# Exploiting Multi-layer Graph Factorization for Multi-attributed Graph Matching

## TL;DR

This paper introduces a novel multi-layer graph factorization approach for multi-attributed graph matching, effectively addressing scalability and back-projection issues, and demonstrating superior performance over existing methods.

## Contribution

It proposes a new algorithm that factorizes multi-layer graph structures into smaller matrices, improving scalability and accuracy in multi-attributed graph matching.

## Key findings

- Outperforms state-of-the-art algorithms in accuracy
- Reduces computational complexity via matrix factorization
- Effectively handles multiple attributes without oversimplification

## Abstract

Multi-attributed graph matching is a problem of finding correspondences between two sets of data while considering their complex properties described in multiple attributes. However, the information of multiple attributes is likely to be oversimplified during a process that makes an integrated attribute, and this degrades the matching accuracy. For that reason, a multi-layer graph structure-based algorithm has been proposed recently. It can effectively avoid the problem by separating attributes into multiple layers. Nonetheless, there are several remaining issues such as a scalability problem caused by the huge matrix to describe the multi-layer structure and a back-projection problem caused by the continuous relaxation of the quadratic assignment problem. In this work, we propose a novel multi-attributed graph matching algorithm based on the multi-layer graph factorization. We reformulate the problem to be solved with several small matrices that are obtained by factorizing the multi-layer structure. Then, we solve the problem using a convex-concave relaxation procedure for the multi-layer structure. The proposed algorithm exhibits better performance than state-of-the-art algorithms based on the single-layer structure.