def test_normalization_factor(self):
"""Test for Gaussian distribution normalization factor."""
gmm = RiemannianEM(self.metric)
variances_range, normalization_factor_var, phi_inv_var = \
gmm.normalization_factor_init(
gs.arange(ZETA_LOWER_BOUND, ZETA_UPPER_BOUND, ZETA_STEP))
self.assertAllClose(normalization_factor_var[4], 0.00291884, TOLERANCE)
self.assertAllClose(phi_inv_var[3], 0.00562326, TOLERANCE)
variances_test = gs.array([0.8, 1.2])
norm_factor_test = find_normalization_factor(variances_test,
variances_range,
normalization_factor_var)
norm_factor_verdict = gs.array([0.79577319, 2.3791778])
self.assertAllClose(norm_factor_test, norm_factor_verdict, TOLERANCE)
norm_factor_test2 = self.metric.normalization_factor(variances_test)
self.assertAllClose(norm_factor_test2, norm_factor_verdict, TOLERANCE)
norm_factor_test3, norm_factor_gradient_test = \
self.metric.norm_factor_gradient(variances_test)
norm_factor_gradient_verdict = gs.array([3.0553115709, 2.53770926])
self.assertAllClose(norm_factor_test3, norm_factor_verdict, TOLERANCE)
self.assertAllClose(norm_factor_gradient_test,
norm_factor_gradient_verdict, TOLERANCE)
find_var_test = find_variance_from_index(
gs.array([0.5, 0.4, 0.3, 0.2]), variances_range, phi_inv_var)
find_var_verdict = gs.array([0.481, 0.434, 0.378, 0.311])
self.assertAllClose(find_var_test, find_var_verdict, TOLERANCE)
def expectation_maximisation_poincare_ball():
"""Apply EM algorithm on three random data clusters."""
dim = 2
n_samples = 5
cluster_1 = gs.random.uniform(low=0.2, high=0.6, size=(n_samples, dim))
cluster_2 = gs.random.uniform(low=-0.6, high=-0.2, size=(n_samples, dim))
cluster_3 = gs.random.uniform(low=-0.3, high=0, size=(n_samples, dim))
cluster_3[:, 0] = -cluster_3[:, 0]
data = gs.concatenate((cluster_1, cluster_2, cluster_3), axis=0)
n_clusters = 3
manifold = PoincareBall(dim=2)
metric = manifold.metric
EM = RiemannianEM(n_gaussians=n_clusters,
metric=metric,
initialisation_method='random')
means, variances, mixture_coefficients = EM.fit(data=data)
# Plot result
plot = plot_gaussian_mixture_distribution(data,
mixture_coefficients,
means,
variances,
plot_precision=100,
save_path='result.png',
metric=metric)
return plot
def test_fit(self):
"""Test fitting data into a GMM."""
gmm_learning = RiemannianEM(
riemannian_metric=self.metric,
n_gaussians=self.n_gaussian,
initialisation_method=self.initialisation_method,
mean_method=self.mean_method)
means, variances, coefficients = gmm_learning.fit(self.data)
self.assertTrue((coefficients < 1).all() and (coefficients > 0).all())
self.assertTrue((variances < 1).all() and (variances > 0).all())
self.assertTrue(self.space.belongs(means).all())
def test_fit_init_random_sphere(self):
"""Test fitting data into a GMM."""
space = Hypersphere(2)
gmm_learning = RiemannianEM(
metric=space.metric,
n_gaussians=2,
initialisation_method=self.initialisation_method,
)
means = space.random_uniform(2)
cluster_1 = space.random_von_mises_fisher(mu=means[0], kappa=20, n_samples=140)
cluster_2 = space.random_von_mises_fisher(mu=means[1], kappa=20, n_samples=140)
data = gs.concatenate((cluster_1, cluster_2), axis=0)
means, variances, coefficients = gmm_learning.fit(data)
self.assertTrue((coefficients < 1).all() and (coefficients > 0).all())
self.assertTrue((variances < 1).all() and (variances > 0).all())
self.assertTrue(space.belongs(means).all())