SVM margin visualisation

svm-visualisation.py

import matplotlib.pyplot as plt
import numpy as np
from numpy.random import multivariate_normal

np.random.seed(100)

num_samples = 20

X = np.concatenate((
    multivariate_normal(mean=np.array([2, 2]),
                        cov=1.0*np.array([[1, 0], [0, 1]]),
                        size=num_samples),
    multivariate_normal(mean=np.array([-2, -2]),
                        cov=1.0*np.array([[1, 0], [0, 1]]),
                        size=num_samples)))

y = np.array(num_samples * [1] + num_samples * [-1])

mins = np.min(X, axis=0)
maxs = np.max(X, axis=0)

delta = 0.25

xlims = [mins[0] - delta, maxs[0] + delta]
ylims = [mins[1] - delta, maxs[1] + delta]

def plot_data(ax, X, xlims, ylims):
    
    num_samples = X.shape[0] // 2

    ax.set_xlabel('x1') ; ax.set_ylabel('x2')
    ax.set_aspect('equal', adjustable='box')

    ax.set_xlim(xlims)
    ax.set_ylim(ylims)

    # plot training data
    plt.scatter(X[:num_samples, 0], X[:num_samples, 1], color='orange', alpha=0.8)
    plt.scatter(X[num_samples:, 0], X[num_samples:, 1], color='blue', alpha=0.8)
    
def plot_projection(ax, b, m, points_coords, xlims, ylims):

    # start with line coordinates
    xs = np.linspace(xlims[0], xlims[-1], 2)
    ys = m * xs + b

    # convert to vectors
    line_vec = np.array([xs[-1] - xs[0], ys[-1] - ys[0]])
    b_vec = np.array([0, b])

    for coords in points_coords:

        point_vec = coords - b_vec

        # compute projection
        proj = (point_vec.dot(line_vec) / line_vec.dot(line_vec)) * line_vec

        proj_coords = b_vec + proj

        # plot data
        ax.plot(xs, ys, 'red', linestyle='dashed')
        ax.plot([coords[0], proj_coords[0]],
                [coords[1], proj_coords[1]],
                linestyle='dashed', color='black', alpha=0.8)

    w = point_vec - proj
    w /= np.linalg.norm(w)

    mag = np.abs((-1 - b) / w.dot(coords))
    w *= mag

    x, y = np.mean(xs), np.mean(ys)

    ax.arrow(x, y, *w, width=0.05, linewidth=0.5, color='purple')

    ax.text(x + w[0] + 0.1, y + w[1], '$||w||_2 = %.02f$' % mag,
            ha='left', va='top')

idx1 = 19     # orange data
idx2 = 37     # blue data

fig, ax = plt.subplots()

plot_data(ax, X, xlims, ylims)
plot_projection(ax, -0.4, -1, [X[idx1], X[idx2]], xlims, ylims)
fig.savefig('fig1.png', bbox_inches='tight')

idx1 = 18     # orange data
idx2 = 24     # blue data

fig, ax = plt.subplots()

plot_data(ax, X, xlims, ylims)
plot_projection(ax, -0.1, -0.05, [X[idx1], X[idx2]], xlims, ylims)
fig.savefig('fig2.png', bbox_inches='tight')