Geometric Matrix Completion with Recurrent Multi-Graph Neural Networks

TL;DR

This paper introduces a geometric deep learning approach combining graph convolutional and recurrent neural networks for matrix completion, effectively capturing local graph structures and reducing parameter count, leading to improved performance.

Contribution

It proposes a novel neural network architecture that leverages graph structures for matrix completion, with a constant parameter count regardless of matrix size.

Findings

Outperforms state-of-the-art methods on synthetic datasets

Demonstrates effectiveness on real-world recommender system data

Reduces model complexity by decoupling parameters from matrix size

Abstract

Matrix completion models are among the most common formulations of recommender systems. Recent works have showed a boost of performance of these techniques when introducing the pairwise relationships between users/items in the form of graphs, and imposing smoothness priors on these graphs. However, such techniques do not fully exploit the local stationarity structures of user/item graphs, and the number of parameters to learn is linear w.r.t. the number of users and items. We propose a novel approach to overcome these limitations by using geometric deep learning on graphs. Our matrix completion architecture combines graph convolutional neural networks and recurrent neural networks to learn meaningful statistical graph-structured patterns and the non-linear diffusion process that generates the known ratings. This neural network system requires a constant number of parameters independent of the matrix size. We apply our method on both synthetic and real datasets, showing that it outperforms state-of-the-art techniques.