Topology-Driven Clustering: Enhancing Performance with Betti Number Filtration

תקציר מקורי באנגליתarXiv:2505.04346v2 Announce Type: replace Abstract: Clustering aims at partitioning data points into groups of similar objects without knowing about the class labels. However, clustering datasets with complex geometric structures, such as nonconvex shapes, multiple scales, or intertwined manifolds, remains challenging for traditional algorithms that primarily rely on Euclidean or kernel-based similarity measures. Topological Data Analysis (TDA), particularly persistent homology, provides a powerful framework for capturing intrinsic structural properties of data, including connected components, loops, and higher-dimensional features across multiple scales. In this work, we propose a novel topological clustering algorithm called \textbf{Betti Number Filtration-based Topological Clustering (B