A Gaussian kernel for Kendall’s space of m-D shapes
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Other documents of the author: Gimeno i Garcia, Vicent; Gual-Arnau, Ximo; Ibáñez Gual, Maria Victoria; Simó, Amelia
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comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
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Title
A Gaussian kernel for Kendall’s space of m-D shapesDate
2023-08-15Publisher
Elsevier ScienceDirectISSN
0031-3203Bibliographic citation
I GARCIA, Vicent Gimeno, et al. A Gaussian kernel for Kendall’s space of mD shapes. Pattern Recognition, 2023, vol. 144, p. 109887.Type
info:eu-repo/semantics/articleVersion
info:eu-repo/semantics/publishedVersionAbstract
In this paper, we develop an approach to exploit kernel methods with data lying on the m-D Kendall shape space. When data arise in a finite-dimensional curved Riemannian manifold, as in this case, the usual Euclidean ... [+]
In this paper, we develop an approach to exploit kernel methods with data lying on the m-D Kendall shape space. When data arise in a finite-dimensional curved Riemannian manifold, as in this case, the usual Euclidean computer vision and machine learning algorithms must be treated carefully. A good approach is to use positive definite kernels on manifolds to embed the manifold with its corresponding metric in a high-dimensional reproducing kernel Hilbert space, where it is possible to utilize algorithms developed for linear spaces. Different Gaussian kernels can be found in the literature on the 2-D Kendall shape space to perform this embedding. The main novelty of this work is to provide a Gaussian kernel for the m-D Kendall shape space. This new Kernel coincides in the case m = 2 with the Gaussian kernels most widely used in the Kendall planar shape space and allows to define an embedding of the m-D Kendall shape space into a reproducible kernel Hilbert space. As far as we know, the complexity of the m-D Kendall shape space has meant that this embedding has not been addressed in the literature until now. This methodology will be tested on a machine learning problem with a simulated and a real data set. [-]
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Pattern Recognition Vol. 144 (2023)Funder Name
Universitat Jaume I | Ministerio de Ciencia, Innovación y Universidades
Project code
UJI-B2020-22 | PID2020-115930GA-100
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info:eu-repo/semantics/openAccess
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