Sparse Partial Least Squares for Coarse Noisy Graph Alignment

TL;DR

This paper introduces a novel sparse partial least squares method for coarse graph alignment, effectively matching community structures across noisy, unaligned graphs using regularization and efficient algorithms.

Contribution

It proposes a new regularized partial least squares approach that captures community-level correspondences in noisy graph data, advancing graph alignment techniques.

Findings

Effective in simulations for noisy graph alignment

Incorporates community structure via sparsity

Provides efficient algorithms for practical use

Abstract

Graph signal processing (GSP) provides a powerful framework for analyzing signals arising in a variety of domains. In many applications of GSP, multiple network structures are available, each of which captures different aspects of the same underlying phenomenon. To integrate these different data sources, graph alignment techniques attempt to find the best correspondence between vertices of two graphs. We consider a generalization of this problem, where there is no natural one-to-one mapping between vertices, but where there is correspondence between the community structures of each graph. Because we seek to learn structure at this higher community level, we refer to this problem as "coarse" graph alignment. To this end, we propose a novel regularized partial least squares method which both incorporates the observed graph structures and imposes sparsity in order to reflect the underlying block community structure. We provide efficient algorithms for our method and demonstrate its effectiveness in simulations.