Perceptron Algorithm

Hi… guys :) For this time I want to tell you about Perceptron Algorithms to solve an Artificial Neural Network (ANN) problem. For example we will make an ANN model to know the XOR statement target as below.

Input		Target
X1	X2	t
1	1	-1
1	0	1
0	1	1
0	0	-1

We need to finish it with α=0.6 , b=0.2 , w1 (weight of x1) = 0.3 , w2= - 0.2 , and θ=0.7

The formula of Perceptron Algorithms as follows:

·         θ is a threshold of activation function to calculating the output of Perceptron Algorithms.

·         Xi is input of ANN

·         t  is the target of ANN

·         wi (w1,w2,…,wn) is weight of input Xi

·         b is bias of input an ANN

·         net = S xiwi + b

·         α is learning rate of Perceptron

·         Activation Function   y=f(net)  =  1 , if  net > θ ;  0 , if  - θ ≤ net ≤ θ ;  -1 , if  net ≤ - θ

·         Dwi = α t xi

·         Db = α t

·         wi (new) = wi (old) + Dwi

·         b (new) = b (old) + Db

Okay , then we try to calculate the Perceptron Algorithms as follows  :

The 1^st  Iteration

Input		Target	net	Output f(net)	Change of weight			weight
X1	X2	t			Dw1	Dw2	Db	w1	w2	b
1	1	-1	-0.3	-1	0	0	0	0.3	-0.2	0.2
1	0	1	0.5	0	0.6	0	0.6	0.9	-0.2	0.8
0	1	1	0.6	0	0	0.6	0.6	0.9	0.4	1.4
0	0	-1	-1.4	-1	0	0	0	0.9	0.4	1.4

Note : if  t = y then fill the value of  Dwi and Db  by Nol

The 2^nd   Iteration

Input		Target	net	Output f(net)	Change of weight			weight
X1	X2	t			Dw1	Dw2	Db	w1	w2	b
1	1	-1	-2.7	-1	0	0	0	0.9	0.4	1.4
1	0	1	2.3	1	0	0	0	0.9	0.4	1.4
0	1	1	1.8	1	0	0	0	0.9	0.4	1.4
0	0	-1	-1.4	-1	0	0	0	0.9	0.4	1.4

so the conclusion is the Perceptron algorithm can solve ANN Problem (XOR Statement) with  α=0.6 , b=0.2 , w1 (weight of x1) = 0.3 , w2= - 0.2 , and θ=0.7 on the 2^nd   Iteration.