完整实现DNN，包括前向传播和反向传播。实现一个2次函数的拟合。
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Sun May 6 16:11:40 2018
@author: wsw
"""
# construct simple DNN
import numpy as np
import matplotlib.pyplot as plt
import sys
def generate_data():
x = np.linspace(-2,2,100)[np.newaxis,:]
noise = np.random.normal(0.0,0.5,size=(1,100))
y = x**2+noise
return x,y
class DNN():
def __init__(self,input_nodes=1,hidden1_nodes=4,hidden2_nodes=4,output_nodes=1):
self.input_nodes = input_nodes
self.hidden1_nodes = hidden1_nodes
self.hidden2_nodes = hidden2_nodes
self.output_nodes = output_nodes
self.build_DNN()
def build_DNN(self):
np.random.seed(1)
# Layer1 parameter
self.w1 = np.random.normal(0.0,0.1,size=(self.hidden1_nodes,self.input_nodes))
self.b1 = np.zeros(shape=(self.hidden1_nodes,1))
# Layer2 parameter
self.w2 = np.random.normal(0.0,0.2,size=(self.hidden2_nodes,self.hidden1_nodes))
self.b2 = np.ones(shape=(self.hidden2_nodes,1))
# Layer3 parameter
self.w3 = np.random.normal(0.0,0.5,size=(self.output_nodes,self.hidden2_nodes))
self.b3 = np.zeros(shape=(self.output_nodes,1))
def forwardPropagation(self,inputs):
self.z1 = np.matmul(self.w1,inputs) + self.b1
self.a1 = 1/(1+np.exp(-self.z1))
self.z2 = np.matmul(self.w2,self.a1) + self.b2
self.a2 = 1/(1+np.exp(-self.z2))
self.z3 = np.matmul(self.w3,self.a2) + self.b3
self.a3 = self.z3
def backwardPropagation(self,da,a,a_1,w,b,last=False):
'''
da:current layer activation output partial devirate result
a:current layer activation output
a_1:previous layer of current layer activation output
w:current parameter
b:current bias
'''
# dz = da/dz
if last:
dz = da
else:
dz = a*(1-a)*da
# dw = dz/dw
nums = da.shape[1]
dw = np.matmul(dz,a_1.T)/nums
db = np.mean(dz,axis=1,keepdims=True)
# da_1 = dz/da_1
da_1 = np.matmul(w.T,dz)
w -= 0.5*dw
b -= 0.5*db
return da_1
def train(self,x,y,max_iter=50000):
for i in range(max_iter):
self.forwardPropagation(x)
#print(self.a3)
loss = 0.5*np.mean((self.a3-y)**2)
da = self.a3-y
da_2 = self.backwardPropagation(da,self.a3,self.a2,self.w3,self.b3,True)
da_1 = self.backwardPropagation(da_2,self.a2,self.a1,self.w2,self.b2)
da_0 = self.backwardPropagation(da_1,self.a1,x,self.w1,self.b1)
self.view_bar(i+1,max_iter,loss)
return self.a3
def view_bar(self,step,total,loss):
rate = step/total
rate_num = int(rate*40)
r = '\rstep-%d loss value-%.4f[%s%s]\t%d%% %d/%d'%(step,loss,'>'*rate_num,'-'*(40-rate_num),
int(rate*100),step,total)
sys.stdout.write(r)
sys.stdout.flush()
if __name__ == '__main__':
x,y = generate_data()
plt.scatter(x,y,c='r')
plt.ion()
print('plot')
dnn = DNN()
predict = dnn.train(x,y)
plt.plot(x.flatten(),predict.flatten(),'-')
plt.show()
