Matched Filters for Noisy Induced Subgraph Detection

• Published in: IEEE transactions on pattern analysis and machine intelligence Vol. 42; no. 11; pp. 2887 - 2900
• Main Authors: Sussman, Daniel L., Park, Youngser, Priebe, Carey E., Lyzinski, Vince
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.11.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Animals; Apexes; Approximation algorithms; Brain - diagnostic imaging; Computer simulation; Computer vision; Connectome; Correlation; Diffusion Tensor Imaging; Drosophila; Graph matching; Graph theory; Graphs; Humans; Image Processing, Computer-Assisted - methods; Matched filters; Models, Statistical; Multiple graph inference; Noise measurement; Optimization; Social networking (online); Social networks; Statistical models; Stochastic processes; subgraph detection; Symmetric matrices
• ISSN: 0162-8828; 1939-3539; 2160-9292; 2160-9292; 1939-3539
• DOI: 10.1109/TPAMI.2019.2914651

The problem of finding the vertex correspondence between two noisy graphs with different number of vertices where the smaller graph is still large has many applications in social networks, neuroscience, and computer vision. We propose a solution to this problem via a graph matching matched filter: centering and padding the smaller adjacency matrix and applying graph matching methods to align it to the larger network. The centering and padding schemes can be incorporated into any algorithm that matches using adjacency matrices. Under a statistical model for correlated pairs of graphs, which yields a noisy copy of the small graph within the larger graph, the resulting optimization problem can be guaranteed to recover the true vertex correspondence between the networks. However, there are currently no efficient algorithms for solving this problem. To illustrate the possibilities and challenges of such problems, we use an algorithm that can exploit a partially known correspondence and show via varied simulations and applications to Drosophila and human connectomes that this approach can achieve good performance.