden_n):error = 0.0for k in range(self.output_n):error+= output_deltas[k]*self.output_weights[j][k]hidden_deltas[j] = sigmoid_derivate(self.hidden_cells[j])*error for h in range(self.hidden_n):for o in range(self.output_n):change = output_deltas[o]*self.hidden_cells[h]#調整權重：上一層每個節點的權重學習*變化+矯正率self.output_weights[h][o] += learn*change #更新輸入->隱藏層的權重for i in range(self.input_n):for h in range(self.hidden_n):change = hidden_deltas[h]*self.input_cells[i]self.input_weights[i][h] += learn*change error = 0for o in range(len(label)):for k in range(self.output_n):error+= 0.5*(label[o] - self.output_cells[k])**2return errordef train(self,cases,labels, limit, learn,correct=0.1):for i in range(limit): error = 0.0# learn = le.arn_speed_start /float(i+1) for j in range(len(cases)):case = cases[j]label = labels[j] error+= self.back_propagate(case, label, learn,correct)if((i+1)%500==0):print("error:",error)def test(self): #學習異或N = 200d = -4r = 10width = 6data_source = moon_data_class(N, d, r, width)data = data_source.dbmoon()# x0 = [1 for x in range(1,401)]input_cells = np.array([np.reshape(data[0:2*N, 0], len(data)), np.reshape(data[0:2*N, 1], len(data))]).transpose()labels_pre = [[1.0] for y in range(1, 201)]labels_pos = [[0.0] for y in range(1, 201)]labels=labels_pre+labels_posself.setup(2,5,1) #初始化神經網絡：輸入層，隱藏層，輸出層元素個數self.train(input_cells,labels,2000,0.05,0.1) #可以更改test_x = []test_y = []test_p = []y_p_old = 0for x in np.arange(-15.,25.,0.1):for y in np.arange(-10.,10.,0.1):y_p =self.predict(np.array([x, y]))if(y_p_old <0.5 and y_p[0] > 0.5):test_x.append(x)test_y.append(y)test_p.append([y_p_old,y_p[0]])y_p_old = y_p[0]#畫決策邊界plt.plot( test_x, test_y, 'g--') plt.plot(data[0:N, 0], data[0:N, 1], 'r*', data[N:2*N, 0], data[N:2*N, 1], 'b*')plt.show() if __name__ == '__main__':nn = BP_NET()nn.test()

4、運行結果

總結

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