Fast Approximate Quadratic Programming for Large (Brain) Graph Matching

TL;DR

The paper introduces FAQ, a fast approximate quadratic assignment algorithm that efficiently matches large brain graphs, outperforming previous methods in speed and accuracy, especially on connectome data.

Contribution

Developed FAQ, a cubic-time local optima algorithm for large QAPs, significantly improving speed and solution quality over prior approaches.

Findings

FAQ is faster than previous algorithms on benchmark QAPs.

FAQ achieves lower objective values in over 80% of tests.

FAQ finds optimal solutions for large brain connectomes in record time.

Abstract

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.