In recent years, recommender systems have advanced rapidly, where embedding learning for users and items plays a critical role. A standard method learns a unique embedding vector for each user and item. However, such a method has two important limitations in real-world applications: 1) it is hard to learn embeddings that generalize well for users and items with rare interactions on their own; and 2) it may incur unbearably high memory costs when the number of users and items scales up. Existing approaches either can only address one of the limitations or have flawed overall performances. In this paper, we propose Clustered Embedding Learning (CEL) as an integrated solution to these two problems. CEL is a plug-and-play embedding learning framework that can be combined with any differentiable feature interaction model. It is capable of achieving improved performance, especially for cold users and items, with reduced memory cost. CEL enables automatic and dynamic clustering of users and items in a top-down fashion, where clustered entities jointly learn a shared embedding. The accelerated version of CEL has an optimal time complexity, which supports efficient online updates. Theoretically, we prove the identifiability and the existence of a unique optimal number of clusters for CEL in the context of nonnegative matrix factorization. Empirically, we validate the effectiveness of CEL on three public datasets and one business dataset, showing its consistently superior performance against current state-of-the-art methods. In particular, when incorporating CEL into the business model, it brings an improvement of $+0.6\%$ in AUC, which translates into a significant revenue gain; meanwhile, the size of the embedding table gets $2650$ times smaller.

翻译：近年来，推荐系统取得了快速发展，其中用户与物品的嵌入学习起着关键作用。标准方法为每个用户和物品学习唯一的嵌入向量。然而，此类方法在实际应用中存在两个重要限制：1) 对于交互稀少的用户和物品，难以学习到泛化能力良好的嵌入；2) 当用户和物品数量扩大时，可能产生难以承受的高额内存成本。现有方法要么只能解决其中一个限制，要么整体性能存在缺陷。本文提出聚类嵌入学习(CEL)作为这两个问题的集成解决方案。CEL是一种即插即用的嵌入学习框架，可与任何可微特征交互模型结合使用。它能够实现性能提升（尤其针对冷启用户和物品），同时降低内存成本。CEL采用自上而下的方式自动动态聚类用户和物品，使聚类实体联合学习共享嵌入。加速版CEL具有最优时间复杂度，支持高效在线更新。理论上，我们证明了在非负矩阵分解背景下，CEL的可辨识性及唯一最优聚类数的存在性。实证方面，我们在三个公开数据集和一个商业数据集上验证了CEL的有效性，显示出其相较当前最先进方法始终更优的性能。特别地，将CEL融入商业模型后，AUC提升+0.6%，转化为显著的收入增长；同时，嵌入表尺寸缩小2650倍。