Implement OR and AND Logic Functions using Perceptron Neural Network

Theory

The perceptron is a fundamental building block of neural networks used to solve binary classification problems. It consists of input values, weights and bias, net sum, and an activation function.

Perceptron Structure:

The perceptron takes input vectors, multiplies them by corresponding weight vectors, adds bias, and passes the result through an activation function.

Perceptron Algorithm:

The Perceptron Algorithm outputs binary values (0 or 1) and can only classify linearly separable vector sets.

Program

            from numpy import array, random, dot
            from random import choice
            from pylab import ylim, plot
            from matplotlib import pyplot as plt

            step_function = lambda x: 0 if x < 0 else 1

            training_dataset = [
                (array([0,0,1]), 0),
                (array([0,1,1]), 1),
                (array([1,0,1]), 1),
                (array([1,1,1]), 1),
            ]

            weights = random.rand(3)
            error = []
            learning_rate = 0.2
            n = 100

            for j in range(n):
                x, expected = choice(training_dataset)
                result = dot(weights, x)
                err = expected - step_function(result)
                error.append(err)
                weights += learning_rate * err * x

            for x, _ in training_dataset:
                result = dot(x, weights)
                print('{}: {} -> {}'.format(x[:2], result, step_function(result)))

            ylim([-1,1])
            plot(error)
            plt.show()