A Fast Projected Fixed-Point Algorithm for Large Graph Matching

TL;DR

This paper introduces a fast, scalable, and robust approximate algorithm for large graph matching based on a new projected fixed-point method, significantly improving speed and accuracy over previous methods.

Contribution

A novel projected fixed-point algorithm with doubly stochastic projection that achieves linear convergence and scales efficiently to large graphs.

Findings

Outperforms previous algorithms in speed and accuracy

Achieves linear convergence rate

Matches large graphs (over 1,000 nodes) in seconds

Abstract

We propose a fast approximate algorithm for large graph matching. A new projected fixed-point method is defined and a new doubly stochastic projection is adopted to derive the algorithm. Previous graph matching algorithms suffer from high computational complexity and therefore do not have good scalability with respect to graph size. For matching two weighted graphs of $n$ nodes, our algorithm has time complexity only $O(n^3)$ per iteration and space complexity $O(n^2)$. In addition to its scalability, our algorithm is easy to implement, robust, and able to match undirected weighted attributed graphs of different sizes. While the convergence rate of previous iterative graph matching algorithms is unknown, our algorithm is theoretically guaranteed to converge at a linear rate. Extensive experiments on large synthetic and real graphs (more than 1,000 nodes) were conducted to evaluate the performance of various algorithms. Results show that in most cases our proposed algorithm achieves better performance than previous state-of-the-art algorithms in terms of both speed and accuracy in large graph matching. In particular, with high accuracy, our algorithm takes only a few seconds (in a PC) to match two graphs of 1,000 nodes.