Math 388.05
Title: Topics in analysis of high-dimensional data: harmonic
analysis, random matrices & algorithms
Instructor: Mauro Maggioni

We discuss several problems, applications and techniques that come
about when studying point clouds in high dimensions. The emphasis will be on
harmonic analysis techniques, in particular in how the connect discrete
objects (e.g. sampled point clouds, graphs) with their continuous
counterparts (e.g. manifolds), as well on random matrices and how they may
be used to study the effects of sampling and noise. Algorithms and
computational techniques related to all of the above will be discussed, in
particular for problems like finding nearest neighbors in high-dimensions,
and randomized algorithms for linear algebra algorithms used for the
analysis of high-dimensional point clouds.