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Density Estimation for a Gaussian mixture#

Plot the density estimation of a mixture of two Gaussians. Data is generated from two Gaussians with different centers and covariance matrices.

Negative log-likelihood predicted by a GMM

# Authors: The scikit-learn developers
# SPDX-License-Identifier: BSD-3-Clause
importmatplotlib.pyplotasplt
importnumpyasnp
frommatplotlib.colorsimport LogNorm
fromsklearnimport 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, -0.7], [3.5, 0.7]])
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.GaussianMixture (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)
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], 0.8)
plt.title ("Negative log-likelihood predicted by a GMM")
plt.axis ("tight")
plt.show ()