Perceptron demo

This is a demo of a perceptron, which is a type of simple neural network that learns a decision boundary between points. In the following demo, you will see the perceptron being trained to learn what part of space corresponds to the red points, and what part of space corresponds to the blue points.

%matplotlib notebook
import numpy as np
import matplotlib.pyplot as plt

from perceptron import gen_data, set_limits, init_plot, calc_normal

def sigmoid(x):
    return 1 / (1 + np.exp(-x))

def demo(m=20, alpha=0.5, loops=10):
    """Run a demo of training a perceptron.
    
    Parameters
    ----------
    m : int
        Number of datapoints per class
    alpha : float
        Initial learning rate
    loops : int
        Number of times to go through the data
        
    """
    # generate some random data
    x, y = gen_data(m)
        
    # initialize helper variables
    X = np.concatenate([x, np.ones((2 * m, 1))], axis=1)
    errors = np.empty(loops * y.size)

    # set up our initial weights and normal vectors
    w = np.array([0, 0.2, 0])
    normal, boundary = calc_normal(np.random.randn(2), w)

    # initialize the plot
    update_plot = init_plot(x, y, boundary, loops)

    for i in range(loops):
        # update the learning rate
        alpha = alpha * 0.5

        for j in range(y.size):
            # number of iterations so far
            k = i * y.size + j
            
            # compute the output of the perceptron and the error to the true labels
            output = sigmoid(np.dot(w, X.T))
            errors[k] = ((y - output) ** 2).sum()
            
            # update our weights and recalculate the normal vector
            w += alpha * (y[j] - output[j]) * output[j] * (1 - output[j]) * X[j]
            normal, boundary = calc_normal(normal, w)

            # update the plot
            update_plot(errors[:k], boundary)

Run the demo!

demo(loops=5)