def fit(
self, adjacency: Union[sparse.csr_matrix,
np.ndarray]) -> 'LaplacianEmbedding':
"""Compute the graph embedding.
Parameters
----------
adjacency :
Adjacency matrix of the graph (symmetric matrix).
Returns
-------
self: :class:`LaplacianEmbedding`
"""
adjacency = check_format(adjacency).asfptype()
check_square(adjacency)
check_symmetry(adjacency)
n = adjacency.shape[0]
regularize: bool = not (self.regularization is None
or self.regularization == 0.)
check_scaling(self.scaling, adjacency, regularize)
if regularize:
solver: EigSolver = LanczosEig()
else:
solver = set_solver(self.solver, adjacency)
n_components = 1 + check_n_components(self.n_components, n - 2)
weights = adjacency.dot(np.ones(n))
regularization = self.regularization
if regularization:
if self.relative_regularization:
regularization = regularization * weights.sum() / n**2
weights += regularization * n
laplacian = LaplacianOperator(adjacency, regularization)
else:
weight_diag = sparse.diags(weights, format='csr')
laplacian = weight_diag - adjacency
solver.which = 'SM'
solver.fit(matrix=laplacian, n_components=n_components)
eigenvalues = solver.eigenvalues_[1:]
eigenvectors = solver.eigenvectors_[:, 1:]
embedding = eigenvectors.copy()
if self.scaling:
eigenvalues_inv_diag = diag_pinv(eigenvalues**self.scaling)
embedding = eigenvalues_inv_diag.dot(embedding.T).T
if self.normalized:
embedding = normalize(embedding, p=2)
self.embedding_ = embedding
self.eigenvalues_ = eigenvalues
self.eigenvectors_ = eigenvectors
self.regularization_ = regularization
return self
def fit(self, adjacency: Union[sparse.csr_matrix,
np.ndarray]) -> 'Spectral':
"""Compute the graph embedding.
Parameters
----------
adjacency :
Adjacency matrix of the graph (symmetric matrix).
Returns
-------
self: :class:`Spectral`
"""
adjacency = check_format(adjacency).asfptype()
check_square(adjacency)
check_symmetry(adjacency)
n = adjacency.shape[0]
solver = set_solver(self.solver, adjacency)
n_components = 1 + check_n_components(self.n_components, n - 2)
regularize: bool = not (self.regularization is None
or self.regularization == 0.)
check_scaling(self.scaling, adjacency, regularize)
weights = adjacency.dot(np.ones(n))
regularization = self.regularization
if regularization:
if self.relative_regularization:
regularization = regularization * weights.sum() / n**2
weights += regularization * n
# Spectral decomposition of the normalized adjacency matrix
weights_inv_sqrt_diag = diag_pinv(np.sqrt(weights))
if regularization:
norm_adjacency = NormalizedAdjacencyOperator(
adjacency, regularization)
else:
norm_adjacency = weights_inv_sqrt_diag.dot(
adjacency.dot(weights_inv_sqrt_diag))
solver.which = 'LA'
solver.fit(matrix=norm_adjacency, n_components=n_components)
eigenvalues = solver.eigenvalues_
index = np.argsort(-eigenvalues)[1:] # skip first eigenvalue
eigenvalues = eigenvalues[index]
eigenvectors = weights_inv_sqrt_diag.dot(solver.eigenvectors_[:,
index])
embedding = eigenvectors.copy()
if self.scaling:
eigenvalues_inv_diag = diag_pinv((1 - eigenvalues)**self.scaling)
embedding = eigenvalues_inv_diag.dot(embedding.T).T
if self.normalized:
embedding = normalize(embedding, p=2)
self.embedding_ = embedding
self.eigenvalues_ = eigenvalues
self.eigenvectors_ = eigenvectors
self.regularization_ = regularization
return self
def fit(self, adjacency: Union[sparse.csr_matrix,
np.ndarray]) -> 'Spectral':
"""Compute the graph embedding.
Parameters
----------
adjacency :
Adjacency matrix of the graph (symmetric matrix).
Returns
-------
self: :class:`Spectral`
"""
adjacency = check_format(adjacency).asfptype()
check_square(adjacency)
check_symmetry(adjacency)
n = adjacency.shape[0]
if self.solver == 'auto':
solver = auto_solver(adjacency.nnz)
if solver == 'lanczos':
self.solver: EigSolver = LanczosEig()
else: # pragma: no cover
self.solver: EigSolver = HalkoEig()
n_components = check_n_components(self.n_components, n - 2)
n_components += 1
if self.equalize and (self.regularization is None
or self.regularization
== 0.) and not is_connected(adjacency):
raise ValueError(
"The option 'equalize' is valid only if the graph is connected or with regularization."
"Call 'fit' either with 'equalize' = False or positive 'regularization'."
)
weights = adjacency.dot(np.ones(n))
regularization = self.regularization
if regularization:
if self.relative_regularization:
regularization = regularization * weights.sum() / n**2
weights += regularization * n
if self.normalized_laplacian:
# Finding the largest eigenvalues of the normalized adjacency is easier for the solver than finding the
# smallest eigenvalues of the normalized laplacian.
weights_inv_sqrt_diag = diag_pinv(np.sqrt(weights))
if regularization:
norm_adjacency = NormalizedAdjacencyOperator(
adjacency, regularization)
else:
norm_adjacency = weights_inv_sqrt_diag.dot(
adjacency.dot(weights_inv_sqrt_diag))
self.solver.which = 'LA'
self.solver.fit(matrix=norm_adjacency, n_components=n_components)
eigenvalues = 1 - self.solver.eigenvalues_
# eigenvalues of the Laplacian in increasing order
index = np.argsort(eigenvalues)[1:]
# skip first eigenvalue
eigenvalues = eigenvalues[index]
# eigenvectors of the Laplacian, skip first eigenvector
eigenvectors = np.array(
weights_inv_sqrt_diag.dot(self.solver.eigenvectors_[:, index]))
else:
if regularization:
laplacian = LaplacianOperator(adjacency, regularization)
else:
weight_diag = sparse.diags(weights, format='csr')
laplacian = weight_diag - adjacency
self.solver.which = 'SM'
self.solver.fit(matrix=laplacian, n_components=n_components)
eigenvalues = self.solver.eigenvalues_[1:]
eigenvectors = self.solver.eigenvectors_[:, 1:]
embedding = eigenvectors.copy()
if self.equalize:
eigenvalues_sqrt_inv_diag = diag_pinv(np.sqrt(eigenvalues))
embedding = eigenvalues_sqrt_inv_diag.dot(embedding.T).T
if self.barycenter:
eigenvalues_diag = sparse.diags(eigenvalues)
subtract = eigenvalues_diag.dot(embedding.T).T
if not self.normalized_laplacian:
weights_inv_diag = diag_pinv(weights)
subtract = weights_inv_diag.dot(subtract)
embedding -= subtract
if self.normalized:
embedding = normalize(embedding, p=2)
self.embedding_ = embedding
self.eigenvalues_ = eigenvalues
self.eigenvectors_ = eigenvectors
self.regularization_ = regularization
return self