Beta-divergence loss functions

A plot that compares the various Beta-divergence loss functions supported by the Multiplicative-Update (‘mu’) solver in sklearn.decomposition.NMF.

Out:

import numpy as np
import matplotlib.pyplot as plt
from sklearn.decomposition.nmf import _beta_divergence

print(__doc__)

x = np.linspace(0.001, 4, 1000)
y = np.zeros(x.shape)

colors = 'mbgyr'
for j, beta in enumerate((0., 0.5, 1., 1.5, 2.)):
    for i, xi in enumerate(x):
        y[i] = _beta_divergence(1, xi, 1, beta)
    name = "beta = %1.1f" % beta
    plt.plot(x, y, label=name, color=colors[j])

plt.xlabel("x")
plt.title("beta-divergence(1, x)")
plt.legend(loc=0)
plt.axis([0, 4, 0, 3])
plt.show()