def _slq_red_var_vnge(matrix, lanczos_steps, nvectors):
"""Approximates Von Neumann Graph Entropy (VNGE) of a given matrix.
Uses the control variates method to reduce the variance of VNGE estimation.
Args:
matrix (sparse matrix): Input adjacency matrix of a graph.
lanczos_steps (int): Number of Lanczos steps.
nvectors (int): Number of random vectors for stochastic estimation.
Returns:
float: Approximated von Neumann graph entropy.
"""
functions = [lambda x: -np.where(x > 0, x * np.log(x), 0), lambda x: x]
traces = slq(matrix, lanczos_steps, nvectors, functions).ravel()
return traces[0] - traces[1] + 1
def _slq_red_var_netlsd(matrix, lanczos_steps, nvectors, timescales):
"""Computes unnormalized NetLSD signatures of a given matrix.
Uses the control variates method to reduce the variance of NetLSD estimation.
Args:
matrix (sparse matrix): Input adjacency matrix of a graph.
lanczos_steps (int): Number of Lanczos steps.
nvectors (int): Number of random vectors for stochastic estimation.
timescales (np.ndarray): Timescale parameter for NetLSD computation. Default
value is the one used in both NetLSD and SLaQ papers.
Returns:
np.ndarray: Approximated NetLSD descriptors.
"""
functions = [np.exp, lambda x: x]
traces = slq(matrix, lanczos_steps, nvectors, functions, -timescales)
subee = traces[0, :] - traces[1, :] / np.exp(timescales)
sub = -timescales * matrix.shape[0] / np.exp(timescales)
return np.array(subee + sub)