# Hyperbolic Gaussian Blurring Mean Shift: A Statistical Mode-Seeking Framework for Clustering in Curved Spaces

arXiv: https://arxiv.org/abs/2512.11448 · HTML: https://mlsanity.com/paper/2512.11448/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 48 references that are in the map.
- First posted on arXiv 12 Dec 2025.

## Builds on (most cited first, 8 of 8)

- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [From Trees to Continuous Embeddings and Back: Hyperbolic Hierarchical Clustering](https://mlsanity.com/paper/2010.00402/) (2020)
- [Hierarchical Clustering: Objective Functions and Algorithms](https://mlsanity.com/paper/1704.02147/) (2017)
- [The Numerical Stability of Hyperbolic Representation Learning](https://mlsanity.com/paper/2211.00181/) (2022)
- [A review of mean-shift algorithms for clustering](https://mlsanity.com/paper/1503.00687/) (2015)
- [Automated Clustering of High-dimensional Data with a Feature Weighted Mean Shift Algorithm](https://mlsanity.com/paper/2012.10929/) (2020)
- [Unsupervised Embedding of Hierarchical Structure in Euclidean Space](https://mlsanity.com/paper/2010.16055/) (2020)
- [GridShift: A Faster Mode-seeking Algorithm for Image Segmentation and Object Tracking](https://mlsanity.com/paper/2206.02200/) (2022)

## Abstract (arXiv)

Clustering is a fundamental unsupervised learning task for uncovering patterns in data. While Gaussian Blurring Mean Shift (GBMS) has proven effective for identifying arbitrarily shaped clusters in Euclidean space, it struggles with datasets exhibiting hierarchical or tree-like structures. In this work, we introduce HypeGBMS, a novel extension of GBMS to hyperbolic space. Our method replaces Euclidean computations with hyperbolic distances and employs M"obius-weighted means to ensure that all updates remain consistent with the geometry of the space. HypeGBMS effectively captures latent hierarchies while retaining the density-seeking behavior of GBMS. We provide theoretical insights into convergence and computational complexity, along with empirical results that demonstrate improved clustering quality in hierarchical datasets. This work bridges classical mean-shift clustering and hyperbolic representation learning, offering a principled approach to density-based clustering in curved spaces. Extensive experimental evaluations on 11 real-world datasets demonstrate that HypeGBMS significantly outperforms conventional mean-shift clustering methods in non-Euclidean settings, underscoring its robustness and effectiveness.