Gotta match 'em all: Solution diversification in graph matching matched filters

TL;DR

This paper introduces a scalable graph matching method that iteratively finds multiple diverse template graphs within large background graphs, supported by theoretical analysis and extensive real-world experiments.

Contribution

It extends the graph-matching-matched-filter technique to discover multiple diverse matchings through iterative penalization and offers algorithmic speed-ups for scalability.

Findings

Successfully discovers multiple templates in large graphs

Theoretically justified in correlated Erdos-Renyi graph models

Validated on real-world datasets including brain connectomes

Abstract

We present a novel approach for finding multiple noisily embedded template graphs in a very large background graph. Our method builds upon the graph-matching-matched-filter technique proposed in Sussman et al., with the discovery of multiple diverse matchings being achieved by iteratively penalizing a suitable node-pair similarity matrix in the matched filter algorithm. In addition, we propose algorithmic speed-ups that greatly enhance the scalability of our matched-filter approach. We present theoretical justification of our methodology in the setting of correlated Erdos-Renyi graphs, showing its ability to sequentially discover multiple templates under mild model conditions. We additionally demonstrate our method's utility via extensive experiments both using simulated models and real-world dataset, include human brain connectomes and a large transactional knowledge base.