Data Analysis with Merge Trees

Explore the world of merge trees (MTs) in this comprehensive lecture on topological data analysis. Delve into the advantages of using MTs over persistence diagrams (PDs) for encoding merging patterns of path-connected components in topological space filtrations. Learn about a novel metric for MTs, computed using linear integer programming, and discover its stability properties, geometric implications, and topological investigations. Understand the concept of Fréchet means and their approximation algorithm in the context of MTs. Gain insights into practical applications of this approach in functional data analysis and medical imaging, specifically in the field of radiomics. This talk provides a deep dive into advanced topological techniques for data analysis, offering valuable knowledge for researchers and practitioners in various scientific disciplines.