Comments on: Shape-based functional data analysis
Pedro Delicado · Test · 2023
The paper under discussion proposes a non-standard way to approach functional data analysis based on the concept of shape-of-a-function. I congratulate the authors for such a stimulating piece of work. Among the most remarkable contributions of the paper, I would like to note the following: a formal definition of the shape of a function f as an equivalence class [ f ], the definition of the square-root velocity function (SRVF) \(q_f\) of a function f and its use to describe the shape [ f ] of f , to align sets of functions optimally, and to define the shape distance \(d_{\mathcal {S}}([f],[g])\equiv d_{\mathcal {S}}([q_f],[q_g])\) between the shapes of two functions f and g . The abundant examples in the article show the advantages of SRVF-based alignment over alternative approaches.