Gotta Match 'Em All: Solution Diversification in Graph Matching Matched Filters

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. (Sussman, 2020), 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 Erdős-Rényi 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 datasets, including human brain connectomes and a large transactional knowledge base.