Source code for netrd.reconstruction.correlation_matrix

Reconstruction of graphs using the correlation matrix.
author: Stefan McCabe
email: stefanmccabe at gmail dot com
Submitted as part of the 2019 NetSI Collabathon
from .base import BaseReconstructor
import numpy as np
from ..utilities import create_graph, threshold

[docs]class CorrelationMatrix(BaseReconstructor): """Uses the correlation matrix."""
[docs] def fit(self, TS, num_eigs=None, threshold_type='range', **kwargs): """Uses the correlation matrix. If ``num_eigs`` is `None`, perform the reconstruction using the unregularized correlation matrix. Otherwise, construct a regularized precision matrix using ``num_eigs`` eigenvectors and eigenvalues of the correlation matrix. For details on the regularization method, see [1]. The results dictionary also stores the raw correlation matrix (potentially regularized) as `'weights_matrix'` and the thresholded version of the correlation matrix as `'thresholded_matrix'`. For details see [2]_. Parameters ---------- TS (np.ndarray) Array consisting of :math:`L` observations from :math:`N` sensors num_eigs (int) The number of eigenvalues to use. (This corresponds to the amount of regularization.) The number of eigenvalues used must be less than :math:`N`. threshold_type (str) Which thresholding function to use on the matrix of weights. See `` for documentation. Pass additional arguments to the thresholder using `**kwargs`. Returns ------- G (nx.Graph) a reconstructed graph. References ---------- .. [1] .. [2] """ # get the correlation matrix cor = np.corrcoef(TS) if num_eigs: N = TS.shape[0] if num_eigs > N: raise ValueError( "The number of eigenvalues used must be less " "than the number of sensors." ) # get eigenvalues and eigenvectors of the correlation matrix vals, vecs = np.linalg.eigh(cor) idx = vals.argsort()[::-1] vals = vals[idx] vecs = vecs[:, idx] # construct the precision matrix and store it P = (vecs[:, :num_eigs]) @ ( 1 / (vals[:num_eigs]).reshape(num_eigs, 1) * (vecs[:, :num_eigs]).T ) P = P / ( np.sqrt(np.diag(P)).reshape(N, 1) @ np.sqrt(np.diag(P)).reshape(1, N) ) mat = P else: mat = cor # store the appropriate source matrix self.results['weights_matrix'] = mat # threshold the correlation matrix A = threshold(mat, threshold_type, **kwargs) self.results['thresholded_matrix'] = A # construct the network self.results['graph'] = create_graph(A) G = self.results['graph'] return G