A Systematic Approach to Tuning Cover Parameters in Mapper for Improved TDA Representation

Topological Data Analysis (TDA) offers a powerful framework for analyzing complex datasets by leveraging algebraic topology to unveil underlying structures. Within TDA, the Mapper algorithm plays a pivotal role in transforming data into a simplified graph representation, known as a simplicial complex. However, selecting appropriate parameters within the Mapper algorithm remains a challenge due to the absence of a standardized approach. In this study, we propose a systematic methodology for choosing Cover parameters by integrating quantitative assessment, using the Netsimile metric and graph topological features, with qualitative visual analysis. We demonstrate the efficacy of our approach using brain features from the Human Connectome Project dataset. Through a comprehensive evaluation, we identify parameter configurations that enhance graph properties stability producing informative graph structures. Our findings highlight the importance of integrating quantitative metrics into the parameter selection process, paving the way for enhanced data exploration and understanding. The open-source nature of our methodology promotes broader adoption and application across diverse datasets and analytical workflows.