Graph Convolutional Matrix Completion

TL;DR

<3-5 sentence high-level summary> GC-MC reframes matrix completion as link prediction on a bipartite user-item graph and introduces a graph auto-encoder that propagates edge-type–specific messages to produce user/item embeddings. A bilinear, multi-class decoder then predicts observed ratings, enabling seamless integration of side information through a dedicated processing path. The model supports scalable training via node dropout and mini-batching and leverages weight sharing to stabilize training across rating levels. Empirical results across MovieLens, Flixster, Douban, and YahooMusic show competitive or state-of-the-art performance, especially when side information is available, with favorable scalability properties. The approach offers a principled, end-to-end alternative to traditional matrix factorization and recurrent graph methods for recommender systems.

Abstract

We consider matrix completion for recommender systems from the point of view of link prediction on graphs. Interaction data such as movie ratings can be represented by a bipartite user-item graph with labeled edges denoting observed ratings. Building on recent progress in deep learning on graph-structured data, we propose a graph auto-encoder framework based on differentiable message passing on the bipartite interaction graph. Our model shows competitive performance on standard collaborative filtering benchmarks. In settings where complimentary feature information or structured data such as a social network is available, our framework outperforms recent state-of-the-art methods.

Figures (3)

• Figure 1: Left: Rating matrix $M$ with entries that correspond to user-item interactions (ratings between 1-5) or missing observations (0). Right: User-item interaction graph with bipartite structure. Edges correspond to interaction events, numbers on edges denote the rating a user has given to a particular item. The matrix completion task (i.e. predictions for unobserved interactions) can be cast as a link prediction problem and modeled using an end-to-end trainable graph auto-encoder.
• Figure 2: Schematic of a forward-pass through the GC-MC model, which is comprised of a graph convolutional encoder $[U, V] = f(X, M_1, \ldots, M_R)$ that passes and transforms messages from user to item nodes, and vice versa, followed by a bilinear decoder model that predicts entries of the (reconstructed) rating matrix $\check{M} = g(U, V)$, based on pairs of user and item embeddings.
• Figure 3: Cold-start analysis for ML-100K. Test set RMSE (average over 5 runs with random initialization) for various settings, where only a small number of ratings $N_r$ is kept for a certain number of cold-start users $N_c$ during training. Standard error is below $0.001$ and therefore not shown. Dashed and solid lines denote experiments without and with side information, respectively.