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.

翻译：群体活动的日益普及增加了对根据用户个体偏好向用户群组提供推荐方法的需求。许多现有的群组推荐系统依赖聚合个体用户偏好，但通常难以处理现实场景中常见的高维且高度稀疏的评分数据。我们提出群组秩约束深度矩阵补全（Group RC-DMC），这是一种新颖的框架，通过利用Set-Transformer聚合器整合群组级表示学习，将RC-DMC扩展为联合利用低秩结构和基于注意力的非线性建模。与大多数现有群组推荐系统不同，Group RC-DMC在单一框架内统一了显式低秩正则化、线性编码器-解码器架构和基于注意力的非线性群组建模，从而在个体和群组级别均能生成准确预测。Group RC-DMC通过低秩矩阵补全处理数据稀疏性，仅从观测评分计算每个用户的潜在表示，并基于周期性奇异值阈值化，通过核范数邻近步骤对潜在空间施加秩约束。解码器参数化为低秩分解形式，从而实现高效推理。在MovieLens和Goodbooks数据集上的实验结果表明，与因子分解前加权（WBF）和因子分解后加权（AF）基线相比，Group RC-DMC在群组均方根误差（RMSE）上实现了更优的重构精度，同时保持了计算效率，并在群组级别的精确率、召回率和F1分数上表现出竞争力。结果凸显了该模型恢复用户-物品交互潜在低秩结构的能力，并能对小型、中型和大型用户群组提供稳健的群组推荐。