def test_fit_matrix(self):
expected = 2
X = self.spd.random_point(n_samples=5)
tpca = TangentPCA(metric=self.spd_metric, n_components=expected)
tpca.fit(X)
result = tpca.n_components_
self.assertAllClose(result, expected)
def test_tangent_pca_error(data):
X = data
trans = TangentPCA(n_components=N_COMPONENTS)
trans.fit(X)
with pytest.raises(ValueError, match="Shape of input is different"):
X_diff_size = np.ones((10, X.shape[1] + 1))
trans.transform(X_diff_size)
def test_tangent_pca_error(self):
X = self.X
tpca = TangentPCA(self.metric, n_components=self.n_components)
tpca.fit(X)
X_diff_size = gs.ones((self.n_samples, gs.shape(X)[1] + 1))
with pytest.raises(ValueError):
tpca.transform(X_diff_size)
def test_fit_to_target_explained_variance(self):
X = self.spd.random_point(n_samples=5)
target = 0.90
tpca = TangentPCA(self.spd_metric, n_components=target)
tpca.fit(X)
result = gs.cumsum(tpca.explained_variance_ratio_)[-1] > target
expected = True
self.assertAllClose(result, expected)
def test_tangent_pca(data):
X = data
trans = TangentPCA(n_components=N_COMPONENTS)
assert trans.demo_param == 'demo'
trans.fit(X)
assert trans.n_features_ == X.shape[1]
X_trans = trans.transform(X)
assert_allclose(X_trans, np.sqrt(X))
X_trans = trans.fit_transform(X)
assert_allclose(X_trans, np.sqrt(X))
def main():
fig = plt.figure(figsize=(15, 5))
data = SO3_GROUP.random_uniform(n_samples=N_SAMPLES)
mean = METRIC.mean(data)
tpca = TangentPCA(metric=METRIC, n_components=N_COMPONENTS)
tpca = tpca.fit(data, base_point=mean)
tangent_projected_data = tpca.transform(data)
print('Coordinates of the Log of the first 5 data points at the mean, '
'projected on the principal components:')
print(tangent_projected_data[:5])
ax_var = fig.add_subplot(121)
xticks = np.arange(1, N_COMPONENTS + 1, 1)
ax_var.xaxis.set_ticks(xticks)
ax_var.set_title('Explained variance')
ax_var.set_xlabel('Number of Principal Components')
ax_var.set_ylim((0, 1))
ax_var.plot(xticks, tpca.explained_variance_ratio_)
ax = fig.add_subplot(122, projection="3d")
plt.setp(ax, xlabel="X", ylabel="Y", zlabel="Z")
ax.set_title('Data in SO3 (black) and Frechet mean (color)')
visualization.plot(data, ax, space='SO3_GROUP', color='black')
visualization.plot(mean, ax, space='SO3_GROUP', linewidth=3)
ax.set_xlim((-2, 2))
ax.set_ylim((-2, 2))
ax.set_zlim((-2, 2))
plt.show()
def test_fit_fit_transform_matrix(self):
X = self.spd.random_uniform(n_samples=5)
tpca = TangentPCA(
metric=self.spd_metric)
expected = tpca.fit_transform(X)
result = tpca.fit(X).transform(X)
self.assertAllClose(result, expected)
def main():
"""Perform tangent PCA at the mean."""
fig = plt.figure(figsize=(15, 5))
hyperbolic_plane = Hyperbolic(dimension=2)
data = hyperbolic_plane.random_uniform(n_samples=140)
mean = hyperbolic_plane.metric.mean(data)
tpca = TangentPCA(metric=hyperbolic_plane.metric, n_components=2)
tpca = tpca.fit(data, base_point=mean)
tangent_projected_data = tpca.transform(data)
geodesic_0 = hyperbolic_plane.metric.geodesic(
initial_point=mean, initial_tangent_vec=tpca.components_[0])
geodesic_1 = hyperbolic_plane.metric.geodesic(
initial_point=mean, initial_tangent_vec=tpca.components_[1])
n_steps = 100
t = np.linspace(-1, 1, n_steps)
geodesic_points_0 = geodesic_0(t)
geodesic_points_1 = geodesic_1(t)
print('Coordinates of the Log of the first 5 data points at the mean, '
'projected on the principal components:')
print(tangent_projected_data[:5])
ax_var = fig.add_subplot(121)
xticks = np.arange(1, 2 + 1, 1)
ax_var.xaxis.set_ticks(xticks)
ax_var.set_title('Explained variance')
ax_var.set_xlabel('Number of Principal Components')
ax_var.set_ylim((0, 1))
ax_var.plot(xticks, tpca.explained_variance_ratio_)
ax = fig.add_subplot(122)
visualization.plot(mean,
ax,
space='H2_poincare_disk',
color='darkgreen',
s=10)
visualization.plot(geodesic_points_0,
ax,
space='H2_poincare_disk',
linewidth=2)
visualization.plot(geodesic_points_1,
ax,
space='H2_poincare_disk',
linewidth=2)
visualization.plot(data,
ax,
space='H2_poincare_disk',
color='black',
alpha=0.7)
plt.show()
def main():
"""Perform tangent PCA at the mean on the sphere."""
fig = plt.figure(figsize=(15, 5))
sphere = Hypersphere(dim=2)
data = sphere.random_von_mises_fisher(kappa=15, n_samples=140)
mean = FrechetMean(metric=sphere.metric)
mean.fit(data)
mean_estimate = mean.estimate_
tpca = TangentPCA(metric=sphere.metric, n_components=2)
tpca = tpca.fit(data, base_point=mean_estimate)
tangent_projected_data = tpca.transform(data)
geodesic_0 = sphere.metric.geodesic(
initial_point=mean_estimate, initial_tangent_vec=tpca.components_[0]
)
geodesic_1 = sphere.metric.geodesic(
initial_point=mean_estimate, initial_tangent_vec=tpca.components_[1]
)
n_steps = 100
t = np.linspace(-1, 1, n_steps)
geodesic_points_0 = geodesic_0(t)
geodesic_points_1 = geodesic_1(t)
logging.info(
"Coordinates of the Log of the first 5 data points at the mean, "
"projected on the principal components:"
)
logging.info("\n{}".format(tangent_projected_data[:5]))
ax_var = fig.add_subplot(121)
xticks = np.arange(1, 2 + 1, 1)
ax_var.xaxis.set_ticks(xticks)
ax_var.set_title("Explained variance")
ax_var.set_xlabel("Number of Principal Components")
ax_var.set_ylim((0, 1))
ax_var.plot(xticks, tpca.explained_variance_ratio_)
ax = fig.add_subplot(122, projection="3d")
visualization.plot(mean_estimate, ax, space="S2", color="darkgreen", s=10)
visualization.plot(geodesic_points_0, ax, space="S2", linewidth=2)
visualization.plot(geodesic_points_1, ax, space="S2", linewidth=2)
visualization.plot(data, ax, space="S2", color="black", alpha=0.7)
plt.show()
def main():
"""Perform tangent PCA at the mean on SO(3)."""
fig = plt.figure(figsize=(15, 5))
data = SO3_GROUP.random_uniform(n_samples=N_SAMPLES)
mean = FrechetMean(metric=METRIC)
mean.fit(data)
mean_estimate = mean.estimate_
tpca = TangentPCA(metric=METRIC, n_components=N_COMPONENTS)
tpca = tpca.fit(data, base_point=mean_estimate)
tangent_projected_data = tpca.transform(data)
logging.info(
'Coordinates of the Log of the first 5 data points at the mean, '
'projected on the principal components:')
logging.info('\n{}'.format(tangent_projected_data[:5]))
ax_var = fig.add_subplot(121)
xticks = np.arange(1, N_COMPONENTS + 1, 1)
ax_var.xaxis.set_ticks(xticks)
ax_var.set_title('Explained variance')
ax_var.set_xlabel('Number of Principal Components')
ax_var.set_ylim((0, 1))
ax_var.plot(xticks, tpca.explained_variance_ratio_)
ax = fig.add_subplot(122, projection='3d')
plt.setp(ax, xlabel='X', ylabel='Y', zlabel='Z')
ax.set_title('Data in SO3 (black) and Frechet mean (color)')
visualization.plot(data, ax, space='SO3_GROUP', color='black')
visualization.plot(mean_estimate, ax, space='SO3_GROUP', linewidth=3)
ax.set_xlim((-2, 2))
ax.set_ylim((-2, 2))
ax.set_zlim((-2, 2))
plt.show()
def test_tangent_pca(self):
X = self.X
trans = TangentPCA(self.metric, n_components=gs.shape(X)[1])
trans.fit(X)
self.assertEquals(trans.n_features_, gs.shape(X)[1])
def test_tangent_pca_error(self):
X = self.X
trans = TangentPCA(self.metric, n_components=self.n_components)
trans.fit(X)
X_diff_size = gs.ones((self.n_samples, gs.shape(X)[1] + 1))
self.assertRaises(ValueError, trans.transform, X_diff_size)
def test_fit_mle(self):
X = self.X
tpca = TangentPCA(self.metric, n_components='mle')
tpca.fit(X)
self.assertEqual(tpca.n_features_, gs.shape(X)[1])
