def test_sfa_parameter_computation(dimension, n_samples):
current_data = mixed_trigonometric_functions(dimension, n_samples)
sfa = SFA()
slow_features = sfa.fit_transform(current_data)
W, b = sfa.affine_parameters()
affine_transformed = np.dot(current_data, W.T) + b
assert np.allclose(slow_features, affine_transformed)
def test_sfa_parameter_computation_rank_deficit_nonzero_fill(
dimension, rank_deficit):
current_data = mixed_trigonometric_functions(dimension,
rank_deficit=rank_deficit)
sfa = SFA(fill_mode="noise")
slow_features = sfa.fit_transform(current_data)
with pytest.raises(RuntimeError):
W, b = sfa.affine_parameters()
def test_sfa_parameter_computation_rank_deficit_zero_fill(
dimension, rank_deficit):
current_data = mixed_trigonometric_functions(dimension,
rank_deficit=rank_deficit)
sfa = SFA(fill_mode="zero")
slow_features = sfa.fit_transform(current_data)
W, b = sfa.affine_parameters()
affine_transformed = np.dot(current_data, W.T) + b
assert np.allclose(slow_features, affine_transformed)
def test_sfa_feature_order(dimension, n_samples):
current_data = mixed_trigonometric_functions(dimension, n_samples)
sfa = SFA()
slow_features = sfa.fit_transform(current_data)
explicit_delta_values = compute_delta(slow_features)
assert np.allclose(explicit_delta_values, np.sort(explicit_delta_values))
def test_sfa_constraints(dimension, n_samples):
current_data = mixed_trigonometric_functions(dimension, n_samples)
sfa = SFA()
slow_features = sfa.fit_transform(current_data)
covariance_matrix = np.cov(slow_features.T)
assert np.allclose(covariance_matrix, np.eye(dimension))
# Generate latent cosine signals
x = np.hstack([np.cos(t), 0.5 * np.cos(t), np.cos(2 * t), 1.5 * np.cos(t)])
# Compute random affine mapping of cosines (observed)
A = np.random.normal(0, 1, (dim, dim))
b = np.random.normal(0, 2, (1, dim))
data = np.dot(x, A) + b
# Extract slow features from observed data
# Plot cosines, mapped data, and extracted features
fig, ax = plt.subplots(2 + len(fill_modes), 1, sharex=True)
fig.set_size_inches(8, 18)
fig.subplots_adjust(hspace=0.5)
for d in range(n_slow_features):
ax[0].plot(x[:, d])
ax[1].plot(data)
for idx, fill_mode in enumerate(fill_modes):
sfa = SFA(n_slow_features, fill_mode=fill_mode)
slow_features = sfa.fit_transform(data)
ax[2 + idx].plot(slow_features[:, :-1])
ax[2 + idx].plot(slow_features[:, -1], linestyle=":", color="purple")
ax[2 + idx].set_title(f"Extracted features, fill_mode='{fill_mode}'")
ax[2 + idx].set_xlabel("Time t")
ax[0].set_title("x(t)")
ax[1].set_title("A⋅x(t) + b")
for idx in range(2 + len(fill_modes)):
ax[idx].set_ylabel("Features")
plt.show()
embedded = lem.fit_transform(data)
A = lem.affinity_matrix_
restart_rate = 500
n_random_samples = 1500
trajectory = randomWalkFromCSC(sp.sparse.csc_matrix(A),
n_random_samples,
restart_rate=restart_rate)
walk_data = data[trajectory]
visited = np.unique(trajectory)
non_visited = np.setdiff1d(np.arange(0, n_points), visited)
pf = PolynomialFeatures(1)
sfa = SFA(2, batch_size=restart_rate if restart_rate > 0 else None)
sf = sfa.fit_transform(pf.fit_transform(walk_data))
oos = sfa.transform(pf.transform(data[non_visited]))
pca = PCA(2)
pc = pca.fit_transform(data)
fig = plt.figure()
fig.set_size_inches(8, 12)
fig.subplots_adjust(hspace=0.5)
ax_3d = fig.add_subplot(321, projection='3d')
ax_3d.set_title("Wavy circle data")
ax_rw = fig.add_subplot(323, projection='3d')
ax_rw.set_title("Random walk samples")
ax_lem = fig.add_subplot(322)
ax_lem.set_title("Spectral embedding")