Geometric Harmonic Analysis

扩散（或推理）几何，提供了大量的数字数据集的组织工具。像微分学一样，它们被用来通过组合“无穷小”（线性）模型来建立对象之间的全局推理关系。这些几何方法为经典微分几何提供了新的见解，使黎曼流形的嵌入定理和坐标系统成为可能。多尺度分析方法为看似非结构化的数据库提供了一个系统的分析工具，并使本体和数据诱导语言的自动生成成为可能。这些方法广泛应用于医学诊断、心理问卷的组织和分析，以及从数据挖掘到机器视觉的机器学习的各个方面。

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.