Perceptron

The perceptron is a classifier model represented by a vector [X], that represents the inputs, and a vector [W] that represents the weights of the model:

The weighted sum y(t) is filtered through a step function f (the Heaviside or sign functions are usually used).

The f of Heaviside function is defined as follows:

f = 1 if y(t) >0
f= 0 if y(t) <=0

If f is the "sign" function:

f = 1 if y(t) >0
f = -1 if y(t) <=0

Implementation of the Perceptron Model to Predict the Output of the OR Boolean table

A	B	Output
0	0	0
0	1	1
1	0	1
1	1	1



In [16]:

    
from random import choice
from numpy import array, dot, random

# Here is the implementation with the Heaviside function.
Heaviside = lambda x: 0 if x <=0 else 1

# For implementation with the sign function:
#step_ = lambda x: -1 if x < 0 else 1

training= [(array([0,0,1]), 0),
           (array([0,1,1]), 1),
           (array([1,0,1]), 1),
           (array([1,1,1]), 1),]
test=[array([0,1,1]),array([0,0,1])]

w=random.rand(3)
print("w initial=", w)
errors =[]
eta= 2/10
n=50

for i in range(n):
    x, expected = choice(training)    
    result=dot(w,x)
    error = expected - Heaviside(result)
    errors.append(error)
    if error!=0:
       w+= eta*error*x
print("w final=", w)    

for x in test:
    result = dot(x,w)
    print('Test Results')
    print("{}:{} -->{}".format(x[:2], result, Heaviside(result)))









    



w initial= [ 0.98784644  0.6091611   0.10710896]
w final= [ 0.98784644  0.6091611  -0.09289104]
Test Results
[0 1]:0.5162700623383536 -->1
Test Results
[0 0]:-0.0928910406643027 -->0

Convergence of the model to error = 0



In [17]:

    
%matplotlib inline
from pylab import plot, ylim
ylim([-1, 1])
plot(errors)









    Out[17]:





[<matplotlib.lines.Line2D at 0x6096930>]