Results 251 to 260 of about 1,044 (284)
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SPIE Proceedings, 2005
Self-Organizing map (SOM) is a widely used tool to find clustering and also to visualize high dimensional data. Several spherical SOMs have been proposed to create a more accurate representation of the data by removing the “border effect”. In this paper, we compare several spherical lattices for the purpose of implementation of a SOM. We then introduce
Yingxin Wu 0001, Masahiro Takatsuka
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Self-Organizing map (SOM) is a widely used tool to find clustering and also to visualize high dimensional data. Several spherical SOMs have been proposed to create a more accurate representation of the data by removing the “border effect”. In this paper, we compare several spherical lattices for the purpose of implementation of a SOM. We then introduce
Yingxin Wu 0001, Masahiro Takatsuka
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Asymptotic behavior of averaged and firmly nonexpansive mappings in geodesic spaces [PDF]
Nonlinear Analysis: Theory, Methods & Applications, 2013 We further study averaged and firmly nonexpansive mappings in the setting of geodesic spaces with a main focus on the asymptotic behavior of their Picard iterates.
Adriana Nicolae
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Optimization of Geodesic Self-Organizing Map
The 2012 International Joint Conference on Neural Networks (IJCNN), 2012The Geodesic Self-Organizing Map (GeoSOM) is a variation of traditional SOM, which uses an icosahedron-based tessellation as spherical lattice to eliminate the border effect to minimize the distortion in the reduction of high-dimensional spaces. Border effect is a problem intrinsic of low-dimensional neural grid, where neurons in the border have a less
Romulo M. de Sousa +1 more
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Geodesic Mappings of Equiaffine and Ricci Symmetric Spaces
Mathematical Notes, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Berezovskii, Volodymyr +2 more
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Geodesic Maps “in the Large” of Ricci-Flat Spaces with $$n$$ Complete Geodesic Lines
Mathematical Notes, 2020The authors study global maps preserving geodesics from a pseudo-Riemannian manifold to Ricci-flat pseudo-Riemannian manifold. Two sufficient conditions for such map to be affine, are found. One of these conditions is the following: The scalar curvature vanishes at a point of the source manifold and complete geodesic lines through this point with ...
Mikeš, Josef +2 more
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On geodesic mappings of equidistant generalized Riemannian spaces
Applied Mathematics and Computation, 2012The notion of \textit{generalized Riemannian space} was introduced by Eisenhart in 1951 as a manifold endowed with a non-symmetric metric tensor \(g=(g_{ij})\). Such a space is called \textit{equidistant} if there exists a \(1\)-form whose covariant derivative is proportional to the symmetric part of \(g\).
Mica S Stanković +1 more
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Semi-supervised geodesic Generative Topographic Mapping
Pattern Recognition Letters, 2010We present a novel semi-supervised model, SS-Geo-GTM, which stems from a geodesic distance-based extension of Generative Topographic Mapping that prioritizes neighbourhood relationships along a generated manifold embedded in the observed data space. With this, it improves the trustworthiness and the continuity of the low-dimensional representations it ...
Raúl Cruz-Barbosa, Alfredo Vellido
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Some Remarks on Geodesic and Curvature Preserving Mappings
Zeitschrift für Analysis und ihre Anwendungen, 1997We ask for the converse of Gauss’ theorema egregium. Because in general isocurved manifolds are not isometric we ask stronger for isocurved, geodesic equivalent manifolds. For these we give a local criterion from which there follows that two-dimensional manifolds \overline{\mathcal M}^2
Belger, M., Beyer, K.-U.
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Almost geodesic curves and geodesic mappings
Итоги науки и техники Серия «Современная математика и ее приложения Тематические обзоры», 2023L. Ryparova, Josef Mikeš, Patrik Peška
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Almost Geodesic Mappings of Spaces with Affine Connection
Journal of Mathematical Sciences, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Berezovskii, V. E., Mikeš, J.
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