def adjacency2laplacian(adj: csc_matrix,
degree: csc_matrix = None,
mode: int = 0) -> csc_matrix:
"""
This function create a graph laplacian matrix from the adjacency matrix.
Parameters
----------
A (sparse matrix): Adjacency matrix.
D (Degree matrix): Optional, diagonal matrix containing the sum over the adjacency row.
mode (int): 0 Returns the standard graph Laplacian, L = D - A.
1 Returns the random walk normalized graph Laplacian, L = I - D^-1 * A.
2 Returns the symmetric normalized graph Laplacian, L = I - D^-0.5 * A D^-0.5.
Returns
-------
L (sparse matrix): graph Laplacian
"""
degree = adjacency2degree(adj) if degree is None else degree
if mode == 0: # standard graph Laplacian
return degree - adj
elif mode == 1: # random walk graph Laplacian
return eye(degree.shape[0], format='csc') - degree.power(-1) * adj
elif mode == 2: # symmetric normalized graph Laplacian
return eye(
degree.shape[0],
format='csc') - degree.power(-0.5) * adj * degree.power(-0.5)
else:
raise NotImplementedError
def matrix_similarity(urm: sp.csc_matrix, shrink: int):
item_weights = np.sqrt(
np.sum(urm.power(2), axis=0)
).A
numerator = urm.T.dot(urm)
denominator = item_weights.T.dot(item_weights) + shrink + 1e-6
weights = numerator / denominator
np.fill_diagonal(item_similarity, 0.0)
return weights
def adjacency2transition(adj: csc_matrix,
degree: csc_matrix = None) -> csc_matrix:
""" Compute the transition matrix associated with the adjacency matrix A"""
degree = adjacency2degree(adj) if degree is None else degree
return adj * degree.power(-1)