[Paper Review] Graph Convolutional Matrix Completion

Rianne van den Berg, Thomas Kipf+1 more|arXiv (Cornell University)|Jun 7, 2017

Advanced Graph Neural Networks23 references1,102 citations

TL;DR

GC-MC proposes a graph auto-encoder for matrix completion by performing graph convolution on a bipartite user-item interaction graph and decoding with a bilinear predictor, achieving competitive to state-of-the-art results especially with side information.

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.

Motivation & Objective

• Frame matrix completion as link prediction on a bipartite user-item graph.
• Develop an end-to-end graph auto-encoder with a graph convolutional encoder and bilinear decoder.
• Incorporate side information (e.g., social graphs, features) to improve cold-start and overall performance.
• Demonstrate scalability via efficient vectorized implementation and mini-batching.

Proposed method

• Construct user and item embeddings via a graph convolutional encoder with edge-type specific messages for each rating level.
• Aggregate messages per node across all neighbors and edge types to form final user/item embeddings.
• Decode ratings with a bilinear decoder that treats each rating level as a separate class and uses a softmax to predict p(M_ij = r).
• Train by minimizing negative log-likelihood over observed ratings with a mask for unobserved entries.
• Apply node dropout and standard dropout for regularization; use mini-batching to scale to large datasets.

Experimental results

Research questions

• RQ1 Can a graph auto-encoder on a bipartite user-item graph accurately predict unobserved ratings?
• RQ2 Does incorporating side information (features or graphs) improve predictive performance, especially in cold-start settings?
• RQ3 How do graph convolutional encoding and bilinear decoding compare to traditional matrix factorization and auto-encoder baselines on standard CF datasets?
• RQ4 Is the approach scalable to large datasets via vectorized sparse operations and mini-batching?
• RQ5 What is the impact of different normalization and aggregation choices on performance?

Key findings

• GC-MC achieves competitive RMSE on standard CF benchmarks, especially when side information is available.
• In ML-100K with side information, GC-MC outperforms related methods by a significant margin.
• GC-MC scales to ML-1M and ML-10M and remains competitive with state-of-the-art CF methods.
• Using side information in Flixster, Douban, and YahooMusic yields state-of-the-art results.
• A simple non-iterative rating reconstruction from learned embeddings can outperform recurrent graph methods in some settings.