Thursday, April 18, 2013
2:00 PM
Gavett Hall Room 310
Mauro Maggioni
Duke University
Multiscale Methods for High Dimensional Data and Graphs
In this talk I will discuss in greater depth some of the ideas presented at a high level in the first talk. I will focus on the construction of multiscale transforms of high-dimensional point clouds, i.e., maps from high-dimensional data to low- dimensional sparse (or compressible) representations based on a geometric multiscale decomposition and coordinatization of the data. I will discuss the computational aspects of this construction, its application to the problem of dictionary learning, and its connections to a novel variation of the compressive sensing paradigm. I will then discuss extensions of this construction to classification and regression tasks, as well as to the problem of producing efficient estimators for probability measures in high dimensions that are concentrated
near low-dimensional sets, drawing upon connections with optimal transportation problems in high dimensions. Finally, I will discuss how some of the above generalizes to studying multiscale structures in large graphs.