Results 291 to 300 of about 73,738 (309)

Geodesic self-organizing map

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, Masahiro Takatsuka
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Almost Geodesic Mappings and Projections of the Sphere

Mathematical Notes, 2022
In the paper under review it is shown that the parallel and central projections of \(n\)-planes onto \(n\)-spheres, as well as the central projections of \(n\)-spheres from their centers onto \(n\)-spheres, are almost geodesic mappings. Examples of almost geodesics mappings of compact spaces are also constructed.
Mikeš, J., Guseva, N. I., Peška, P., Rýparová, L.   +3 more
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Optimization of Geodesic Self-Organizing Map

The 2012 International Joint Conference on Neural Networks (IJCNN), 2012
The 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, Roberto C. L. Oliveira   +1 more
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Geodesic Mappings of Equiaffine and Ricci Symmetric Spaces

Mathematical Notes, 2021
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Berezovskii, V. E., Guseva, N. I., Mikeš, J.   +2 more
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Semi-supervised geodesic Generative Topographic Mapping

Pattern Recognition Letters, 2010
We 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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Almost geodesic curves and geodesic mappings

Итоги науки и техники Серия «Современная математика и ее приложения Тематические обзоры», 2023
L. Ryparova, Josef Mikeš, Patrik Peška
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Some Remarks on Geodesic and Curvature Preserving Mappings

Zeitschrift für Analysis und ihre Anwendungen, 1997
We 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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Totally geodesic maps into metric spaces

Mathematische Zeitschrift, 2003
The author proves that a totally geodesic mapping \(f\) from a Riemannian manifold \(M\) to a metric space \(X\) can be represented as a composite of a totally geodesic mapping from \(M\) to a Finsler manifold \(F\) and a locally isometric embedding from \(F\) to \(X\).
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Almost Geodesic Mappings of Spaces with Affine Connection

Journal of Mathematical Sciences, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Berezovskii, V. E., Mikeš, J.
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Geodesics in Brownian surfaces (Brownian maps)

2014
We define a class a metric spaces we call Brownian surfaces, arising as the scaling limits of random maps on general orientable surfaces with a boundary and we study the geodesics from a uniformly chosen random point. These metric spaces generalize the well-known Brownian map and our results generalize the properties shown by Le Gall on geodesics in ...
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