Geometric Harmonic Analysis

Yale University, New Haven CT

Investigators

Abstract

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