3.4.8.15. Example of linear and non-linear modelsΒΆ

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=plt.cm.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"]
)
plot svm non linear
<matplotlib.contour.QuadContourSet object at 0x7fd237f78f10>

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=plt.cm.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()
plot svm non linear

Total running time of the script: (0 minutes 0.069 seconds)

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