Geometric Matrix Completion via Sylvester Multi-Graph Neural Network

TL;DR

This paper introduces SYMGNN, a neural network framework that extends Sylvester equation methods to model non-linear relations in geometric matrix completion, achieving better performance and lower memory usage.

Contribution

It proposes a novel end-to-end neural framework that generalizes Sylvester equation methods for improved geometric matrix completion.

Findings

Outperforms baseline methods on real-world datasets.

Reduces memory consumption by 16.98% with low-rank instantiation.

Effectively models non-linear relations in graph data.

Abstract

Despite the success of the Sylvester equation empowered methods on various graph mining applications, such as semi-supervised label learning and network alignment, there also exists several limitations. The Sylvester equation's inability of modeling non-linear relations and the inflexibility of tuning towards different tasks restrict its performance. In this paper, we propose an end-to-end neural framework, SYMGNN, which consists of a multi-network neural aggregation module and a prior multi-network association incorporation learning module. The proposed framework inherits the key ideas of the Sylvester equation, and meanwhile generalizes it to overcome aforementioned limitations. Empirical evaluations on real-world datasets show that the instantiations of SYMGNN overall outperform the baselines in geometric matrix completion task, and its low-rank instantiation could further reduce the memory consumption by 16.98\% on average.