Geometric Matrix Completion via Sylvester Multi-Graph Neural Network
This work addresses geometric matrix completion, a problem in graph mining for applications like semi-supervised learning, but it is incremental as it builds upon existing Sylvester equation methods.
The paper tackles the limitations of Sylvester equation methods in graph mining by proposing SYMGNN, an end-to-end neural framework that generalizes these methods to handle non-linear relations and improve task flexibility, resulting in overall outperformance in geometric matrix completion and a 16.98% average reduction in memory consumption with its low-rank instantiation.
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.