Enhancing a Kernel Method for Shape Analysis in Kendall Space
Year: 2025
Type: article
Abstract: In learning methods defined on a manifold, it is often important to embed the manifold into a Hilbert space to apply kernel methods, as it enables the utilization of linear techniques in the transformed space, thereby facilitating complex data analysis and classification tasks with nonlinear structures [10]. In [6], the authors define an embedding of the $$\textit{m}$$ m -dimensional Kendall shape space into an $$\mathbb {R}^{\textit{N}}$$ R N space, from which kernel methods are introduced in the Kendall shape space. In this paper, we significantly simplify this result by achieving an embedding of the Kendall shape space into a Euclidean space $$\mathbb {R}^{\textit{n}}$$ R n of much lower dimension $$\textit{n}$$ n than $$\textit{N}$$ N , greatly simplifying calculations and computational costs of applications. Additionally, we characterize the image of the Kendall shape space in $$\mathbb {R}^{\textit{n}}$$ R n , allowing us to define a new extrinsic mean of shapes in the Kendall shape space.
Authors: Ximo Gual-Arnau, Juan Monterde
Institutions: Universitat Jaume I, Universitat de València
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Funder: Universitat Jaume I
OpenAlex ID: W4408675368