Data-Driven, Soft Alignment of Functional Data Using Shapes and Landmarks
This work addresses a specific limitation in statistical analysis of functions and shapes for researchers in that field, representing an incremental improvement.
The paper tackles the problem of functional data alignment by extending the SRVF method to incorporate landmark information, resulting in a soft alignment approach that balances curve and landmark matching, and demonstrates superior performance in certain practical scenarios.
Alignment or registration of functions is a fundamental problem in statistical analysis of functions and shapes. While there are several approaches available, a more recent approach based on Fisher-Rao metric and square-root velocity functions (SRVFs) has been shown to have good performance. However, this SRVF method has two limitations: (1) it is susceptible to over alignment, i.e., alignment of noise as well as the signal, and (2) in case there is additional information in form of landmarks, the original formulation does not prescribe a way to incorporate that information. In this paper we propose an extension that allows for incorporation of landmark information to seek a compromise between matching curves and landmarks. This results in a soft landmark alignment that pushes landmarks closer, without requiring their exact overlays to finds a compromise between contributions from functions and landmarks. The proposed method is demonstrated to be superior in certain practical scenarios.