Euclidean distance

Pure mathematics

Hyperbolic space

Statistics

Social psychology

Computer security

Theoretical computer science

Curse of dimensionality

Operating system

Economics

Data mining

Computer science

Embedding

Psychology

Preference

Metric space

Mathematics

Mathematical analysis

Operations management

Artificial intelligence

Geometry

Information retrieval

Point (geometry)

Metric (unit)

Recommender system

Euclidean space

Space (punctuation)

Popularity

Key (lock)

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.