  Considering the prevalence of the power-law distribution in user-item
networks, hyperbolic space has attracted considerable attention and achieved
impressive performance in the recommender system recently. The advantage of
hyperbolic recommendation lies in that its exponentially increasing capacity is
well-suited to describe the power-law distributed user-item network whereas the
Euclidean equivalent is deficient. Nonetheless, it remains unclear which kinds
of items can be effectively recommended by the hyperbolic model and which
cannot. To address the above concerns, we take the most basic recommendation
technique, collaborative filtering, as a medium, to investigate the behaviors
of hyperbolic and Euclidean recommendation models. The results reveal that (1)
tail items get more emphasis in hyperbolic space than that in Euclidean space,
but there is still ample room for improvement; (2) head items receive modest
attention in hyperbolic space, which could be considerably improved; (3) and
nonetheless, the hyperbolic models show more competitive performance than
Euclidean models. Driven by the above observations, we design a novel learning
method, named hyperbolic informative collaborative filtering (HICF), aiming to
compensate for the recommendation effectiveness of the head item while at the
same time improving the performance of the tail item. The main idea is to adapt
the hyperbolic margin ranking learning, making its pull and push procedure
geometric-aware, and providing informative guidance for the learning of both
head and tail items. Extensive experiments back up the analytic findings and
also show the effectiveness of the proposed method. The work is valuable for
personalized recommendations since it reveals that the hyperbolic space
facilitates modeling the tail item, which often represents user-customized
preferences or new products.
