NEural Networks

The following code demonstrates how to visualize decision boundaries of a Perceptron classifier using a synthetic dataset. It trains a Perceptron classifier (a simple linear classifier) on a synthetic 2D dataset and plot the decision regions using a custom function.

#
# Helper Function to Plot Decision Regions
#
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.colors import ListedColormap  # for assigning custom colors
from sklearn.linear_model import Perceptron   # classifier
from sklearn.datasets import make_classification  # data generator

# This function visualizes decision boundaries and data points
def plot_decision_regions(X, y, classifier, resolution=0.02):
    # set up marker types and colors to represent different classes
    markers = ('s', 'x', 'o', '^', 'v')
    colors = ('red', 'blue', 'lightgreen', 'gray', 'cyan')

    # define a color map with as many unique colors as there are classes in y
    cmap = ListedColormap(colors[:len(np.unique(y))])

    #
    # plot the decision surface (background prediction)
    #
    # determine the bounds of the plot area with padding.
    x1_min, x1_max = X[:, 0].min() - 1, X[:, 0].max() + 1
    x2_min, x2_max = X[:, 1].min() - 1, X[:, 1].max() + 1

    # create a grid of points spanning the plot area.
    xx1, xx2 = np.meshgrid(np.arange(x1_min, x1_max, resolution),
                          np.arange(x2_min, x2_max, resolution))

    # predict the class for each point in the grid
    Z = classifier.predict(np.array([xx1.ravel(), xx2.ravel()]).T)

    # reshape predictions to match the shape of the meshgrid for plotting
    Z = Z.reshape(xx1.shape)

    # draw filled contours to represent decision regions
    plt.contourf(xx1, xx2, Z, alpha=0.4, cmap=cmap)
    plt.xlim(xx1.min(), xx1.max())
    plt.ylim(xx2.min(), xx2.max())

    #
    # plot the actual data points
    #
    for idx, cl in enumerate(np.unique(y)):
        plt.scatter(x=X[y == cl, 0], y=X[y == cl, 1],
                    alpha=0.8, c=[cmap(idx)],
                    marker=markers[idx], label=f"Class {cl}")

#
# Train a Perceptron on Synthetic Data
#
# create a binary classification dataset with:
#      30 samples, 2 features (for 2D plotting)
#      2 informative features, no redundant features
#      balanced classes with ~30% weight each
#      random_state=300 ensures reproducibility
X, y = make_classification(n_samples=30, n_features=2, n_informative=2, n_redundant=0,
                          n_clusters_per_class=1, weights=[0.5, 0.5], random_state=300)

# visualize the data points before training
plt.scatter(X[:, 0], X[:, 1], s=50)
plt.title('Raw Data')
plt.show()

# initialize the Perceptron classifier
pct = Perceptron(max_iter=100, eta0=0.002, fit_intercept=True, random_state=300)

# train it using .fit(X, y)
pct.fit(X, y)

#
# plot decision boundary
#
plot_decision_regions(X, y, classifier=pct)
plt.title('Perceptron Decision Regions')
plt.xlabel('Feature 1')
plt.ylabel('Feature 2')
plt.legend()
plt.show()