A Tutorial on Functional Data Analysis for High-Throughput Experiments

In this tutorial, I will describe a novel mathematical framework called ‘Function Data Analysis’ that combines tools from Statistics and Riemannian differential geometry to analyze data of a functional form. Functional data are ubiquitous in material science such as Spectroscopy, X-ray scattering, and Diffraction to list a few examples. Analyzing functions using traditional ‘vector-based’ methods is challenging as information is encoded in both the x-axis (warping or phase) and y-axis (intensity or amplitude). Intuitively, we analyze functional data such as those listed above using a notion of ‘shape’ that is hard to capture and analyze in a statistical sense. This tutorial will cover a basic introduction to performing statistics on Riemannian manifolds, relations between multi-variate and functional data analysis, and a few example applications to high-throughout polymeric material design and discovery problems. We will also include some code walkthroughs using synthetic datasets. Attendees will learn about performing tasks such as dimensionality reduction and clustering and have the opportunity to try them on a dataset of their own choice.