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• W2006554089 abstract "We provide a framework for structural multiscale geometric organization of graphs and subsets of R(n). 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. The process of iterating or diffusing the Markov matrix is seen as a generalization of some aspects of the Newtonian paradigm, in which local infinitesimal transitions of a system lead to global macroscopic descriptions by integration. We provide a unified view of ideas from data analysis, machine learning, and numerical analysis." @default.
• W2006554089 created "2016-06-24" @default.
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• W2006554089 date "2005-05-17" @default.
• W2006554089 modified "2023-10-10" @default.
• W2006554089 title "Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps" @default.
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• W2006554089 doi "https://doi.org/10.1073/pnas.0500334102" @default.
• W2006554089 hasPubMedCentralId "https://www.ncbi.nlm.nih.gov/pmc/articles/1140422" @default.
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