# Fuzzy Clustering by Hyperbolic Smoothing

arXiv: https://arxiv.org/abs/2207.04261 · HTML: https://mlsanity.com/paper/2207.04261/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 19 references that are in the map.
- First posted on arXiv 9 Jul 2022.

## Built on by (most cited first, 1 of 1)

- [Hyperbolic Fuzzy C-Means with Adaptive Weight-based Filtering for Efficient Clustering](https://mlsanity.com/paper/2505.04335/) (2025)

## Abstract (arXiv)

We propose a novel method for building fuzzy clusters of large data sets, using a smoothing numerical approach. The usual sum-of-squares criterion is relaxed so the search for good fuzzy partitions is made on a continuous space, rather than a combinatorial space as in classical methods citeHartigan. The smoothing allows a conversion from a strongly non-differentiable problem into differentiable subproblems of optimization without constraints of low dimension, by using a differentiable function of infinite class. For the implementation of the algorithm we used the statistical software R and the results obtained were compared to the traditional fuzzy C--means method, proposed by Bezdek.