Sparse Partial Least Squares for Coarse Noisy Graph Alignment
This addresses the problem of integrating multiple network data sources with community-level correspondence for researchers in graph signal processing, but it appears incremental as it builds on existing graph alignment techniques.
The paper tackles the problem of coarse graph alignment, where the goal is to find correspondence between community structures rather than individual vertices in graphs, by proposing a novel regularized partial least squares method with sparsity to reflect block community structure. The result demonstrates effectiveness in simulations, though no concrete numbers are provided.
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.