OptFuse: Low-rank factor estimation by optimal data-driven linear fusion of multiple signal-plus-noise matrices

We consider the setting where we are given multiple signal-plus-noise matrices. The signal matrices are modeled as low-rank with the same factors (or eigenvectors) but arbitrary (modulo a fixed ordering) eigen-SNRs. One motivating example is the determination of community structure from multiple, independent adjacency matrices. The objective is to combine them linearly so that the eigenvectors of the resulting matrix are as close as possible to the unknown, latent factors. We utilize recent results from random matrix theory to recast this as a constrained data-driven optimization problem and develop an efficient algorithm (OptFuse) for solving it. We demonstrate the improved performance of the algorithm relative to an equal weighting scheme.