Rank-Constrained Deep Matrix Completion for Group Recommendation
2026-06-01 • Information Retrieval
Information RetrievalArtificial Intelligence
AI summaryⓘ
The authors created a new method called Group RC-DMC to recommend items to groups of users by learning from their individual preferences. Their method handles missing and sparse data well by using a mathematical technique called low-rank matrix completion, combined with a special neural network called a Set-Transformer to understand group preferences. They tested their approach on movie and book datasets and found it predicted group choices more accurately and efficiently than some existing methods. Overall, their work helps improve group recommendations by better capturing both individual and group tastes in one system.
group recommender systemslow-rank matrix completionSet-Transformerlatent representationsnuclear normsingular value thresholdingencoder-decoder architectureroot mean square error (RMSE)precisionrecall
Authors
Mubaraka Sani Ibrahim, Lehel Csató, Isah Charles Saidu
Abstract
The growing popularity of group activities has increased the need for methods that provide recommendations to groups of users given their individual preferences. Many existing group recommender systems rely on aggregating individual user preferences, but they often struggle with high-dimensional and highly sparse rating data commonly found in real-world scenarios. We propose Group Rank-Constrained Deep Matrix Completion (Group RC-DMC), a novel framework that extends RC-DMC by integrating group-level representation learning via a Set-Transformer aggregator, jointly leveraging low-rank structure and attention-based nonlinear modeling. Unlike most existing group recommender systems, Group RC-DMC unifies explicit low-rank regularization, linear encoder-decoder architectures, and attention-based nonlinear group modeling within a single framework, yielding accurate predictions at both the individual and group levels. Group RC-DMC addresses data sparsity through low-rank matrix completion, computing per-user latent representations from observed ratings only, and enforcing a rank constraint on the latent space using a nuclear-norm proximal step based on periodic singular value thresholding. The decoder is parametrized as a low-rank factorization, enabling efficient inference. Experimental results on the MovieLens and Goodbooks datasets demonstrate that Group RC-DMC achieves superior reconstruction accuracy, measured by lower group RMSE, while remaining computationally efficient and competitive in group-level performance in terms of precision, recall, and F1 score compared with weighted-before-factorization (WBF) and after-factorization (AF) baselines. The results highlight the model's ability to recover the underlying low-rank structure of user-item interactions and provide robust group recommendations across small, medium, and large user groups.