# Knowledge-based Multiple Adaptive Spaces Fusion for Recommendation

arXiv: https://arxiv.org/abs/2308.15244 · HTML: https://mlsanity.com/paper/2308.15244/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 39 references that are in the map.
- First posted on arXiv 29 Aug 2023.

## Builds on (most cited first, 24 of 24)

- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Neural Graph Collaborative Filtering](https://mlsanity.com/paper/1905.08108/) (2019)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [KGAT: Knowledge Graph Attention Network for Recommendation](https://mlsanity.com/paper/1905.07854/) (2019)
- [Learning Convolutional Neural Networks for Graphs](https://mlsanity.com/paper/1605.05273/) (2016)
- [A Comprehensive Survey of Graph Embedding: Problems, Techniques and Applications](https://mlsanity.com/paper/1709.07604/) (2017)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [RippleNet: Propagating User Preferences on the Knowledge Graph for Recommender Systems](https://mlsanity.com/paper/1803.03467/) (2018)
- [DKN: Deep Knowledge-Aware Network for News Recommendation](https://mlsanity.com/paper/1801.08284/) (2018)
- [Knowledge Graph Convolutional Networks for Recommender Systems](https://mlsanity.com/paper/1904.12575/) (2019)
- [Revisiting Graph based Collaborative Filtering: A Linear Residual Graph Convolutional Network Approach](https://mlsanity.com/paper/2001.10167/) (2020)
- [Hyperbolic Vision Transformers: Combining Improvements in Metric Learning](https://mlsanity.com/paper/2203.10833/) (2022)
- [Constant Curvature Graph Convolutional Networks](https://mlsanity.com/paper/1911.05076/) (2019)
- [Learning Intents behind Interactions with Knowledge Graph for Recommendation](https://mlsanity.com/paper/2102.07057/) (2021)
- [Mixed-curvature Variational Autoencoders](https://mlsanity.com/paper/1911.08411/) (2019)
- [Clipped Hyperbolic Classifiers Are Super-Hyperbolic Classifiers](https://mlsanity.com/paper/2107.11472/) (2021)
- [HyperML: A Boosting Metric Learning Approach in Hyperbolic Space for Recommender Systems](https://mlsanity.com/paper/1809.01703/) (2018)
- [Modeling Scale-free Graphs with Hyperbolic Geometry for Knowledge-aware Recommendation](https://mlsanity.com/paper/2108.06468/) (2021)
- [DyERNIE: Dynamic Evolution of Riemannian Manifold Embeddings for Temporal Knowledge Graph Completion](https://mlsanity.com/paper/2011.03984/) (2020)
- [HICF: Hyperbolic Informative Collaborative Filtering](https://mlsanity.com/paper/2207.09051/) (2022)
- [An End-to-End Neighborhood-based Interaction Model for Knowledge-enhanced Recommendation](https://mlsanity.com/paper/1908.04032/) (2019)
- [Are Hyperbolic Representations in Graphs Created Equal?](https://mlsanity.com/paper/2007.07698/) (2020)

## Built on by (most cited first, 2 of 2)

- [Hyperbolic Diffusion Recommender Model](https://mlsanity.com/paper/2504.01541/) (2025)
- [FCKT: Fine-Grained Cross-Task Knowledge Transfer with Semantic Contrastive Learning for Targeted Sentiment Analysis](https://mlsanity.com/paper/2505.21040/) (2025)

## Abstract (arXiv)

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.