Topology-Driven Clustering: Enhancing Performance with Betti Number Filtration
This work addresses the problem of inconsistent clustering performance on highly complicated datasets for researchers and practitioners in unsupervised learning, representing an incremental improvement over existing topological clustering algorithms.
The paper tackled the challenge of clustering complex datasets with intertwined shapes by proposing a topology-driven algorithm using Vietoris-Rips complexes and Betti number filtration, which demonstrated commendable performance on synthetic and real-world datasets compared to existing topology-based methods.
Clustering aims to form groups of similar data points in an unsupervised regime. Yet, clustering complex datasets containing critically intertwined shapes poses significant challenges. The prevailing clustering algorithms widely depend on evaluating similarity measures based on Euclidean metrics. Exploring topological characteristics to perform clustering of complex datasets inevitably presents a better scope. The topological clustering algorithms predominantly perceive the point set through the lens of Simplicial complexes and Persistent homology. Despite these approaches, the existing topological clustering algorithms cannot somehow fully exploit topological structures and show inconsistent performances on some highly complicated datasets. This work aims to mitigate the limitations by identifying topologically similar neighbors through the Vietoris-Rips complex and Betti number filtration. In addition, we introduce the concept of the Betti sequences to capture flexibly essential features from the topological structures. Our proposed algorithm is adept at clustering complex, intertwined shapes contained in the datasets. We carried out experiments on several synthetic and real-world datasets. Our algorithm demonstrated commendable performances across the datasets compared to some of the well-known topology-based clustering algorithms.