A path-based recommendations approach for online systems via hyperbolic network embedding

In this paper we introduce and demonstrate new recommendation algorithms for large-scale online systems, such as e-shops and cloud services. The proposed algorithms are based on the combination of network embedding in hyperbolic space with greedy routing, exploiting properties of hyperbolic metric spaces. Contrary to the existing recommender systems that rank products in order to propose the highest ranked ones to the users, our proposed recommender system creates a progressive path of recommendations towards a final (known or inferred) target product using greedy routing over networks embedded in hyperbolic space. Thus, it prepares the user by intermediate recommendations for maximizing the chances that he/she accepts the recommendation of the target product(s). This casts the problem of locating a suitable recommendation as a path problem, where leveraging on the efficiency of greedy routing in graphs embedded in hyperbolic spaces and exploiting special network structure, if any, pays dividends. Two variants of our recommendation approach are provided, namely Hyperbolic Recommendation-Known Destination (HRKD), Hyperbolic Recommendation-Unknown Destination (HRUD), when the target product is known or unknown, respectively. We demonstrate how the proposed approach can be used for producing efficient recommendations in online systems, along with studying the impact of the several parameters involved in its performance via proper emulation of user activity over suitably defined graphs.