Hierarchical topological clustering

2025-12-31

Soft Computing - A Fusion of Foundations, Methodologies and Applications

AI Summary

This work proposes a hierarchical clustering algorithm grounded in topological data analysis to address the challenge of identifying clusters of arbitrary shape and salient outliers without requiring prior assumptions about data distribution. The method operates under any distance metric and eschews distributional assumptions by constructing a topological hierarchy and incorporating persistence analysis to rigorously assess cluster stability and outlier significance. Experimental evaluations on real-world datasets from domains such as image analysis, healthcare, and economics demonstrate that the algorithm yields semantically coherent and robust clustering results even in complex scenarios where conventional approaches fail, substantially enhancing the detection of non-convex structures and critical anomalous points.

Technology Category

Data Mining & Knowledge Management: Anomaly/Outlier DetectionMachine Learning: ClusteringSearch and Optimization: Distributed Search

Application Category

Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphsWeb Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web textSemantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Topological methods have the potential of exploring data clouds without making assumptions on their the structure. Here we propose a hierarchical topological clustering algorithm that can be implemented with any distance choice. The persistence of outliers and clusters of arbitrary shape is inferred from the resulting hierarchy. We demonstrate the potential of the algorithm on selected datasets in which outliers play relevant roles, consisting of images, medical and economic data. These methods can provide meaningful clusters in situations in which other techniques fail to do so.

Problem

• topological clustering
• hierarchical clustering
• outlier detection
• arbitrary-shaped clusters
• data structure assumptions

Innovation

• hierarchical topological clustering
• topological data analysis
• outlier detection
• arbitrary-shaped clusters
• distance-agnostic algorithm