Title: Group RC-DMC: A Rank-Constrained Approach to Deep Matrix Completion for Group Recommendations

Abstract: As group-based activities gain traction, there is an escalating demand for recommendation systems capable of serving groups by synthesizing individual user preferences. Traditional group recommender systems typically depend on aggregating individual preferences, yet they frequently encounter difficulties when processing the high-dimensional and extremely sparse rating data prevalent in practical applications. To address these challenges, we introduce Group Rank-Constrained Deep Matrix Completion (Group RC-DMC), an innovative framework that builds upon RC-DMC by incorporating group-level representation learning through a Set-Transformer aggregator. This approach synergistically combines low-rank structural constraints with attention-driven nonlinear modeling. Distinct from most current group recommender systems, Group RC-DMC integrates explicit low-rank regularization, linear encoder-decoder structures, and attention-based nonlinear group modeling into a cohesive framework, thereby delivering precise predictions for both individual and group levels.

To mitigate data sparsity, Group RC-DMC employs low-rank matrix completion techniques. It derives per-user latent representations exclusively from observed ratings and imposes a rank constraint on the latent space via a nuclear-norm proximal step, which relies on periodic singular value thresholding. Furthermore, the decoder is defined by a low-rank factorization, facilitating efficient inference processes. Evaluations on the MovieLens and Goodbooks datasets reveal that Group RC-DMC attains superior reconstruction accuracy, evidenced by reduced group RMSE. The model maintains computational efficiency and demonstrates competitive performance in group-level metrics, including precision, recall, and F1 score, when compared against weighted-before-factorization (WBF) and after-factorization (AF) baselines. These findings underscore the model’s proficiency in uncovering the latent low-rank structure of user-item interactions and delivering reliable group recommendations across groups of varying sizes, from small to large.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC