With the increasing popularity of location-aware social media services, next-Point-of-Interest (POI) recommendation has gained significant research interest. The key challenge of next-POI recommendation is to precisely learn users' sequential movements from sparse check-in data. To this end, various embedding methods have been proposed to learn the representations of check-in data in the Euclidean space. However, their ability to learn complex patterns, especially hierarchical structures, is limited by the dimensionality of the Euclidean space. To this end, we propose a new research direction that aims to learn the representations of check-in activities in a hyperbolic space, which yields two advantages. First, it can effectively capture the underlying hierarchical structures, which are implied by the power-law distributions of user movements. Second, it provides high representative strength and enables the check-in data to be effectively represented in a low-dimensional space. Specifically, to solve the next-POI recommendation task, we propose a novel hyperbolic metric embedding (HME) model, which projects the check-in data into a hyperbolic space. The HME jointly captures sequential transition, user preference, category and region information in a unified approach by learning embeddings in a shared hyperbolic space. To the best of our knowledge, this is the first study to explore a non-Euclidean embedding model for next-POI recommendation. We conduct extensive experiments on three check-in datasets to demonstrate the superiority of our hyperbolic embedding approach over the state-of-the-art next-POI recommendation algorithms. Moreover, we conduct experiments on another four online transaction datasets for next-item recommendation to further demonstrate the generality of our proposed model.

This paper investigates the notion of learning user and item representations in non-Euclidean space. Specifically, we study the connection between metric learning in hyperbolic space and collaborative filtering by exploring Mobius gyrovector spaces where the formalism of the spaces could be utilized to generalize the most common Euclidean vector operations. Overall, this work aims to bridge the gap between Euclidean and hyperbolic geometry in recommender systems through metric learning approach. We propose HyperML (Hyperbolic Metric Learning), a conceptually simple but highly effective model for boosting the performance. Via a series of extensive experiments, we show that our proposed HyperML not only outperforms their Euclidean counterparts, but also achieves state-of-the-art performance on multiple benchmark datasets, demonstrating the effectiveness of personalized recommendation in hyperbolic geometry.

This paper proposes Quaternion Collaborative Filtering (QCF), a novel representation learning method for recommendation. Our proposed QCF relies on and exploits computation with Quaternion algebra, benefiting from the expressiveness and rich representation learning capability of Hamilton products. Quaternion representations, based on hypercomplex numbers, enable rich inter-latent dependencies between imaginary components. This encourages intricate relations to be captured when learning user-item interactions, serving as a strong inductive bias as compared with the real-space inner product. All in all, we conduct extensive experiments on six real-world datasets, demonstrating the effectiveness of Quaternion algebra in recommender systems. The results exhibit that QCF outperforms a wide spectrum of strong neural baselines on all datasets. Ablative experiments confirm the effectiveness of Hamilton-based composition over multi-embedding composition in real space.

This paper proposes Medley of Sub-Attention Networks (MoSAN), a new novel neural architecture for the group recommendation task. Group-level recommendation is known to be a challenging task, in which intricate group dynamics have to be considered. As such, this is to be contrasted with the standard recommendation problem where recommendations are personalized with respect to a single user. Our proposed approach hinges upon the key intuition that the decision making process (in groups) is generally dynamic, i.e., a user's decision is highly dependent on the other group members. All in all, our key motivation manifests in a form of an attentive neural model that captures fine-grained interactions between group members. In our MoSAN model, each sub-attention module is representative of a single member, which models a user's preference with respect to all other group members. Subsequently, a Medley of Sub-Attention modules is then used to collectively make the group's final decision. Overall, our proposed model is both expressive and effective. Via a series of extensive experiments, we show that MoSAN not only achieves state-of-the-art performance but also improves standard baselines by a considerable margin.