Inductive Matrix Completion Based on Graph Neural Networks (1904.12058v3)

Abstract: We propose an inductive matrix completion model without using side information. By factorizing the (rating) matrix into the product of low-dimensional latent embeddings of rows (users) and columns (items), a majority of existing matrix completion methods are transductive, since the learned embeddings cannot generalize to unseen rows/columns or to new matrices. To make matrix completion inductive, most previous works use content (side information), such as user's age or movie's genre, to make predictions. However, high-quality content is not always available, and can be hard to extract. Under the extreme setting where not any side information is available other than the matrix to complete, can we still learn an inductive matrix completion model? In this paper, we propose an Inductive Graph-based Matrix Completion (IGMC) model to address this problem. IGMC trains a graph neural network (GNN) based purely on 1-hop subgraphs around (user, item) pairs generated from the rating matrix and maps these subgraphs to their corresponding ratings. It achieves highly competitive performance with state-of-the-art transductive baselines. In addition, IGMC is inductive -- it can generalize to users/items unseen during the training (given that their interactions exist), and can even transfer to new tasks. Our transfer learning experiments show that a model trained out of the MovieLens dataset can be directly used to predict Douban movie ratings with surprisingly good performance. Our work demonstrates that: 1) it is possible to train inductive matrix completion models without using side information while achieving similar or better performances than state-of-the-art transductive methods; 2) local graph patterns around a (user, item) pair are effective predictors of the rating this user gives to the item; and 3) Long-range dependencies might not be necessary for modeling recommender systems.

• The paper introduces IGMC, an inductive matrix completion approach that generalizes to unseen user-item pairs.
• IGMC utilizes localized subgraph patterns and GNNs to predict ratings without relying on side information.
• The model demonstrates competitive performance across benchmarks, outperforming transductive methods on sparse datasets.

Inductive Matrix Completion Based on Graph Neural Networks

The paper "Inductive Matrix Completion Based on Graph Neural Networks" presents a novel approach to solving matrix completion problems, specifically within the context of recommender systems. The authors introduce the Inductive Graph-based Matrix Completion (IGMC) model, which relies on Graph Neural Networks (GNNs) to perform matrix completion in an inductive fashion, without the need for side information.

Key Contributions

1. Inductive Matrix Completion: Traditional matrix completion methods are predominantly transductive, meaning they struggle with generalization to unseen rows or columns, necessitating retraining with any alterations to the input matrix. In contrast, the IGMC model is inductive, capable of generalizing to new (user, item) pairs that were not present during training. This capability makes IGMC particularly useful in dynamic environments where timely recommendations are critical.
2. No Side Information Required: While previous inductive methods have depended heavily on user/item content data (e.g., user demographics or item attributes), such side information is not always readily available or easy to extract. The IGMC approach circumvents the need for side information by exclusively utilizing patterns within small subgraphs (1-hop neighborhoods) surrounding each (user, item) pair.
3. Use of Graph Neural Networks: IGMC leverages GNNs' superior ability to learn graph-structured data, mapping local graph substructures to their corresponding ratings. This model employs a relational GCN to capture the diverse structural features within the extracted subgraphs, transforming the task into a link prediction problem. This approach is robust against changes in the dataset, adaptable to unseen data points, and transferrable across different datasets.

Performance and Evaluation

The IGMC model demonstrates competitive performance against state-of-the-art transductive and inductive matrix completion methods across various benchmark datasets, including Flixster, Douban, YahooMusic, MovieLens-100K, and MovieLens-1M. For instance, IGMC outperforms transductive methods like GC-MC on sparse matrices, showing its strength in situations where data is limited. Moreover, IGMC's transfer learning capability stands out, achieving notable performance when transferred from the MovieLens-100K dataset to other movie rating platforms such as Douban, without requiring retraining.

Practical and Theoretical Implications

From a practical standpoint, the ability to perform matrix completion without retraining and without the need for auxiliary information is invaluable. It enables rapid updates and predictions in real-time environments. Theoretically, this work underscores the potential of leveraging local graph patterns and GNNs for tasks typically reliant on factorization methods. It also opens pathways for further exploration of graph-based methods in other domains where matrix completion is applicable.

The authors also highlight that while IGMC does not directly handle the "cold-start" problem (predicting ratings for entirely new users or items without any interaction history), the model is suitable for instances where some interaction history is present. Exploring ways to extend IGMC to address the cold-start scenario remains a future research direction.

Conclusion

The paper makes significant strides in the field of matrix completion by introducing a methodology that achieves high performance and adaptability through the use of localized graph patterns without side information. IGMC presents a compelling case for the application of contemporary GNN architectures to conventional problems in recommender systems, marking a shift from transductive to inductive approaches in matrix completion. This research opens the doors to scalable and efficient implementations in rapidly evolving systems, enhancing real-time recommendation capabilities.