Topological data analysis: Concepts, computation, and applications in chemical engineering

A primary hypothesis that drives scientific and engineering studies is data has structure. The dominant paradigms for describing such structure are statistics (e.g., moments, correlation functions) signal processing convolutional neural nets, Fourier series). Topological Data Analysis (TDA) a field of mathematics analyzes from fundamentally different perspective. TDA represents datasets as geometric objects provides dimensionality reduction techniques project onto low-dimensional descriptors. key properties these descriptors (also known topological features) they provide multiscale information stable under perturbations noise, translation, rotation). In this work, we review the mathematical concepts methods present applications in chemical engineering.