Selecting the elasticity penalty parameter λ in penalized elastic shape alignment

Determine principled, context-dependent criteria and methods for selecting the elasticity penalty parameter λ in penalized elastic shape analysis of multidimensional ground reaction force curves under the Fisher–Rao metric with Square Root Velocity Function representation, so that warping smoothness is appropriately regulated for different analytical objectives (such as predictive performance or signal estimation).

Background

The paper aligns multidimensional ground reaction force curves using elastic shape analysis with a Fisher–Rao metric and SRVF representation, introducing a penalty on the roughness of warping functions controlled by λ to avoid over-alignment and preserve curve shape, especially for atypical gait curves.

In practice, the authors selected λ heuristically via visual inspection, noting that formal criteria could depend on specific analytical goals (e.g., predictive modeling versus estimation of a common signal). They discuss potential approaches such as cross-validation and scale-space methods but emphasize that defining optimality and choosing λ tailored to different objectives is not yet established.