用双曲几何改进模糊聚类，更好处理复杂层次数据。

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 Poincaré 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.