Bala Krishnamoorthy - Steinhaus Filtration and Stable Paths in the Mapper

Explore the intersection of topological data analysis and data science in this 58-minute lecture from the Applied Algebraic Topology Network. Delve into the Steinhaus filtration, a novel approach based on generalized Steinhaus distance, and its applications in Mapper construction. Learn about stability results, equivalence to Čech filtration, and the relationship with Vietoris-Rips filtration. Discover how stable paths within this filtration can be applied to recommendation systems and explainable machine learning, with practical examples using movie datasets and image classification models. Gain insights into the potential of topological methods for analyzing complex data structures and improving data-driven decision-making processes.

Intro
Descriptors of Energy Landscapes Using Topological Analysis
MAPPER: APPLICATIONS
MAPPER: STABILITY → use framework of persistence
ABSTRACT COVERS?
RESULTS
JACCARD DISTANCE
STEINHAUS DISTANCE
STEINHAUS FILTRATION
ČECH EQUIVALENCE ?
STABLE PATHS
MoviE RECOMMENDATIONS
EXPLANATIONS IN ML MODEL → Fashion-MNIST clothing
OPEN QUESTIONS