def test_run_mot_embedding_sparse_no_restrict():
np.random.seed(9235)
adj_mat = sparse.csr_matrix(np.array([
0, 2, 0,
0, 0, 3,
4, 0, 0
]).reshape((3, 3)))
# answers
ans_adj_mat = np.array([
0, 2, 0,
0, 0, 3,
4, 0, 0
]).reshape((3, 3))
ans_motif_adj_mat = np.array([
0, 3, 3,
3, 0, 3,
3, 3, 0
]).reshape((3, 3))
ans_vals = [0, 1.5]
ans_vects = np.array([
0.577, -0.293,
0.577, 0.806,
0.577, -0.513
]).reshape((3, 2))
# run motif embedding
emb_list = mcsp.run_motif_embedding(adj_mat, "M1", "func", "mean", "dense", 2,
"rw", restrict=False)
# flip eigenvector signs if necessary
for i in range(len(ans_vals)):
if np.sign(emb_list["vects"][0, i]) != np.sign(ans_vects[0, i]):
emb_list["vects"][:, i] = -emb_list["vects"][:, i]
assert np.allclose(ans_adj_mat, emb_list["adj_mat"].toarray())
assert np.allclose(ans_motif_adj_mat, emb_list["motif_adj_mat"].toarray())
assert np.allclose(ans_vals, emb_list["vals"], atol=0.01)
assert np.allclose(ans_vects, emb_list["vects"], atol=0.01)
def run_motif_clustering(adj_mat, motif_name,
motif_type="struc",
mam_weight_type="unweighted",
mam_method="sparse",
num_eigs=2,
type_lap="comb",
num_clusts=2,
restrict=True,
gr_method="sparse"):
"""
Run motif-based clustering.
Run motif-based clustering on the adjacency matrix of a
(weighted directed) network,
using a specified motif, motif type, weighting scheme,
embedding dimension, number of clusters and Laplacian type.
Optionally restrict to the largest connected component
before clustering.
Parameters
----------
adj_mat : matrix
Adjacency matrix to be embedded.
motif_name : str
Motif used for the motif adjacency matrix.
motif_type : str
Type of motif adjacency matrix to use.
One of `"func"` or `"struc"`.
mam_weight_type : str
Weighting scheme for the motif adjacency matrix.
One of `"unweighted"`, `"mean"` or `"product"`.
mam_method : str
The method to use for building the motif adjacency matrix.
One of `"sparse"` or `"dense"`.
num_eigs : int
Number of eigenvalues and eigenvectors for the embedding.
type_lap : str
Type of Laplacian for the embedding.
One of `"comb"` or `"rw"`.
num_clusts : int
The number of clusters to find.
restrict : bool
Whether or not to restrict the motif adjacency matrix
to its largest connected component before embedding.
gr_method : str
Format to use for getting largest component.
One of `"sparse"` or `"dense"`.
Returns
-------
adj_mat : sparse matrix
The original adjacency matrix.
motif_adj_mat : sparse matrix
The motif adjacency matrix.
comps : list
The indices of the largest connected component
of the motif adjacency matrix
(if restrict=True).
adj_mat_comps : matrix
The original adjacency matrix restricted
to the largest connected component of the motif adjacency matrix
(if restrict=True).
motif_adj_mat_comps : matrix
The motif adjacency matrix restricted
to its largest connected component
(if restrict=True).
vals : list
A length-`num_eigs` list containing the
eigenvalues associated with the Laplace embedding
of the (restricted) motif adjacency matrix.
vects : matrix
A matrix containing the eigenvectors associated with the Laplace
embedding of the (restricted) motif adjacency matrix.
clusts :
A vector containing integers representing the
cluster assignment of each vertex in the (restricted) graph.
Examples
--------
>>> adj_mat = np.array(range(1, 10)).reshape((3, 3))
>>> run_motif_clustering(adj_mat, "M1")
"""
assert motif_type in ["struc", "func"]
assert mam_weight_type in ["unweighted", "mean", "product"]
assert mam_method in ["sparse", "dense"]
assert isinstance(restrict, bool)
assert type_lap in ["comb", "rw"]
spectrum = mcsp.run_motif_embedding(adj_mat, motif_name, motif_type, mam_weight_type,
mam_method, num_eigs, type_lap, restrict, gr_method)
cluster_assigns = cluster_spectrum(spectrum, num_clusts)
ans = {
"adj_mat": adj_mat,
"motif_adj_mat": spectrum["motif_adj_mat"],
"comps": spectrum["comps"],
"adj_mat_comps": spectrum["adj_mat_comps"],
"motif_adj_mat_comps": spectrum["motif_adj_mat_comps"],
"vals": spectrum["vals"],
"vects": spectrum["vects"],
"clusts": cluster_assigns
}
return ans