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.

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