Geometric Harmonic Analysis

点击翻译按钮获取中文摘要

Diffusion (or inference) geometries , provide tools for organization ofmassive digital data sets. Like differential calculus, they are used tobuild global inference relations between objects by combining ``infinitesimal" (linear) models. Harmonic analysis on such structuresleads to multiscale folder building paradigms leading to powerful toolsfor functional regression and analysis of massive complex data.These geometric methods provide new insights in classical differentialgeometry enabling explicit embedding theorems and coordinate systems forRiemannian manifolds.The multiscale analytic methods lead to a systematic analysis tool forseemingly unstructured data bases, and enables the automatic generationof Ontologies and data induced languages. These methods are broadlyapplicable in medical diagnostics, in the organization and analysis ofpsychological questionnaires, as well as in all aspects of machinelearning from data mining to machine vision.