3.4.8.15. Example of linear and non-linear models

This is an example plot from the tutorial which accompanies an explanation of the support vector machine GUI.

import numpy as np
import matplotlib.pyplot as plt

from sklearn import svm


rng = np.random.default_rng(27446968)

data that is linearly separable

def linear_model(rseed=42, n_samples=30):
    "Generate data according to a linear model"
    np.random.seed(rseed)

    data = np.random.normal(0, 10, (n_samples, 2))
    data[: n_samples // 2] -= 15
    data[n_samples // 2 :] += 15

    labels = np.ones(n_samples)
    labels[: n_samples // 2] = -1

    return data, labels


X, y = linear_model()
clf = svm.SVC(kernel="linear")
clf.fit(X, y)

plt.figure(figsize=(6, 4))
ax = plt.subplot(111, xticks=[], yticks=[])
ax.scatter(X[:, 0], X[:, 1], c=y, cmap="bone")

ax.scatter(
    clf.support_vectors_[:, 0],
    clf.support_vectors_[:, 1],
    s=80,
    edgecolors="k",
    facecolors="none",
)

delta = 1
y_min, y_max = -50, 50
x_min, x_max = -50, 50
x = np.arange(x_min, x_max + delta, delta)
y = np.arange(y_min, y_max + delta, delta)
X1, X2 = np.meshgrid(x, y)
Z = clf.decision_function(np.c_[X1.ravel(), X2.ravel()])
Z = Z.reshape(X1.shape)

ax.contour(
    X1, X2, Z, [-1.0, 0.0, 1.0], colors="k", linestyles=["dashed", "solid", "dashed"]
)

<matplotlib.contour.QuadContourSet object at 0x7f78e72a1d60>

data with a non-linear separation

def nonlinear_model(rseed=27446968, n_samples=30):
    rng = np.random.default_rng(rseed)

    radius = 40 * rng.random(n_samples)
    far_pts = radius > 20
    radius[far_pts] *= 1.2
    radius[~far_pts] *= 1.1

    theta = rng.random(n_samples) * np.pi * 2

    data = np.empty((n_samples, 2))
    data[:, 0] = radius * np.cos(theta)
    data[:, 1] = radius * np.sin(theta)

    labels = np.ones(n_samples)
    labels[far_pts] = -1

    return data, labels


X, y = nonlinear_model()
clf = svm.SVC(kernel="rbf", gamma=0.001, coef0=0, degree=3)
clf.fit(X, y)

plt.figure(figsize=(6, 4))
ax = plt.subplot(1, 1, 1, xticks=[], yticks=[])
ax.scatter(X[:, 0], X[:, 1], c=y, cmap="bone", zorder=2)

ax.scatter(
    clf.support_vectors_[:, 0],
    clf.support_vectors_[:, 1],
    s=80,
    edgecolors="k",
    facecolors="none",
)

delta = 1
y_min, y_max = -50, 50
x_min, x_max = -50, 50
x = np.arange(x_min, x_max + delta, delta)
y = np.arange(y_min, y_max + delta, delta)
X1, X2 = np.meshgrid(x, y)
Z = clf.decision_function(np.c_[X1.ravel(), X2.ravel()])
Z = Z.reshape(X1.shape)

ax.contour(
    X1,
    X2,
    Z,
    [-1.0, 0.0, 1.0],
    colors="k",
    linestyles=["dashed", "solid", "dashed"],
    zorder=1,
)

plt.show()