PHIDA: Persistence-Guided Node-to-Cluster Mapping for Online Clustering

TL;DR

PHIDA introduces a novel persistence-guided node-to-cluster mapping method for online clustering, enhancing stability and performance by leveraging Persistent Homology within an ART-based framework.

Contribution

It combines Inverse-Distance ART with PH constraints to improve online clustering stability and accuracy, especially in nonstationary data environments.

Findings

PHIDA outperforms recent stationary-only clustering methods on 24 benchmark datasets.

It improves aggregate performance in nonstationary online clustering scenarios.

PHIDA's gains are linked to PH-constrained mapping preserving raw PH components.

Abstract

Online clustering methods that adaptively create and update nodes as data arrive often make node learning explicit, whereas the mapping from the learned node state to output clusters often remains implicit or simplified. Implicit mappings make output clusters sensitive to weak graph bridges or local relations based on distance in the graph over learned nodes, leaving no explicit constraint on which node groups remain intact during mapping. This paper addresses this gap by proposing PHIDA, a persistence-guided node-to-cluster mapping method for online clustering with learned nodes. PHIDA implements this mapping within Adaptive Resonance Theory (ART)-based online clustering by combining Inverse-Distance ART (IDA) node learning with node-to-cluster mapping constrained by Persistent Homology (PH). Experiments on 24 benchmark datasets show that PHIDA achieves the best average ranks in stationary comparisons that include the recent stationary-only clustering methods, while also improving aggregate performance in the nonstationary setting over the evaluated online methods that adaptively create and update nodes. Ablations and comparisons with conventional node-to-cluster mappings indicate that the observed gains are associated with PH-constrained mapping that preserves raw PH components, together with the use of the PH component view during node learning. Source code is available at https://github.com/Masuyama-lab/PHIDA