APPLIED MATH SEMINAR

Speaker: Ronald R. Coifman, Yale University

Title: Harmonic Analysis and Geometries of Digital Data Bases

When/where: Tuesday, November 3rd, 4:15 PM, AKW 200

Ronald Coifman , Matan Gavish  Yale University
Given a matrix (of Data) we describe methodologies to build two multiscale
(inference) Geometries/Harmonic Analysis one on the rows, the other on the
columns. The geometries are designed to simplify the representation of the data
base. We will provide a number of examples including; matrices of operators,
psychological questionnaires, vector valued images, scientific articles, etc.
In all these cases tensor Haar orthogonal bases play a crucial role in
organizing the data base viewed as a function of two variables (row, column) 
in the case of potential operators we relate to Calderon Zygmund
decompositions, while for other data this is a "data agnostic analytic learning
tool"
For the example of the matrix of eigenfunctions of a discretized Laplace
operator (say, on a compact manifold) we obtain  both the Geometry of the
domain of the Laplace operator as well as a dual  multiscale Geometry of the
eigenvectors...