def test_estimate_so_matrix(self):
points = self.so.random_uniform(2)
mean_vec = ExponentialBarycenter(group=self.so)
mean_vec.fit(points)
logs = self.so.log(points, mean_vec.estimate_)
result = gs.sum(logs, axis=0)
expected = gs.zeros_like(points[0])
self.assertAllClose(result, expected)
def test_fit_matrix_se(self):
se_mat = SpecialEuclidean(n=3, default_point_type='matrix')
X = se_mat.random_uniform(self.n_samples)
estimator = ExponentialBarycenter(se_mat)
estimator.fit(X)
mean = estimator.estimate_
tpca = TangentPCA(metric=se_mat, point_type='matrix')
tangent_projected_data = tpca.fit_transform(X, base_point=mean)
result = tpca.inverse_transform(tangent_projected_data)
expected = X
self.assertAllClose(result, expected)
def test_linear_mean(self):
euclidean = Euclidean(3)
point = euclidean.random_point(self.n_samples)
estimator = ExponentialBarycenter(euclidean)
estimator.fit(point)
result = estimator.estimate_
expected = gs.mean(point, axis=0)
self.assertAllClose(result, expected)
def test_coincides_with_frechet_so(self):
gs.random.seed(0)
point = self.so.random_uniform(self.n_samples)
estimator = ExponentialBarycenter(self.so, max_iter=40, epsilon=1e-10)
estimator.fit(point)
result = estimator.estimate_
frechet_estimator = FrechetMean(self.so.bi_invariant_metric,
max_iter=40,
epsilon=1e-10)
frechet_estimator.fit(point)
expected = frechet_estimator.estimate_
self.assertAllClose(result, expected)
def test_coincides_with_frechet_so(self):
point = self.so.random_uniform(self.n_samples)
estimator = ExponentialBarycenter(self.so, max_iter=32, epsilon=1e-12)
estimator.fit(point)
result = estimator.estimate_
print(self.so.default_point_type)
so_vector = SpecialOrthogonal(3, default_point_type='vector')
frechet_estimator = FrechetMean(so_vector.bi_invariant_metric,
max_iter=32,
epsilon=1e-10,
point_type='vector')
vector_point = so_vector.rotation_vector_from_matrix(point)
frechet_estimator.fit(vector_point)
mean = frechet_estimator.estimate_
expected = so_vector.matrix_from_rotation_vector(mean)
result = estimator.estimate_
self.assertAllClose(result, expected)
def test_estimate_one_sample_se(self):
point = self.se_mat.random_point()
estimator = ExponentialBarycenter(self.se_mat)
estimator.fit(point)
result = estimator.estimate_
expected = point
self.assertAllClose(result, expected)
point = self.so_vec.random_uniform(1)
estimator = ExponentialBarycenter(self.so_vec)
estimator.fit(point)
result = estimator.estimate_
expected = point
self.assertAllClose(result, expected)
def test_estimate_and_belongs_so(self):
point = self.so.random_uniform(self.n_samples)
estimator = ExponentialBarycenter(self.so)
estimator.fit(point)
barexp = estimator.estimate_
result = self.so.belongs(barexp)
expected = True
self.assertAllClose(result, expected)
point = self.so_vec.random_uniform(self.n_samples)
estimator = ExponentialBarycenter(self.so_vec)
estimator.fit(point)
barexp = estimator.estimate_
result = self.so_vec.belongs(barexp)
expected = True
self.assertAllClose(result, expected)
def test_estimate_and_reach_max_iter_se(self):
point = self.se_mat.random_point(1)
estimator = ExponentialBarycenter(self.se_mat, max_iter=2)
points = gs.array([point, point])
estimator.fit(points)
result = estimator.estimate_
expected = point
self.assertAllClose(result, expected)
point = self.so_vec.random_uniform(1)
estimator = ExponentialBarycenter(self.so_vec, max_iter=2)
points = gs.array([point, point])
estimator.fit(points)
result = estimator.estimate_
expected = point
self.assertAllClose(result, expected)
def test_estimate_weights(self):
point = self.so.random_uniform(self.n_samples)
estimator = ExponentialBarycenter(self.so, verbose=True)
weights = gs.arange(self.n_samples)
estimator.fit(point, weights=weights)
barexp = estimator.estimate_
result = self.so.belongs(barexp)
expected = True
self.assertAllClose(result, expected)
point = self.so_vec.random_uniform(self.n_samples)
estimator = ExponentialBarycenter(self.so_vec)
estimator.fit(point, weights=weights)
barexp = estimator.estimate_
result = self.so_vec.belongs(barexp)
expected = True
self.assertAllClose(result, expected)
def __init__(self, geometry, **kwargs):
if isinstance(geometry, LieGroup):
self._used_geometry = geometry
self.estimator = ExponentialBarycenter(group=self._used_geometry,
**kwargs)
else:
if hasattr(geometry, 'metric'):
self._used_geometry = geometry.metric
elif isinstance(geometry, RiemannianMetric):
self._used_geometry = geometry
else:
raise ValueError('The input geometry must be either a '
'Manifold equipped with a '
'RiemannianMetric, or a RiemannianMetric or a'
' LieGroup')
self.estimator = FrechetMean(metric=self._used_geometry, **kwargs)
self.point_type = geometry.default_point_type
self.geometry = geometry