SGD: Separating hyperplane with weighted classes

Fit linear SVMs with and without class weighting. Allows to handle problems with unbalanced classes.

Python source code: plot_sgd_weighted_classes.py

print __doc__

import numpy as np
import pylab as pl
from scikits.learn.linear_model import SGDClassifier

# we create 40 separable points
np.random.seed(0)
n_samples_1 = 1000
n_samples_2 = 100
X = np.r_[1.5*np.random.randn(n_samples_1, 2),
          0.5*np.random.randn(n_samples_2, 2) + [2, 2]]
y = np.array([0]*(n_samples_1) + [1]*(n_samples_2), dtype=np.float64)
idx = np.arange(y.shape[0])
np.random.shuffle(idx)
X = X[idx]
y = y[idx]
mean = X.mean(axis=0)
std = X.std(axis=0)
X = (X - mean) / std

# fit the model and get the separating hyperplane
clf = SGDClassifier(n_iter=100, alpha=0.01)
clf.fit(X, y)

w = clf.coef_
a = -w[0] / w[1]
xx = np.linspace(-5, 5)
yy = a * xx - clf.intercept_ / w[1]


# get the separating hyperplane using weighted classes
wclf = SGDClassifier(n_iter=100, alpha=0.01)
wclf.fit(X, y, class_weight={1: 10})

ww = wclf.coef_
wa = -ww[0] / ww[1]
wyy = wa * xx - wclf.intercept_ / ww[1]

# plot separating hyperplanes and samples
pl.set_cmap(pl.cm.Paired)
h0 = pl.plot(xx, yy, 'k-')
h1 = pl.plot(xx, wyy, 'k--')
pl.scatter(X[:,0], X[:,1], c=y)
pl.legend((h0, h1), ('no weights', 'with weights'))

pl.axis('tight')
pl.show()