Since Knowledge Graphs (KGs) contain rich semantic information, recently there has been an influx of KG-enhanced recommendation methods. Most of existing methods are entirely designed based on euclidean space without considering curvature. However, recent studies have revealed that a tremendous graph-structured data exhibits highly non-euclidean properties. Motivated by these observations, in this work, we propose a knowledge-based multiple adaptive spaces fusion method for recommendation, namely MCKG. Unlike existing methods that solely adopt a specific manifold, we introduce the unified space that is compatible with hyperbolic, euclidean and spherical spaces. Furthermore, we fuse the multiple unified spaces in an attention manner to obtain the high-quality embeddings for better knowledge propagation. In addition, we propose a geometry-aware optimization strategy which enables the pull and push processes benefited from both hyperbolic and spherical spaces. Specifically, in hyperbolic space, we set smaller margins in the area near to the origin, which is conducive to distinguishing between highly similar positive items and negative ones. At the same time, we set larger margins in the area far from the origin to ensure the model has sufficient error tolerance. The similar manner also applies to spherical spaces. Extensive experiments on three real-world datasets demonstrate that the MCKG has a significant improvement over state-of-the-art recommendation methods. Further ablation experiments verify the importance of multi-space fusion and geometry-aware optimization strategy, justifying the rationality and effectiveness of MCKG.

翻译：知识图谱（KGs）包含丰富的语义信息，近年来涌现出大量融合KG的推荐方法。现有方法大多完全基于欧氏空间设计，未考虑曲率特性。然而近期研究表明，大量图结构数据呈现出高度非欧几里得性质。受此启发，本文提出一种基于知识的多自适应空间融合推荐方法——MCKG。与仅采用特定流形结构的现有方法不同，我们引入了兼容双曲空间、欧氏空间和球面空间的统一空间。进一步地，我们通过注意力机制融合多个统一空间，以获得高质量嵌入表示，实现更优的知识传播。此外，我们提出几何感知优化策略，使推拉过程受益于双曲空间和球面空间的协同作用。具体而言，在双曲空间中，我们在原点附近区域设置较小边界，有助于区分高度相似的正负样本；同时在远离原点的区域设置较大边界，确保模型具有足够容错能力。类似策略同样适用于球面空间。在三个真实数据集上的大量实验表明，MCKG相比现有最先进的推荐方法具有显著性能提升。进一步的消融实验验证了多空间融合与几何感知优化策略的重要性，证明了MCKG的合理性与有效性。