Fast Approximate Quadratic Programming for Large (Brain) Graph Matching

Quadratic assignment problems (QAPs) arise in a wide variety of domains, ranging from operations research to graph theory to computer vision to neuroscience. In the age of big data, graph valued data is becoming more prominent, and with it, a desire to run algorithms on ever larger graphs. Because Q...

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Bibliographic Details
Published inarXiv.org
Main Authors Vogelstein, Joshua T, Conroy, John M, Lyzinski, Vince, Podrazik, Louis J, Kratzer, Steven G, Harley, Eric T, Fishkind, Donniell E, R Jacob Vogelstein, Priebe, Carey E
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 13.09.2014
Subjects
Algorithms
Apexes
Brain
Computer vision
Data management
Domains
Graph matching
Graph theory
Graphs
Operations research
Optimization
Quadratic programming
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Summary:Quadratic assignment problems (QAPs) arise in a wide variety of domains, ranging from operations research to graph theory to computer vision to neuroscience. In the age of big data, graph valued data is becoming more prominent, and with it, a desire to run algorithms on ever larger graphs. Because QAP is NP-hard, exact algorithms are intractable. Approximate algorithms necessarily employ an accuracy/efficiency trade-off. We developed a fast approximate quadratic assignment algorithm (FAQ). FAQ finds a local optima in (worst case) time cubic in the number of vertices, similar to other approximate QAP algorithms. We demonstrate empirically that our algorithm is faster and achieves a lower objective value on over 80% of the suite of QAP benchmarks, compared with the previous state-of-the-art. Applying the algorithms to our motivating example, matching C. elegans connectomes (brain-graphs), we find that FAQ achieves the optimal performance in record time, whereas none of the others even find the optimum.
ISSN:2331-8422