def fit(self, input_matrix: Union[sparse.csr_matrix,
np.ndarray]) -> 'Ward':
"""Applies embedding method followed by the Ward algorithm.
Parameters
----------
input_matrix :
Adjacency matrix or biadjacency matrix of the graph.
Returns
-------
self: :class:`Ward`
"""
self._init_vars()
# input
check_format(input_matrix)
# embedding
embedding, self.bipartite = get_embedding(input_matrix,
self.embedding_method,
self.co_cluster)
# clustering
ward = WardDense()
self.dendrogram_ = ward.fit_transform(embedding)
# output
if self.co_cluster:
self._split_vars(input_matrix.shape)
return self
def fit(self, biadjacency: Union[sparse.csr_matrix, np.ndarray],
seeds_row: Optional[Union[dict, np.ndarray]] = None,
seeds_col: Optional[Union[dict, np.ndarray]] = None) -> 'CoPageRank':
"""Fit algorithm to data.
Parameters
----------
biadjacency :
Biadjacency matrix.
seeds_row :
Seed rows, as a dict or a vector.
seeds_col :
Seed columns, as a dict or a vector.
If both seeds_row and seeds_col are ``None``, the uniform distribution is used.
Returns
-------
self: :class:`CoPageRank`
"""
biadjacency = check_format(biadjacency)
n_row, n_col = biadjacency.shape
operator = CoNeighborsOperator(biadjacency, True)
seeds_row = seeds2probs(n_row, seeds_row)
self.scores_row_ = get_pagerank(operator, seeds_row, damping_factor=self.damping_factor, solver=self.solver,
n_iter=self.n_iter, tol=self.tol)
operator = CoNeighborsOperator(biadjacency.T.tocsr(), True)
seeds_col = seeds2probs(n_col, seeds_col)
self.scores_col_ = get_pagerank(operator, seeds_col, damping_factor=self.damping_factor, solver=self.solver,
n_iter=self.n_iter, tol=self.tol)
self.scores_ = self.scores_row_
return self
def fit(self, adjacency: Union[sparse.csr_matrix, np.ndarray]) -> 'PCA':
"""Compute the embedding of the graph.
Parameters
----------
adjacency :
Adjacency or biadjacency matrix of the graph.
Returns
-------
self: :class:`PCA`
"""
adjacency = check_format(adjacency).asfptype()
n_row, n_col = adjacency.shape
adjacency_centered = SparseLR(
adjacency,
(-np.ones(n_row), adjacency.T.dot(np.ones(n_row)) / n_row))
if isinstance(self.solver, str):
self.solver = set_svd_solver(self.solver, adjacency)
svd = self.solver
svd.fit(adjacency_centered, self.n_components)
self.embedding_row_ = svd.singular_vectors_left_
self.embedding_col_ = svd.singular_vectors_right_
self.embedding_ = svd.singular_vectors_left_
self.singular_values_ = svd.singular_values_
self.singular_vectors_left_ = svd.singular_vectors_left_
self.singular_vectors_right_ = svd.singular_vectors_right_
return self
def fit(self, adjacency: Union[sparse.csr_matrix,
np.ndarray]) -> 'Closeness':
"""Closeness centrality for connected graphs.
Parameters
----------
adjacency :
Adjacency matrix of the graph.
Returns
-------
self: :class:`Closeness`
"""
adjacency = check_format(adjacency)
check_square(adjacency)
check_connected(adjacency)
n = adjacency.shape[0]
if self.method == 'exact':
n_sources = n
sources = np.arange(n)
elif self.method == 'approximate':
n_sources = min(int(log(n) / self.tol**2), n)
sources = np.random.choice(np.arange(n), n_sources, replace=False)
else:
raise ValueError(
"Method should be either 'exact' or 'approximate'.")
dists = distance(adjacency, n_jobs=self.n_jobs, sources=sources)
self.scores_ = (
(n - 1) * n_sources / n) / dists.T.dot(np.ones(n_sources))
return self
def connected_components(adjacency: sparse.csr_matrix,
connection: str = 'weak') -> np.ndarray:
"""Extract the connected components of the graph.
* Graphs
* Digraphs
Based on SciPy (scipy.sparse.csgraph.connected_components).
Parameters
----------
adjacency :
Adjacency matrix of the graph.
connection :
Must be ``'weak'`` (default) or ``'strong'``. The type of connection to use for directed graphs.
Returns
-------
labels : np.ndarray
Connected component of each node.
"""
adjacency = check_format(adjacency)
if len(adjacency.data) == 0:
raise ValueError('The graph is empty (no edge).')
return sparse.csgraph.connected_components(adjacency,
not is_symmetric(adjacency),
connection, True)[1]
def fit(self, adjacency: Union[sparse.csr_matrix, np.ndarray, LinearOperator],
seeds: Optional[Union[dict, np.ndarray]] = None) -> 'PageRank':
"""Fit algorithm to data.
Parameters
----------
adjacency :
Adjacency matrix.
seeds :
Parameter to be used for Personalized PageRank.
Restart distribution as a vector or a dict (node: weight).
If ``None``, the uniform distribution is used (no personalization, default).
Returns
-------
self: :class:`PageRank`
"""
if not isinstance(adjacency, LinearOperator):
adjacency = check_format(adjacency)
check_square(adjacency)
seeds = seeds2probs(adjacency.shape[0], seeds)
self.scores_ = get_pagerank(adjacency, seeds, damping_factor=self.damping_factor, n_iter=self.n_iter,
solver=self.solver, tol=self.tol)
return self
def fit(self, biadjacency: Union[sparse.csr_matrix, np.ndarray],
seeds_row: Optional[Union[dict, np.ndarray]] = None, seeds_col: Optional[Union[dict, np.ndarray]] = None) \
-> 'BiPageRank':
"""Fit algorithm to data.
Parameters
----------
biadjacency :
Biadjacency matrix.
seeds_row :
Seed rows, as a dict or a vector.
seeds_col :
Seed columns, as a dict or a vector.
If both seeds_row and seeds_col are ``None``, the uniform distribution is used.
Returns
-------
self: :class:`BiPageRank`
"""
biadjacency = check_format(biadjacency)
n_row, n_col = biadjacency.shape
adjacency = bipartite2undirected(biadjacency)
seeds = stack_seeds(n_row, n_col, seeds_row, seeds_col)
PageRank.fit(self, adjacency, seeds)
self._split_vars(n_row)
self.scores_row_ /= self.scores_row_.sum()
self.scores_col_ /= self.scores_col_.sum()
self.scores_ = self.scores_row_
return self
def fit(self, biadjacency: Union[sparse.csr_matrix, np.ndarray],
seeds_row: Optional[Union[dict, np.ndarray]] = None, seeds_col: Optional[Union[dict, np.ndarray]] = None,
initial_state: Optional = None) -> 'BiDiffusion':
"""Compute the diffusion (temperature at equilibrium).
Parameters
----------
biadjacency :
Biadjacency matrix, shape (n_row, n_col).
seeds_row :
Temperatures of row border nodes (dictionary or vector of size n_row). Negative temperatures ignored.
seeds_col :
Temperatures of column border nodes (dictionary or vector of size n_row). Negative temperatures ignored.
initial_state :
Initial state of temperatures.
Returns
-------
self: :class:`BiDiffusion`
"""
biadjacency = check_format(biadjacency)
n_row, n_col = biadjacency.shape
seeds = stack_seeds(n_row, n_col, seeds_row, seeds_col)
adjacency = bipartite2undirected(biadjacency)
Diffusion.fit(self, adjacency, seeds)
self._split_vars(n_row)
return self
def fit(self, biadjacency: Union[sparse.csr_matrix, np.ndarray],
seeds_row: Optional[Union[dict, np.ndarray]] = None, seeds_col: Optional[Union[dict, np.ndarray]] = None) \
-> 'BiPageRank':
"""Fit algorithm to data.
Parameters
----------
biadjacency :
Biadjacency matrix.
seeds_row, seeds_col :
Parameter to be used for Personalized BiPageRank.
Restart distribution as vectors or dicts on rows, columns (node: weight).
If both seeds_row and seeds_col are ``None`` (default), the uniform distribution on rows is used.
Returns
-------
self: :class:`BiPageRank`
"""
biadjacency = check_format(biadjacency)
n_row, n_col = biadjacency.shape
adjacency = bipartite2undirected(biadjacency)
seeds = stack_seeds(n_row, n_col, seeds_row, seeds_col)
PageRank.fit(self, adjacency, seeds)
self._split_vars(n_row)
self.scores_row_ /= self.scores_row_.sum()
self.scores_col_ /= self.scores_col_.sum()
self.scores_ = self.scores_row_
return self
def fit(
self, biadjacency: Union[sparse.csr_matrix,
np.ndarray]) -> 'BiLouvainHierarchy':
"""Applies Louvain hierarchical clustering to
:math:`A = \\begin{bmatrix} 0 & B \\\\ B^T & 0 \\end{bmatrix}`
where :math:`B` is the biadjacency matrix of the graphs.
Parameters
----------
biadjacency:
Biadjacency matrix of the graph.
Returns
-------
self: :class:`BiLouvainHierarchy`
"""
biadjacency = check_format(biadjacency)
adjacency = bipartite2undirected(biadjacency)
self.dendrogram_ = self.louvain_hierarchy.fit_transform(adjacency)
self._split_vars(biadjacency.shape)
return self
def fit(self,
biadjacency: Union[sparse.csr_matrix, np.ndarray],
seeds_row: Optional[Union[dict, np.ndarray]] = None,
seeds_col: Optional[Union[dict, np.ndarray]] = None,
init: Optional[float] = None) -> 'BiDirichlet':
"""Compute the solution to the Dirichlet problem (temperatures at equilibrium).
Parameters
----------
biadjacency :
Biadjacency matrix, shape (n_row, n_col).
seeds_row :
Temperatures of seed rows (dictionary or vector of size n_row). Negative temperatures ignored.
seeds_col :
Temperatures of seed columns (dictionary or vector of size n_col). Negative temperatures ignored.
init :
Temperature of non-seed nodes in initial state.
If ``None``, use the average temperature of seed nodes (default).
Returns
-------
self: :class:`BiDirichlet`
"""
biadjacency = check_format(biadjacency)
n_row, n_col = biadjacency.shape
seeds = stack_seeds(n_row, n_col, seeds_row, seeds_col)
adjacency = bipartite2undirected(biadjacency)
Dirichlet.fit(self, adjacency, seeds, init)
self._split_vars(n_row)
return self
def get_adjacency(input_matrix: Union[sparse.csr_matrix, np.ndarray], allow_directed: bool = True,
force_bipartite: bool = False, force_directed: bool = False)\
-> Tuple[sparse.csr_matrix, bool]:
"""Check the input matrix and return a proper adjacency matrix.
Parameters
----------
input_matrix :
Adjacency matrix of biadjacency matrix of the graph.
allow_directed :
If ``True`` (default), allow the graph to be directed.
force_bipartite : bool
If ``True``, return the adjacency matrix of a bipartite graph.
Otherwise (default), do it only if the input matrix is not square or not symmetric
with ``allow_directed=False``.
force_directed :
If ``True`` return :math:`A = \\begin{bmatrix} 0 & B \\\\ 0 & 0 \\end{bmatrix}`.
Otherwise (default), return :math:`A = \\begin{bmatrix} 0 & B \\\\ B^T & 0 \\end{bmatrix}`.
"""
input_matrix = check_format(input_matrix)
bipartite = False
if force_bipartite or not is_square(input_matrix) or not (
allow_directed or is_symmetric(input_matrix)):
bipartite = True
if bipartite:
if force_directed:
adjacency = bipartite2directed(input_matrix)
else:
adjacency = bipartite2undirected(input_matrix)
else:
adjacency = input_matrix
return adjacency, bipartite
def fit(self, adjacency: Union[sparse.csr_matrix,
np.ndarray]) -> 'Harmonic':
"""Harmonic centrality for connected graphs.
Parameters
----------
adjacency :
Adjacency matrix of the graph.
Returns
-------
self: :class:`Harmonic`
"""
adjacency = check_format(adjacency)
check_square(adjacency)
n = adjacency.shape[0]
indices = np.arange(n)
paths = shortest_path(adjacency, n_jobs=self.n_jobs, indices=indices)
np.fill_diagonal(paths, 1)
inv = (1 / paths)
np.fill_diagonal(inv, 0)
self.scores_ = inv.dot(np.ones(n))
return self
def fit(
self,
biadjacency: Union[sparse.csr_matrix, np.ndarray],
seeds_row: Union[np.ndarray, dict],
seeds_col: Optional[Union[np.ndarray,
dict]] = None) -> 'BiPropagation':
"""Node classification by k-nearest neighbors in the embedding space.
Parameters
----------
biadjacency :
Biadjacency matrix of the graph.
seeds_row :
Seed rows. Can be a dict {node: label} or an array where "-1" means no label.
seeds_col :
Seed columns (optional). Same format.
Returns
-------
self: :class:`BiPropagation`
"""
n_row, n_col = biadjacency.shape
biadjacency = check_format(biadjacency)
adjacency = bipartite2undirected(biadjacency)
seeds = stack_seeds(n_row, n_col, seeds_row, seeds_col).astype(int)
Propagation.fit(self, adjacency, seeds)
self._split_vars(n_row)
return self
def fit(
self, biadjacency: Union[sparse.csr_matrix, np.ndarray]
) -> 'BiPropagationClustering':
"""Clustering.
Parameters
----------
biadjacency :
Biadjacency matrix of the graph.
Returns
-------
self: :class:`BiPropagationClustering`
"""
n_row, n_col = biadjacency.shape
biadjacency = check_format(biadjacency)
adjacency = bipartite2undirected(biadjacency)
propagation = PropagationClustering(self.n_iter, self.node_order,
self.weighted)
self.labels_ = propagation.fit_transform(adjacency)
self._split_vars(n_row)
self._secondary_outputs(biadjacency)
return self
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 dasgupta_cost(adjacency: sparse.csr_matrix,
dendrogram: np.ndarray,
weights: str = 'uniform',
normalized: bool = False) -> float:
"""Dasgupta's cost of a hierarchy.
Expected size (weights = ``'uniform'``) or expected volume (weights = ``'degree'``) of the cluster induced by
random edge sampling (closest ancestor of the two nodes in the hierarchy).
Parameters
----------
adjacency :
Adjacency matrix of the graph.
dendrogram :
Dendrogram.
weights :
Weights of nodes.
``'degree'`` or ``'uniform'`` (default).
normalized :
If ``True``, normalized cost (between 0 and 1).
Returns
-------
cost : float
Cost.
Example
-------
>>> from sknetwork.hierarchy import dasgupta_score, Paris
>>> from sknetwork.data import house
>>> paris = Paris()
>>> adjacency = house()
>>> dendrogram = paris.fit_transform(adjacency)
>>> cost = dasgupta_cost(adjacency, dendrogram)
>>> np.round(cost, 2)
3.33
References
----------
Dasgupta, S. (2016). A cost function for similarity-based hierarchical clustering.
Proceedings of ACM symposium on Theory of Computing.
"""
adjacency = check_format(adjacency)
check_square(adjacency)
n = adjacency.shape[0]
check_min_size(n, 2)
edge_sampling, _, cluster_weight = get_sampling_distributions(
adjacency, dendrogram, weights)
cost = edge_sampling.dot(cluster_weight)
if not normalized:
if weights == 'degree':
cost *= adjacency.data.sum()
else:
cost *= n
return cost
def co_neighbor_graph(adjacency: Union[sparse.csr_matrix, np.ndarray],
normalized: bool = True,
method='knn',
n_neighbors: int = 5,
n_components: int = 8) -> sparse.csr_matrix:
"""Compute the co-neighborhood adjacency.
* Graphs
* Digraphs
* Bigraphs
:math:`\\tilde{A} = AF^{-1}A^T`,
where F is a weight matrix.
Parameters
----------
adjacency:
Adjacency of the input graph.
normalized:
If ``True``, F is the diagonal in-degree matrix :math:`F = \\text{diag}(A^T1)`.
Otherwise, F is the identity matrix.
method:
Either ``'exact'`` or ``'knn'``. If 'exact' the output is computed with matrix multiplication.
However, the density can be much higher than in the input graph and this can trigger Memory errors.
If ``'knn'``, the co-neighborhood is approximated through KNNDense-search in an appropriate spectral embedding
space.
n_neighbors:
Number of neighbors for the KNNDense search. Only useful if ``method='knn'``.
n_components:
Dimension of the embedding space. Only useful if ``method='knn'``.
Returns
-------
adjacency : sparse.csr_matrix
Adjacency of the co-neighborhood.
"""
adjacency = check_format(adjacency).astype(float)
if method == 'exact':
if normalized:
forward = normalize(adjacency.T).tocsr()
else:
forward = adjacency.T
return adjacency.dot(forward)
elif method == 'knn':
if normalized:
algo = GSVD(n_components, regularization=None)
else:
algo = SVD(n_components, regularization=None)
embedding = algo.fit_transform(adjacency)
knn = KNNDense(n_neighbors, undirected=True)
knn.fit(embedding)
return knn.adjacency_
else:
raise ValueError('method must be "exact" or "knn".')
def largest_connected_component(adjacency: Union[sparse.csr_matrix,
np.ndarray],
return_labels: bool = False):
"""Extract the largest connected component of a graph. Bipartite graphs are treated as undirected.
* Graphs
* Digraphs
* Bigraphs
Parameters
----------
adjacency :
Adjacency or biadjacency matrix of the graph.
return_labels : bool
Whether to return the indices of the new nodes in the original graph.
Returns
-------
new_adjacency : sparse.csr_matrix
Adjacency or biadjacency matrix of the largest connected component.
indices : array or tuple of array
Indices of the nodes in the original graph. For biadjacency matrices,
``indices[0]`` corresponds to the rows and ``indices[1]`` to the columns.
"""
adjacency = check_format(adjacency)
n_row, n_col = adjacency.shape
if not is_square(adjacency):
bipartite: bool = True
full_adjacency = sparse.bmat([[None, adjacency], [adjacency.T, None]],
format='csr')
else:
bipartite: bool = False
full_adjacency = adjacency
labels = connected_components(full_adjacency)
unique_labels, counts = np.unique(labels, return_counts=True)
component_label = unique_labels[np.argmax(counts)]
component_indices = np.where(labels == component_label)[0]
if bipartite:
split_ix = np.searchsorted(component_indices, n_row)
row_ix, col_ix = component_indices[:split_ix], component_indices[
split_ix:] - n_row
else:
row_ix, col_ix = component_indices, component_indices
new_adjacency = adjacency[row_ix, :]
new_adjacency = (new_adjacency.tocsc()[:, col_ix]).tocsr()
if return_labels:
if bipartite:
return new_adjacency, (row_ix, col_ix)
else:
return new_adjacency, row_ix
else:
return new_adjacency
def fit(self, adjacency: Union[sparse.csr_matrix, np.ndarray], seeds: Union[np.ndarray, dict] = None) \
-> 'Propagation':
"""Node classification by label propagation.
Parameters
----------
adjacency :
Adjacency matrix of the graph.
seeds :
Seed nodes. Can be a dict {node: label} or an array where "-1" means no label.
Returns
-------
self: :class:`Propagation`
"""
adjacency = check_format(adjacency)
n = adjacency.shape[0]
index_seed, index_remain, labels_seed = self._instanciate_vars(
adjacency, seeds)
if self.node_order == 'random':
np.random.shuffle(index_remain)
elif self.node_order == 'decreasing':
index = np.argsort(-adjacency.T.dot(np.ones(n))).astype(np.int32)
index_remain = index[index_remain]
elif self.node_order == 'increasing':
index = np.argsort(adjacency.T.dot(np.ones(n))).astype(np.int32)
index_remain = index[index_remain]
labels = -np.ones(n, dtype=np.int32)
labels[index_seed] = labels_seed
labels_remain = np.zeros_like(index_remain, dtype=np.int32)
indptr = adjacency.indptr.astype(np.int32)
indices = adjacency.indices.astype(np.int32)
if self.weighted:
data = adjacency.data.astype(np.float32)
else:
data = np.ones(n, dtype=np.float32)
t = 0
while t < self.n_iter and not np.array_equal(labels_remain,
labels[index_remain]):
t += 1
labels_remain = labels[index_remain].copy()
labels = np.asarray(
vote_update(indptr, indices, data, labels, index_remain))
membership = membership_matrix(labels)
membership = normalize(adjacency.dot(membership))
self.labels_ = labels
self.membership_ = membership
return self
def fit(self, adjacency: Union[sparse.csr_matrix, np.ndarray],
seeds: Optional[Union[dict, np.ndarray]] = None, initial_state: Optional = None) -> 'Diffusion':
"""Compute the diffusion (temperature at equilibrium).
Parameters
----------
adjacency :
Adjacency matrix of the graph.
seeds :
Temperatures of border nodes (dictionary or vector). Negative temperatures ignored.
initial_state :
Initial state of temperatures.
Returns
-------
self: :class:`Diffusion`
"""
adjacency = check_format(adjacency)
check_square(adjacency)
n: int = adjacency.shape[0]
if seeds is None:
self.scores_ = np.ones(n) / n
return self
seeds = check_seeds(seeds, n)
b, border = limit_conditions(seeds)
tmin, tmax = np.min(b[border]), np.max(b)
interior: sparse.csr_matrix = sparse.diags(~border, shape=(n, n), format='csr', dtype=float)
diffusion_matrix = interior.dot(normalize(adjacency))
if initial_state is None:
if tmin != tmax:
initial_state = b[border].mean() * np.ones(n)
else:
initial_state = np.zeros(n)
initial_state[border] = b[border]
if self.n_iter > 0:
scores = initial_state
for i in range(self.n_iter):
scores = diffusion_matrix.dot(scores)
scores[border] = b[border]
else:
a = sparse.eye(n, format='csr', dtype=float) - diffusion_matrix
scores, info = bicgstab(a, b, atol=0., x0=initial_state)
self._scipy_solver_info(info)
if tmin != tmax:
self.scores_ = np.clip(scores, tmin, tmax)
else:
self.scores_ = scores
return self
def __init__(self, adjacency: Union[sparse.csr_matrix, np.ndarray], normalized: bool = True):
adjacency = check_format(adjacency).astype(float)
n = adjacency.shape[0]
super(CoNeighborsOperator, self).__init__(dtype=float, shape=(n, n))
if normalized:
self.forward = normalize(adjacency.T).tocsr()
else:
self.forward = adjacency.T
self.backward = adjacency
def fit(self, input_matrix: Union[sparse.csr_matrix, np.ndarray]) -> 'KMeans':
"""Apply embedding method followed by K-means.
Parameters
----------
input_matrix :
Adjacency matrix or biadjacency matrix of the graph.
Returns
-------
self: :class:`KMeans`
"""
self._init_vars()
# input
check_format(input_matrix)
if self.co_cluster:
check_n_clusters(self.n_clusters, np.sum(input_matrix.shape))
else:
check_n_clusters(self.n_clusters, input_matrix.shape[0])
# embedding
embedding, self.bipartite = get_embedding(input_matrix, self.embedding_method, self.co_cluster)
# clustering
kmeans = KMeansDense(self.n_clusters)
kmeans.fit(embedding)
# sort
if self.sort_clusters:
labels = reindex_labels(kmeans.labels_)
else:
labels = kmeans.labels_
# output
self.labels_ = labels
if self.co_cluster:
self._split_vars(input_matrix.shape)
self._secondary_outputs(input_matrix)
return self
def __init__(self, adjacency: Union[sparse.csr_matrix, np.ndarray],
coeffs: np.ndarray):
if coeffs.shape[0] == 0:
raise ValueError('A polynome requires at least one coefficient.')
adjacency = check_format(adjacency)
check_square(adjacency)
shape = adjacency.shape
dtype = adjacency.dtype
super(Polynome, self).__init__(dtype=dtype, shape=shape)
self.adjacency = adjacency
self.coeffs = coeffs
def fit(self,
adjacency: Union[sparse.csr_matrix, np.ndarray],
seeds: Optional[Union[dict, np.ndarray]] = None,
init: Optional[float] = None) -> 'Dirichlet':
"""Compute the solution to the Dirichlet problem (temperatures at equilibrium).
Parameters
----------
adjacency :
Adjacency matrix of the graph.
seeds :
Temperatures of seed nodes (dictionary or vector). Negative temperatures ignored.
init :
Temperature of non-seed nodes in initial state.
If ``None``, use the average temperature of seed nodes (default).
Returns
-------
self: :class:`Dirichlet`
"""
adjacency = check_format(adjacency)
check_square(adjacency)
n: int = adjacency.shape[0]
if seeds is None:
self.scores_ = np.ones(n) / n
return self
seeds = check_seeds(seeds, n)
border = (seeds >= 0)
if init is None:
scores = seeds[border].mean() * np.ones(n)
else:
scores = init * np.ones(n)
scores[border] = seeds[border]
if self.n_iter > 0:
diffusion = DirichletOperator(adjacency, self.damping_factor,
border)
for i in range(self.n_iter):
scores = diffusion.dot(scores)
scores[border] = seeds[border]
else:
a = DeltaDirichletOperator(adjacency, self.damping_factor, border)
b = -seeds
b[~border] = 0
scores, info = bicgstab(a, b, atol=0., x0=scores)
self._scipy_solver_info(info)
tmin, tmax = seeds[border].min(), seeds[border].max()
self.scores_ = np.clip(scores, tmin, tmax)
return self
def fit(self, adjacency: Union[sparse.csr_matrix, np.ndarray], seeds: Union[np.ndarray, dict]) \
-> 'Propagation':
"""Node classification by label propagation.
Parameters
----------
adjacency :
Adjacency or biadjacency matrix of the graph.
seeds :
Seed nodes. Can be a dict {node: label} or an array where "-1" means no label.
Returns
-------
self: :class:`Propagation`
"""
adjacency = check_format(adjacency)
n = adjacency.shape[0]
index_seed, index_remain, labels_seed = self._instanciate_vars(
adjacency, seeds)
labels = -np.ones(n, dtype=int)
labels[index_seed] = labels_seed
labels_remain = np.zeros_like(index_remain, dtype=int)
t = 0
while t < self.n_iter and not np.array_equal(labels_remain,
labels[index_remain]):
t += 1
labels_remain = labels[index_remain].copy()
for i in index_remain:
labels_ = labels[
adjacency.indices[adjacency.indptr[i]:adjacency.indptr[i +
1]]]
labels_ = labels_[labels_ >= 0]
if len(labels_):
labels_unique, counts = np.unique(labels_,
return_counts=True)
labels[i] = labels_unique[np.argmax(counts)]
membership = membership_matrix(labels)
membership = normalize(adjacency.dot(membership))
self.labels_ = labels
self.membership_ = membership
return self
def fit(self, adjacency: Union[sparse.csr_matrix, np.ndarray]):
"""Fit algorithm to the data.
Parameters
----------
adjacency :
Adjacency matrix of the graph
Returns
-------
self : :class:`FirstOrder`
"""
adjacency = check_format(adjacency)
adjacency.sort_indices()
self.indptr_ = adjacency.indptr.astype(np.int32)
self.indices_ = adjacency.indices.astype(np.int32)
return self
def fit(self, biadjacency: Union[sparse.csr_matrix, np.ndarray]) -> 'BiRandomProjection':
"""Compute the embedding.
Parameters
----------
biadjacency:
Biadjacency matrix of the graph.
Returns
-------
self: :class:`BiRandomProjection`
"""
biadjacency = check_format(biadjacency)
n_row, _ = biadjacency.shape
RandomProjection.fit(self, bipartite2undirected(biadjacency))
self._split_vars(n_row)
return self
def fit(self, adjacency: Union[sparse.csr_matrix, np.ndarray]) -> 'HITS':
"""Compute HITS algorithm with a spectral method.
Parameters
----------
adjacency :
Adjacency or biadjacency matrix of the graph.
Returns
-------
self: :class:`HITS`
"""
adjacency = check_format(adjacency)
if self.solver == 'auto':
solver = auto_solver(adjacency.nnz)
if solver == 'lanczos':
self.solver: SVDSolver = LanczosSVD()
else:
self.solver: SVDSolver = HalkoSVD()
self.solver.fit(adjacency, 1)
hubs: np.ndarray = self.solver.singular_vectors_left_.reshape(-1)
authorities: np.ndarray = self.solver.singular_vectors_right_.reshape(
-1)
h_pos, h_neg = (hubs > 0).sum(), (hubs < 0).sum()
a_pos, a_neg = (authorities > 0).sum(), (authorities < 0).sum()
if h_pos > h_neg:
hubs = np.clip(hubs, a_min=0., a_max=None)
else:
hubs = np.clip(-hubs, a_min=0., a_max=None)
if a_pos > a_neg:
authorities = np.clip(authorities, a_min=0., a_max=None)
else:
authorities = np.clip(-authorities, a_min=0., a_max=None)
self.scores_row_ = hubs
self.scores_col_ = authorities
self.scores_ = hubs
return self
def fit(self, biadjacency: Union[sparse.csr_matrix, np.ndarray]) -> 'BiKatz':
"""Katz centrality.
Parameters
----------
biadjacency :
Biadjacency matrix of the graph.
Returns
-------
self: :class:`BiKatz`
"""
biadjacency = check_format(biadjacency)
n_row, n_col = biadjacency.shape
adjacency = bipartite2undirected(biadjacency)
Katz.fit(self, adjacency)
self._split_vars(n_row)
return self