Rank-Constrained Deep Matrix Completion for Group Recommendation

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.

Enhancing Group Recommendation using Soft Impute Singular Value Decomposition

The growing popularity of group activities increased the need to develop methods for providing recommendations to a group of users based on the collective preferences of the group members. Several group recommender systems have been proposed, but these methods often struggle due to sparsity and high-dimensionality of the available data, common in many real-world applications. In this paper, we propose a group recommender system called Group Soft-Impute SVD, which leverages soft-impute singular value decomposition to enhance group recommendations. This approach addresses the challenge of sparse high-dimensional data using low-rank matrix completion. We compared the performance of Group Soft-Impute SVD with Group MF based approaches and found that our method outperforms the baselines in recall for small user groups while achieving comparable results across all group sizes when tasked on Goodbooks, Movielens, and Synthetic datasets. Furthermore, our method recovers lower matrix ranks than the baselines, demonstrating its effectiveness in handling high-dimensional data.