Implementation of Perceptron Algorithm for NOT Logic in Python

Implementation of Perceptron Algorithm for NOT Logic in Python
Fig: NOT gate

In this article, you’ll learn how to implement the perceptron algorithm for NOT logic in python. The steps that we’ll follow will also enable you to easily implement any other logic function using the perceptron algorithm.

Perceptron algorithm for NOT logic in Python

Fig: A perceptron with two inputs
Fig: A perceptron with two inputs

A Perceptron can simply be defined as a feed-forward neural network with a single hidden layer. It takes a certain number of inputs (x1 and x2 in this case), processes them using the perceptron algorithm, and then finally produce the output which can either be 0 or 1. As can take only two values, a perceptron can also act as a linear classifier. According to the perceptron algorithm,

y = Wx + b, where Wx = w1x1 + w2x2, W = perceptron model weights and b = bias
Also, y = 1 if  Wx + b > 0 and 0 if  Wx + b ≤ 0

The steps that we’ll use to implement the NOT logic using a perceptron is similar to how a neural network is trained.

  • First, we’ll initialize the weights and the bias of the perceptron.
  • Then the input will be forward propagated through the network and output ‘y’ will be produced.
  • This obtained result will then be compared with the actual result and the error obtained will be backpropagated through the network to adjust the weights and the bias of the model. This will minimize the error obtained.
  • We’ll then repeat the above steps for all the inputs present.

NOT Logic

NOT gate performs complementation function i.e. its output is just the complement of its input. They are also termed as inverters because they simply invert the input signal. The truth table of a NOT gate is shown below:

+---+---+
| x | y |
+---+---+
| 0 | 1 |
+---+---+
| 1 | 0 |
+---+---+

Perceptron Algorithm

As discussed above, according to the perceptron algorithm y = Wx+ b. As NOT gate is a single input gate, Wx = w1x1 in this case. To begin with, let us assume  w1 = 1 and b = 1. Let, the result obtained using the perceptron algorithm be y’ and the actual result be (given in the truth table).

  • Now, using the first row of the truth table (x = 0) as our input, we get y’ = 1.0 + 1 = 1 which is same as y.
  • Using the second row as our input (x=1) , we get y’ = 1.1 + 1 = 2 ≠ y. To make y = y’, let w1 = -1. This makes y’ = (-1).1 + 1 = 0 = y. By calculation, you’ll observe that these values of the weight and the bias satisfy the NOT logic for both the rows.

Therefore, the model to implement the NOT logic using the perceptron algorithm will be:

y = (-1).x1 + 1

Code

# Importing the required libraries
import numpy as np

# Defining the activation function
def activation_function(y):
    if y > 0:
        y = 1
    elif y <= 0:
        y = 0
    return y

# W = weights of the perceptron model
W = np.array([-1])
# b = bias of the model
b = 1

# Defining the perceptron algorithm
def perceptron_algorithm(x):
    # y = w1x1 + b
    y = np.dot(W, x) + b
    # y = 1 if Wx+b > 0 else y = 0 
    y = activation_function(y)
    return y

# Input values to verify the NOT logic 
input1 = np.array([0])
input2 = np.array([1])

# Printing the results
print('NOT Logic: \n')
print(f'x = 0 => y = {perceptron_algorithm(input1)}')
print(f'x = 1 => y = {perceptron_algorithm(input2)}')

OUTPUT:

NOT Logic:

x = 0 => y = 1
x = 1 => y = 0

As we can see, the model predictions are the same as the actual results. Hence, we successfully implemented the Perceptron Algorithm for NOT Logic. You can also try implementing other logic functions by following the same steps and obtaining the correct values of the model weights and bias.

Also read:

Predicting video game sales using Machine Learning in Python

Understanding Artificial Neural network (ANN)

How to choose number of epochs to train a neural network in Keras

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