Projected Power Iteration for Network Alignment

TL;DR

This paper introduces Projected Power Alignment, an enhanced spectral algorithm for network alignment that improves recovery rates over EigenAlign and offers a theoretical framework for performance guarantees.

Contribution

It proposes a novel projected power iteration algorithm for network alignment, extending EigenAlign with improved empirical performance and potential theoretical guarantees.

Findings

Improves recovery rates compared to EigenAlign

Numerical experiments demonstrate enhanced performance

Provides a theoretical basis for performance guarantees

Abstract

The network alignment problem asks for the best correspondence between two given graphs, so that the largest possible number of edges are matched. This problem appears in many scientific problems (like the study of protein-protein interactions) and it is very closely related to the quadratic assignment problem which has graph isomorphism, traveling salesman and minimum bisection problems as particular cases. The graph matching problem is NP-hard in general. However, under some restrictive models for the graphs, algorithms can approximate the alignment efficiently. In that spirit the recent work by Feizi and collaborators introduce EigenAlign, a fast spectral method with convergence guarantees for Erd\H{o}s-Reny\'i graphs. In this work we propose the algorithm Projected Power Alignment, which is a projected power iteration version of EigenAlign. We numerically show it improves the recovery rates of EigenAlign and we describe the theory that may be used to provide performance guarantees for Projected Power Alignment.