# Hyperbolic Fuzzy C-Means with Adaptive Weight-based Filtering for Efficient Clustering

arXiv: https://arxiv.org/abs/2505.04335 · HTML: https://mlsanity.com/paper/2505.04335/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 52 references that are in the map.
- First posted on arXiv 7 May 2025.

## Builds on (most cited first, 4 of 4)

- [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 Centroid Auto-Fused Hierarchical Fuzzy c-Means Clustering](https://mlsanity.com/paper/2004.12756/) (2020)
- [Fuzzy Clustering by Hyperbolic Smoothing](https://mlsanity.com/paper/2207.04261/) (2022)

## Abstract (arXiv)

Clustering algorithms play a pivotal role in unsupervised learning by identifying and grouping similar objects based on shared characteristics. Although traditional clustering techniques, such as hard and fuzzy center-based clustering, have been widely used, they struggle with complex, high-dimensional, and non-Euclidean datasets. In particular, the fuzzy C-Means (FCM) algorithm, despite its efficiency and popularity, exhibits notable limitations in non-Euclidean spaces. Euclidean spaces assume linear separability and uniform distance scaling, limiting their effectiveness in capturing complex, hierarchical, or non-Euclidean structures in fuzzy clustering. To overcome these challenges, we introduce Filtration-based Hyperbolic Fuzzy C-Means (HypeFCM), a novel clustering algorithm tailored for better representation of data relationships in non-Euclidean spaces. HypeFCM integrates the principles of fuzzy clustering with hyperbolic geometry and employs a weight-based filtering mechanism to improve performance. The algorithm initializes weights using a Dirichlet distribution and iteratively refines cluster centroids and membership assignments based on a hyperbolic metric in the Poincar'e Disc model. Extensive experimental evaluations on 6 synthetic and 12 real-world datasets demonstrate that HypeFCM significantly outperforms conventional fuzzy clustering methods in non-Euclidean settings, underscoring its robustness and effectiveness.