Results 251 to 260 of about 72,164 (263)
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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
Masahiro Takatsuka, Yingxin Wu
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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
Masahiro Takatsuka, Yingxin Wu
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Totally geodesic maps into metric spaces
Mathematische Zeitschrift, 2003The 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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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
Roberto Célio Limão de Oliveira +1 more
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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
Klaus Beyer, M. Belger
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Geodesic mappings of affine-connected and Riemannian spaces
Journal of Mathematical Sciences, 1996The author gives a review of geodesic mappings. The fundamental paragraphs of the review are: 1) General problems of geodesic mappings; 2) concircular vector fields and geodesic mappings; 3) geodesic mappings and deformation of surfaces; 4) geodesic mappings of generalized semisymmetric space; 5) geodesic mappings from Einsteinian spaces and their ...
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Geodesic mappings of Einstein spaces
Mathematical Notes of the Academy of Sciences of the USSR, 1980openaire +2 more sources
Geodesic Mappings of the Ellipsoid
Geometry and Topology of Submanifolds X, 2000openaire +2 more sources
A Geodesic Map Projection for Quadrilaterals
Cartography and Geographic Information Science, 2009openaire +2 more sources
The geodesic mappings in Riemannian and pseudo-Riemannian manifolds [PDF]
, 2008 openaire +3 more sources