GraphCroc: Cross-Correlation Autoencoder for Graph Structural Reconstruction

TL;DR

GraphCroc introduces a cross-correlation autoencoder that improves graph structure reconstruction, especially in multi-graph scenarios, by addressing limitations of self-correlation methods through a novel mirrored encoding-decoding process.

Contribution

The paper presents GraphCroc, a novel GAE leveraging cross-correlation for better structural reconstruction and flexible architectures, overcoming self-correlation limitations in multi-graph contexts.

Findings

Outperforms existing self-correlation GAEs in structure reconstruction

Effectively handles multi-graph and small graph scenarios

Provides theoretical and numerical validation of improvements

Abstract

Graph-structured data is integral to many applications, prompting the development of various graph representation methods. Graph autoencoders (GAEs), in particular, reconstruct graph structures from node embeddings. Current GAE models primarily utilize self-correlation to represent graph structures and focus on node-level tasks, often overlooking multi-graph scenarios. Our theoretical analysis indicates that self-correlation generally falls short in accurately representing specific graph features such as islands, symmetrical structures, and directional edges, particularly in smaller or multiple graph contexts. To address these limitations, we introduce a cross-correlation mechanism that significantly enhances the GAE representational capabilities. Additionally, we propose GraphCroc, a new GAE that supports flexible encoder architectures tailored for various downstream tasks and ensures robust structural reconstruction, through a mirrored encoding-decoding process. This model also tackles the challenge of representation bias during optimization by implementing a loss-balancing strategy. Both theoretical analysis and numerical evaluations demonstrate that our methodology significantly outperforms existing self-correlation-based GAEs in graph structure reconstruction.