# Where are we in embedding spaces? A Comprehensive Analysis on Network Embedding Approaches for Recommender Systems

arXiv: https://arxiv.org/abs/2105.08908 · HTML: https://mlsanity.com/paper/2105.08908/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 34 references that are in the map.
- First posted on arXiv 19 May 2021.

## Builds on (most cited first, 11 of 11)

- [Neural Collaborative Filtering](https://mlsanity.com/paper/1708.05031/) (2017)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Ups and Downs: Modeling the Visual Evolution of Fashion Trends with One-Class Collaborative Filtering](https://mlsanity.com/paper/1602.01585/) (2016)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Embedding Text in Hyperbolic Spaces](https://mlsanity.com/paper/1806.04313/) (2018)
- [HyperML: A Boosting Metric Learning Approach in Hyperbolic Space for Recommender Systems](https://mlsanity.com/paper/1809.01703/) (2018)
- [Latent Relational Metric Learning via Memory-based Attention for Collaborative Ranking](https://mlsanity.com/paper/1707.05176/) (2017)
- [Scalable Hyperbolic Recommender Systems](https://mlsanity.com/paper/1902.08648/) (2019)

## Built on by (most cited first, 24 of 24)

- [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)
- [Unsupervised Graph Poisoning Attack via Contrastive Loss Back-propagation](https://mlsanity.com/paper/2201.07986/) (2022)
- [Self-Supervised Temporal Graph learning with Temporal and Structural Intensity Alignment](https://mlsanity.com/paper/2302.07491/) (2023)
- [HICF: Hyperbolic Informative Collaborative Filtering](https://mlsanity.com/paper/2207.09051/) (2022)
- [Hyper Meta-Path Contrastive Learning for Multi-Behavior Recommendation](https://mlsanity.com/paper/2109.02859/) (2021)
- [Dual Space Graph Contrastive Learning](https://mlsanity.com/paper/2201.07409/) (2022)
- [HGWaveNet: A Hyperbolic Graph Neural Network for Temporal Link Prediction](https://mlsanity.com/paper/2304.07302/) (2023)
- [Graph Masked Autoencoders with Transformers](https://mlsanity.com/paper/2202.08391/) (2022)
- [H2TNE: Temporal Heterogeneous Information Network Embedding in Hyperbolic Spaces](https://mlsanity.com/paper/2304.06970/) (2023)
- [Towards Improving Embedding Based Models of Social Network Alignment via Pseudo Anchors](https://mlsanity.com/paper/2111.11335/) (2021)
- [Hyperbolic Graph Representation Learning: A Tutorial](https://mlsanity.com/paper/2211.04050/) (2022)
- [Large Language Models Enhanced Hyperbolic Space Recommender Systems](https://mlsanity.com/paper/2504.05694/) (2025)
- [EdgePruner: Poisoned Edge Pruning in Graph Contrastive Learning](https://mlsanity.com/paper/2312.07022/) (2023)
- [Towards Non-Euclidean Foundation Models: Advancing AI Beyond Euclidean Frameworks](https://mlsanity.com/paper/2505.14417/) (2025)
- [SINGA-Easy: An Easy-to-Use Framework for MultiModal Analysis](https://mlsanity.com/paper/2108.02572/) (2021)
- [VisualTextRank: Unsupervised Graph-based Content Extraction for Automating Ad Text to Image Search](https://mlsanity.com/paper/2108.02725/) (2021)
- [Text is NOT Enough: Integrating Visual Impressions into Open-domain Dialogue Generation](https://mlsanity.com/paper/2109.05778/) (2021)
- [Discovering Personalized Semantics for Soft Attributes in Recommender Systems using Concept Activation Vectors](https://mlsanity.com/paper/2202.02830/) (2022)
- [Reinforced MOOCs Concept Recommendation in Heterogeneous Information Networks](https://mlsanity.com/paper/2203.11011/) (2022)
- [Explanation-Guided Fairness Testing through Genetic Algorithm](https://mlsanity.com/paper/2205.08335/) (2022)
- [Using Graph Neural Networks for Program Termination](https://mlsanity.com/paper/2207.14648/) (2022)
- [Tribe or Not? Critical Inspection of Group Differences Using TribalGram](https://mlsanity.com/paper/2303.09664/) (2023)
- [Adversarial Robustness of Link Sign Prediction in Signed Graphs](https://mlsanity.com/paper/2401.10590/) (2024)

## Abstract (arXiv)

Hyperbolic space and hyperbolic embeddings are becoming a popular research field for recommender systems. However, it is not clear under what circumstances the hyperbolic space should be considered. To fill this gap, This paper provides theoretical analysis and empirical results on when and where to use hyperbolic space and hyperbolic embeddings in recommender systems. Specifically, we answer the questions that which type of models and datasets are more suited for hyperbolic space, as well as which latent size to choose. We evaluate our answers by comparing the performance of Euclidean space and hyperbolic space on different latent space models in both general item recommendation domain and social recommendation domain, with 6 widely used datasets and different latent sizes. Additionally, we propose a new metric learning based recommendation method called SCML and its hyperbolic version HSCML. We evaluate our conclusions regarding hyperbolic space on SCML and show the state-of-the-art performance of hyperbolic space by comparing HSCML with other baseline methods.