Gene

Scale (ratio)

Pure mathematics

Hyperbolic space

Semantic space

Cartography

Computational geometry

Theoretical computer science

Precision and recall

ENCODE

Unification

Biochemistry

Computer science

Semantics (computer science)

Graph

Mathematics

Geography

Artificial intelligence

Geometry

Information retrieval

Chemistry

Programming language

Recommender system

Knowledge graph

Aiming to alleviate data sparsity and cold-start problems of tradi- tional recommender systems, incorporating knowledge graphs (KGs) to supplement auxiliary information has recently gained considerable attention. Via unifying the KG with user-item interactions into a tripartite graph, recent works explore the graph topologies to learn the low-dimensional representations of users and items with rich semantics. These real-world tripartite graphs are usually scale-free, however, the intrinsic hierarchical graph structures of which are underemphasized in existing works, consequently, leading to suboptimal recommendation performance. To address this issue and provide more accurate recommendation, we propose a knowledge-aware recommendation method with Lorentz model of the hyperbolic geometry, namely Lorentzian Knowledge-enhanced Graph convolutional networks for Recommendation (LKGR). LKGR facilitates better modeling of scale-free tripartite graphs after the data unification. Specifically, we employ different information propagation strategies in the hyperbolic space to explicitly encode heterogeneous information from historical interactions and KGs. Additionally, our proposed knowledge-aware attention mechanism enables the model to automatically measure the information contribution, producing the coherent information aggregation in the hyperbolic space. Extensive experiments on three real-world benchmarks demonstrate that LKGR outperforms state-of-the-art methods by 3.6-15.3% of [email protected] on Top-K recommendation.

Modeling Scale-free Graphs with Hyperbolic Geometry for Knowledge-aware Recommendation