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A Gaussian kernel for Kendall’s space of m-D shapes
dc.contributor.author | Gimeno i Garcia, Vicent | |
dc.contributor.author | Gual-Arnau, Ximo | |
dc.contributor.author | Ibáñez Gual, Maria Victoria | |
dc.contributor.author | Simó, Amelia | |
dc.date.accessioned | 2023-10-02T07:21:35Z | |
dc.date.available | 2023-10-02T07:21:35Z | |
dc.date.issued | 2023-08-15 | |
dc.identifier.citation | I GARCIA, Vicent Gimeno, et al. A Gaussian kernel for Kendall’s space of mD shapes. Pattern Recognition, 2023, vol. 144, p. 109887. | ca_CA |
dc.identifier.issn | 0031-3203 | |
dc.identifier.uri | http://hdl.handle.net/10234/204370 | |
dc.description.abstract | 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. | ca_CA |
dc.description.sponsorShip | Funding for open access charge: CRUE-Universitat Jaume I | |
dc.format.extent | 36 p. | ca_CA |
dc.format.mimetype | application/pdf | ca_CA |
dc.language.iso | eng | ca_CA |
dc.publisher | Elsevier ScienceDirect | ca_CA |
dc.relation.isPartOf | Pattern Recognition Vol. 144 (2023) | ca_CA |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | ca_CA |
dc.subject | Riemannian manifold | ca_CA |
dc.subject | Kendall shape space | ca_CA |
dc.subject | embedding | ca_CA |
dc.subject | reproducible kernel Hilbert space | ca_CA |
dc.title | A Gaussian kernel for Kendall’s space of m-D shapes | ca_CA |
dc.type | info:eu-repo/semantics/article | ca_CA |
dc.identifier.doi | https://doi.org/10.1016/j.patcog.2023.109887 | |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca_CA |
dc.type.version | info:eu-repo/semantics/publishedVersion | ca_CA |
project.funder.name | Universitat Jaume I | ca_CA |
project.funder.name | Ministerio de Ciencia, Innovación y Universidades | ca_CA |
oaire.awardNumber | UJI-B2020-22 | ca_CA |
oaire.awardNumber | PID2020-115930GA-100 | ca_CA |
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