# Breaking the Euclidean Barrier: Hyperboloid-Based Biological Sequence Analysis

arXiv: https://arxiv.org/abs/2510.01118 · HTML: https://mlsanity.com/paper/2510.01118/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 70 references that are in the map.
- First posted on arXiv 1 Oct 2025.

## Builds on (most cited first, 18 of 18)

- [Unsupervised Deep Embedding for Clustering Analysis](https://mlsanity.com/paper/1511.06335/) (2015)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [A Comprehensive Survey of Graph Embedding: Problems, Techniques and Applications](https://mlsanity.com/paper/1709.07604/) (2017)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [Embedding Multimodal Relational Data for Knowledge Base Completion](https://mlsanity.com/paper/1809.01341/) (2018)
- [Hyperbolic Interaction Model For Hierarchical Multi-Label Classification](https://mlsanity.com/paper/1905.10802/) (2019)
- [Spike2Vec: An Efficient and Scalable Embedding Approach for COVID-19 Spike Sequences](https://mlsanity.com/paper/2109.05019/) (2021)
- [A k-mer Based Approach for SARS-CoV-2 Variant Identification](https://mlsanity.com/paper/2108.03465/) (2021)
- [PWM2Vec: An Efficient Embedding Approach for Viral Host Specification from Coronavirus Spike Sequences](https://mlsanity.com/paper/2201.02273/) (2022)
- [Efficient Approximate Kernel Based Spike Sequence Classification](https://mlsanity.com/paper/2209.04952/) (2022)
- [Neural Distance Embeddings for Biological Sequences](https://mlsanity.com/paper/2109.09740/) (2021)
- [Unsupervised Hyperbolic Representation Learning via Message Passing Auto-Encoders](https://mlsanity.com/paper/2103.16046/) (2021)
- [Robust Representation and Efficient Feature Selection Allows for Effective Clustering of SARS-CoV-2 Variants](https://mlsanity.com/paper/2110.09622/) (2021)
- [Reads2Vec: Efficient Embedding of Raw High-Throughput Sequencing Reads Data](https://mlsanity.com/paper/2211.08267/) (2022)
- [Distributed Representations for Biological Sequence Analysis](https://mlsanity.com/paper/1608.05949/) (2016)
- [Evaluating COVID-19 Sequence Data Using Nearest-Neighbors Based Network Model](https://mlsanity.com/paper/2211.10546/) (2022)
- [T Cell Receptor Protein Sequences and Sparse Coding: A Novel Approach to Cancer Classification](https://mlsanity.com/paper/2304.13145/) (2023)
- [Sequence Analysis Using the Bezier Curve](https://mlsanity.com/paper/2503.14574/) (2025)

## Abstract (arXiv)

Genomic sequence analysis plays a crucial role in various scientific and medical domains. Traditional machine-learning approaches often struggle to capture the complex relationships and hierarchical structures of sequence data when working in high-dimensional Euclidean spaces. This limitation hinders accurate sequence classification and similarity measurement. To address these challenges, this research proposes a method to transform the feature representation of biological sequences into the hyperboloid space. By applying a transformation, the sequences are mapped onto the hyperboloid, preserving their inherent structural information. Once the sequences are represented in the hyperboloid space, a kernel matrix is computed based on the hyperboloid features. The kernel matrix captures the pairwise similarities between sequences, enabling more effective analysis of biological sequence relationships. This approach leverages the inner product of the hyperboloid feature vectors to measure the similarity between pairs of sequences. The experimental evaluation of the proposed approach demonstrates its efficacy in capturing important sequence correlations and improving classification accuracy.