How to implement two-layer neural network and perceptron model in Python

This article will share with you how to use Python to implement a two-layer neural network and perceptron model. The specific content and examples are as follows for your reference

python 3.4 Because numpy is used

Here we first implement a perceptron model to achieve the following correspondence

[[0,0,1], ——- 0 
 [0,1,1], ——- 1 
 [1,0,1], ——- 0 
 [1,1,1]] ——- 1

It can be seen from the above data: the input is three channels, and the output It's single channel.

Activation hereFunctionWe use the sigmoid function f(x)=1/(1+exp(-x))

The derivative derivation is as follows:

L0=W*X;
 z=f(L0);
 error=y-z;
 delta =error * f'(L0) * X;
 W=W+delta;

The python code is as follows:

import numpy as np
 
#sigmoid function
 
def nonlin(x, deriv = False):
  if(deriv==True):
    return x*(1-x)
  return 1/(1+np.exp(-x))
 
 
# input dataset
 
X=np.array([[0,0,1],
      [0,1,1],
      [1,0,1],
      [1,1,1]])
 
# output dataset
 
y=np.array([[0,1,0,1]]).T
 
#seed( ) 用于指定随机数生成时所用算法开始的整数值，
#如果使用相同的seed( )值，则每次生成的随即数都相同，
#如果不设置这个值，则系统根据时间来自己选择这个值，
#此时每次生成的随机数因时间差异而不同。
np.random.seed(1) 
 
# init weight value with mean 0
 
syn0 = 2*np.random.random((3,1))-1  
 
for iter in range(1000):
  # forward propagation
  L0=X
  L1=nonlin(np.dot(L0,syn0))
 
  # error
  L1_error=y-L1
 
  L1_delta = L1_error*nonlin(L1,True)
 
  # updata weight
  syn0+=np.dot(L0.T,L1_delta)
 
print("Output After Training:")
print(L1)

It can be seen from the output results that the corresponding relationship is basically achieved.

Next, a two-layer network is used to achieve the above task. A hidden layer is added here, and the hidden layer contains 4 neurons.

   
import numpy as np
 
def nonlin(x, deriv = False):
  if(deriv == True):
    return x*(1-x)
  else:
    return 1/(1+np.exp(-x))
 
#input dataset
X = np.array([[0,0,1],
       [0,1,1],
       [1,0,1],
       [1,1,1]])
 
#output dataset
y = np.array([[0,1,1,0]]).T
 
#the first-hidden layer weight value
syn0 = 2*np.random.random((3,4)) - 1
 
#the hidden-output layer weight value
syn1 = 2*np.random.random((4,1)) - 1
 
for j in range(60000):
  l0 = X     
  #the first layer,and the input layer
  l1 = nonlin(np.dot(l0,syn0))
  #the second layer,and the hidden layer
  l2 = nonlin(np.dot(l1,syn1))
  #the third layer,and the output layer
 
 
  l2_error = y-l2   
  #the hidden-output layer error
 
  if(j%10000) == 0:
    print "Error:"+str(np.mean(l2_error))
 
  l2_delta = l2_error*nonlin(l2,deriv = True)
 
  l1_error = l2_delta.dot(syn1.T)  
  #the first-hidden layer error
 
  l1_delta = l1_error*nonlin(l1,deriv = True)
 
  syn1 += l1.T.dot(l2_delta)
  syn0 += l0.T.dot(l1_delta)
 
print "outout after Training:"
print l2

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