Maximum Common Subgraph Guided Graph Retrieval: Late and Early Interaction Networks

TL;DR

This paper introduces neural network models for graph retrieval that approximate maximum common subgraph measures, balancing accuracy and speed through late and early interaction approaches.

Contribution

It proposes novel neural formulations for MCES and MCCS, including a differentiable network for MCCS size estimation, and compares late and early interaction methods.

Findings

Late interaction models are highly scalable and accurate.

Early interaction models achieve state-of-the-art accuracy.

Proposed methods outperform existing models in speed and accuracy.

Abstract

The graph retrieval problem is to search in a large corpus of graphs for ones that are most similar to a query graph. A common consideration for scoring similarity is the maximum common subgraph (MCS) between the query and corpus graphs, usually counting the number of common edges (i.e., MCES). In some applications, it is also desirable that the common subgraph be connected, i.e., the maximum common connected subgraph (MCCS). Finding exact MCES and MCCS is intractable, but may be unnecessary if ranking corpus graphs by relevance is the goal. We design fast and trainable neural functions that approximate MCES and MCCS well. Late interaction methods compute dense representations for the query and corpus graph separately, and compare these representations using simple similarity functions at the last stage, leading to highly scalable systems. Early interaction methods combine information from both graphs right from the input stages, are usually considerably more accurate, but slower. We propose both late and early interaction neural MCES and MCCS formulations. They are both based on a continuous relaxation of a node alignment matrix between query and corpus nodes. For MCCS, we propose a novel differentiable network for estimating the size of the largest connected common subgraph. Extensive experiments with seven data sets show that our proposals are superior among late interaction models in terms of both accuracy and speed. Our early interaction models provide accuracy competitive with the state of the art, at substantially greater speeds.