Geometric diffusions as a tool for harmonic analysis and structure definition of data: Multiscale methods
نویسندگان
چکیده
منابع مشابه
Geometric diffusions as a tool for harmonic analysis and structure definition of data: multiscale methods.
In the companion article, a framework for structural multiscale geometric organization of subsets of R(n) and of graphs was introduced. Here, diffusion semigroups are used to generate multiscale analyses in order to organize and represent complex structures. We emphasize the multiscale nature of these problems and build scaling functions of Markov matrices (describing local transitions) that le...
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We provide a framework for structural multiscale geometric organization of graphs and subsets of Rn. We use diffusion semigroups to generate multiscale geometries in order to organize and represent complex structures. We show that appropriately selected eigenfunctions or scaling functions of Markov matrices, which describe local transitions, lead to macroscopic descriptions at different scales....
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Harmonic analysis on manifolds and graphs has recently led to mathematical developments in the field of data analysis. The resulting new tools can be used to compress and analyze large and complex data sets, such as those derived from sensor networks or neuronal activity datasets, obtained in the laboratory or through computer modeling. The nature of the algorithms (based on diffusion maps and ...
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 2005
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.0500896102