Hyperbolic Fuzzy $C$-Means with Adaptive Weight-based Filtering for Clustering in Non-Euclidean Spaces

• URL: http://arxiv.org/abs/2505.04335v1
• Date: Wed, 07 May 2025 11:32:53 GMT
• Title: Hyperbolic Fuzzy $C$-Means with Adaptive Weight-based Filtering for Clustering in Non-Euclidean Spaces
• Authors: Swagato Das, Arghya Pratihar, Swagatam Das,
• Abstract summary: Fuzzy $C$-Means (FCM) algorithm exhibits notable limitations in non-Euclidean spaces.<n>HypeFCM integrates the principles of fuzzy clustering with hyperbolic geometry.<n>HypeFCM significantly outperforms conventional fuzzy clustering methods in non-Euclidean settings.
• Score: 14.904264782690639
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Clustering algorithms play a pivotal role in unsupervised learning by identifying and grouping similar objects based on shared characteristics. While 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 demonstrate that HypeFCM significantly outperforms conventional fuzzy clustering methods in non-Euclidean settings, underscoring its robustness and effectiveness.

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