# HyperML: A Boosting Metric Learning Approach in Hyperbolic Space for Recommender Systems

arXiv: https://arxiv.org/abs/1809.01703 · HTML: https://mlsanity.com/paper/1809.01703/

## Key facts

- Cited by 47 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Sep 2018.

## Built on by (most cited first, 30 of 47)

- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [Hyperbolic Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/2305.06611/) (2023)
- [A Survey on Accuracy-oriented Neural Recommendation: From Collaborative Filtering to Information-rich Recommendation](https://mlsanity.com/paper/2104.13030/) (2021)
- [Hypformer: Exploring Efficient Transformer Fully in Hyperbolic Space](https://mlsanity.com/paper/2407.01290/) (2024)
- [Hyperbolic Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/2202.13852/) (2022)
- [HRCF: Enhancing Collaborative Filtering via Hyperbolic Geometric Regularization](https://mlsanity.com/paper/2204.08176/) (2022)
- [Where are we in embedding spaces? A Comprehensive Analysis on Network Embedding Approaches for Recommender Systems](https://mlsanity.com/paper/2105.08908/) (2021)
- [HICF: Hyperbolic Informative Collaborative Filtering](https://mlsanity.com/paper/2207.09051/) (2022)
- [Symmetric Spaces for Graph Embeddings: A Finsler-Riemannian Approach](https://mlsanity.com/paper/2106.04941/) (2021)
- [Hyperbolic Representation Learning: Revisiting and Advancing](https://mlsanity.com/paper/2306.09118/) (2023)
- [kHGCN: Tree-likeness Modeling via Continuous and Discrete Curvature Learning](https://mlsanity.com/paper/2212.01793/) (2022)
- [Extracting Event Temporal Relations via Hyperbolic Geometry](https://mlsanity.com/paper/2109.05527/) (2021)
- [Knowledge-Enhanced Top-K Recommendation in Poincar'e Ball](https://mlsanity.com/paper/2101.04852/) (2021)
- [Dual Metric Learning for Effective and Efficient Cross-Domain Recommendations](https://mlsanity.com/paper/2104.08490/) (2021)
- [Hyperbolic Diffusion Recommender Model](https://mlsanity.com/paper/2504.01541/) (2025)
- [Recommender systems based on graph embedding techniques: A comprehensive review](https://mlsanity.com/paper/2109.09587/) (2021)
- [SHMamba: Structured Hyperbolic State Space Model for Audio-Visual Question Answering](https://mlsanity.com/paper/2406.09833/) (2024)
- [A Fashion Item Recommendation Model in Hyperbolic Space](https://mlsanity.com/paper/2409.02599/) (2024)
- [Switch Spaces: Learning Product Spaces with Sparse Gating](https://mlsanity.com/paper/2102.08688/) (2021)
- [Hierarchical Latent Relation Modeling for Collaborative Metric Learning](https://mlsanity.com/paper/2108.04655/) (2021)
- [HSR: Hyperbolic Social Recommender](https://mlsanity.com/paper/2102.09389/) (2021)
- [AMCAD: Adaptive Mixed-Curvature Representation based Advertisement Retrieval System](https://mlsanity.com/paper/2203.14683/) (2022)
- [Hyperbolic Geometry in Computer Vision: A Survey](https://mlsanity.com/paper/2304.10764/) (2023)
- [SINCERE: Sequential Interaction Networks representation learning on Co-Evolving RiEmannian manifolds](https://mlsanity.com/paper/2305.03883/) (2023)
- [Improving Heterogeneous Graph Learning with Weighted Mixed-Curvature Product Manifold](https://mlsanity.com/paper/2307.04514/) (2023)
- [Capacity Bounds for Hyperbolic Neural Network Representations of Latent Tree Structures](https://mlsanity.com/paper/2308.09250/) (2023)
- [Anchor-aware Deep Metric Learning for Audio-visual Retrieval](https://mlsanity.com/paper/2404.13789/) (2024)
- [Augmenting the User-Item Graph with Textual Similarity Models](https://mlsanity.com/paper/2109.09358/) (2021)
- [Time-aware Hyperbolic Graph Attention Network for Session-based Recommendation](https://mlsanity.com/paper/2301.03780/) (2023)
- [Contrastive Sequential Interaction Network Learning on Co-Evolving Riemannian Spaces](https://mlsanity.com/paper/2401.01243/) (2024)

## Abstract (arXiv)

This paper investigates the notion of learning user and item representations in non-Euclidean space. Specifically, we study the connection between metric learning in hyperbolic space and collaborative filtering by exploring Mobius gyrovector spaces where the formalism of the spaces could be utilized to generalize the most common Euclidean vector operations. Overall, this work aims to bridge the gap between Euclidean and hyperbolic geometry in recommender systems through metric learning approach. We propose HyperML (Hyperbolic Metric Learning), a conceptually simple but highly effective model for boosting the performance. Via a series of extensive experiments, we show that our proposed HyperML not only outperforms their Euclidean counterparts, but also achieves state-of-the-art performance on multiple benchmark datasets, demonstrating the effectiveness of personalized recommendation in hyperbolic geometry.