Primer: Integrating topological data analysis (TDA) with statistical learning techniques
Crawford Lab, Brown University
Topological data analysis (TDA) has emerged as a scalable way to extract key information from large data sets, while not depending on metrics or geodesics. As data has continually increased in size and complexity, TDA has progressed beyond the original persistence diagram to techniques that offer better interpretability, higher computational efficiency, and amenability with a wide range of frequently used statistical and machine learning techniques --- all while maintaining robustness and stability to noise. In this talk, we explore the development of topological invariants since the persistence diagram, such as the persistence landscape and the smooth Euler characteristic transform. We will discuss where these topological techniques have been applied and posit how early results in these areas have motivated novel methods we may see in the future.