New automated approach to selection of mapper clustering parameters

Topological methods have recently gained traction as powerful tools for extracting insights from high-dimensional data, forming the foundation of an approach known as Topological Data Analysis (TDA). Among the key developments in TDA is the Mapper algorithm, which constructs graph-based representations of complex datasets, capturing their topological structure at a user-defined resolution. The Mapper algorithm has shown promise across various applications, particularly in biomedical data analysis. However, its application requires careful selection of several parameters, especially the clustering algorithm and its settings. Without prior knowledge and a deep understanding of the data, these choices are non-trivial and can be a major barrier for researchers aiming to leverage Mapper effectively. In this work, we introduce enhancements to the Mapper algorithm to address this challenge. Specifically, we investigate the integration of ensemble learning (EL) techniques into Mapper’s graph construction to eliminate the need for arbitrary parameter selection. Additionally, we propose a data-driven criterion for selecting the clustering method best suited to the Mapper algorithm. Our experimental results demonstrate that the proposed approach enables the construction of Mapper graphs that accurately capture the underlying structure of the input data, all without manual parameter tuning.