Comments on: Shape-based functional data analysis

This discussion paper applauds the authors for their impactful contribution to functional data analysis (FDA). Their primary insight lies in a formal mathematical definition of the “shape” of a curve, which they connect to familiar intuitive notions through a number of examples. Notably, the paper highlights the pitfalls of less well-thought-out curve registration approaches. The authors’ application of COVID-19 data enriches the discussion, highlighting the work’s practical relevance. We discuss connections of this work with object-oriented data analysis and propose enhancements to the authors’ shape-based functional principal component analysis. Additionally, we illustrate the practical significance of adaptive alignment with an example from our own research.