SVM: Separating hyperplane for unbalanced classes

Find the optimal separating hyperplane using an SVC for classes that are unbalanced.

We first find the separating plane with a plain SVC and then plot (dashed) the separating hyperplane with automatically correction for unbalanced classes.

Note

This example will also work by replacing SVC(kernel="linear") with SGDClassifier(loss="hinge"). Setting the loss parameter of the SGDClassifier equal to hinge will yield behaviour such as that of a SVC with a linear kernel.

For example try instead of the SVC:

clf = SGDClassifier(n_iter=100, alpha=0.01)

import numpy as np
import matplotlib.pyplot as plt
from sklearn import svm
from sklearn.datasets import make_blobs

# we create two clusters of random points
n_samples_1 = 1000
n_samples_2 = 100
centers = [[0.0, 0.0], [2.0, 2.0]]
clusters_std = [1.5, 0.5]
X, y = make_blobs(
    n_samples=[n_samples_1, n_samples_2],
    centers=centers,
    cluster_std=clusters_std,
    random_state=0,
    shuffle=False,
)

# fit the model and get the separating hyperplane
clf = svm.SVC(kernel="linear", C=1.0)
clf.fit(X, y)

# fit the model and get the separating hyperplane using weighted classes
wclf = svm.SVC(kernel="linear", class_weight={1: 10})
wclf.fit(X, y)

# plot the samples
plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.Paired, edgecolors="k")

# plot the decision functions for both classifiers
ax = plt.gca()
xlim = ax.get_xlim()
ylim = ax.get_ylim()

# create grid to evaluate model
xx = np.linspace(xlim[0], xlim[1], 30)
yy = np.linspace(ylim[0], ylim[1], 30)
YY, XX = np.meshgrid(yy, xx)
xy = np.vstack([XX.ravel(), YY.ravel()]).T

# get the separating hyperplane
Z = clf.decision_function(xy).reshape(XX.shape)

# plot decision boundary and margins
a = ax.contour(XX, YY, Z, colors="k", levels=[0], alpha=0.5, linestyles=["-"])

# get the separating hyperplane for weighted classes
Z = wclf.decision_function(xy).reshape(XX.shape)

# plot decision boundary and margins for weighted classes
b = ax.contour(XX, YY, Z, colors="r", levels=[0], alpha=0.5, linestyles=["-"])

plt.legend(
    [a.collections[0], b.collections[0]],
    ["non weighted", "weighted"],
    loc="upper right",
)
plt.show()