Density Estimation for a mixture of GaussiansΒΆ
Plot the density estimation of a mixture of two gaussians. Data is generated from two gaussians with different centers and covariance matrices.
Python source code: plot_gmm_pdf.py
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.colors import LogNorm
from sklearn import mixture
n_samples = 300
# generate random sample, two components
np.random.seed(0)
# generate spherical data centered on (20, 20)
shifted_gaussian = np.random.randn(n_samples, 2) + np.array([20, 20])
# generate zero centered stretched gaussian data
C = np.array([[0., -0.7], [3.5, .7]])
stretched_gaussian = np.dot(np.random.randn(n_samples, 2), C)
# concatenate the two datasets into the final training set
X_train = np.vstack([shifted_gaussian, stretched_gaussian])
# fit a Gaussian Mixture Model with two components
clf = mixture.GMM(n_components=2, covariance_type='full')
clf.fit(X_train)
# display predicted scores by the model as a contour plot
x = np.linspace(-20.0, 30.0)
y = np.linspace(-20.0, 40.0)
X, Y = np.meshgrid(x, y)
XX = np.array([X.ravel(), Y.ravel()]).T
Z = -clf.score_samples(XX)[0]
Z = Z.reshape(X.shape)
CS = plt.contour(X, Y, Z, norm=LogNorm(vmin=1.0,vmax=1000.0),
levels=np.logspace(0, 3, 10))
CB = plt.colorbar(CS, shrink=0.8, extend='both')
plt.scatter(X_train[:, 0], X_train[:, 1], .8)
plt.title('Negative log-likelihood predicted by a GMM')
plt.axis('tight')
plt.show()