Eigenmaps and minimal and bandlimited immersions of graphs into Euclidean spaces
| Autor: | Meyer Z. Pesenson, Isaac Z. Pesenson |
|---|---|
| Rok vydání: | 2010 |
| Předmět: |
Bandlimiting
Reduction (recursion theory) Euclidean space Applied Mathematics ComputingMilieux_PERSONALCOMPUTING Eigenmaps Image processing Combinatorial weighted graphs Bandlimited immersions Interpolation Combinatorics Combinatorial Laplace operator ComputerApplications_MISCELLANEOUS Euclidean geometry Mathematics::Differential Geometry Minimal immersions into Euclidean spaces Reconstruction Laplace operator Approximation Smoothing Analysis Mathematics ComputingMethodologies_COMPUTERGRAPHICS |
| Zdroj: | Journal of Mathematical Analysis and Applications. 366(1):137-152 |
| ISSN: | 0022-247X |
| DOI: | 10.1016/j.jmaa.2009.10.062 |
| Popis: | We introduce concepts of minimal immersions and bandlimited (Paley–Wiener) immersions of combinatorial weighted graphs (finite or infinite) into Euclidean spaces. The notion of bandlimited immersions generalizes the known concept of eigenmaps of graphs. It is shown that our minimal immersions can be used to perform interpolation, smoothing and approximation of immersions of graphs into Euclidean spaces. It is proved that under certain conditions minimal immersions converge to bandlimited immersions. Explicit expressions of minimal immersions in terms of eigenmaps are given. The results can find applications for data dimension reduction, image processing, computer graphics, visualization and learning theory. |
| Databáze: | OpenAIRE |
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