Learning functions on data defined on manifolds

02/06/2012 - 3:00pm
02/06/2012 - 4:00pm
H.N. Mhaskar, California State University, Los Angeles and California Institute of Technology, Pasadena

A major problem in learning theory is the following: given a finite amount of data of the form {(xk,yk)}Mk=1, construct a function f that underlies the data. Many new applications deal with the case when the points {xk} form a large subset of a very high dimensional Euclidean space. Moreover, one does not have any control on how to choose the points xk. One can assume that the data set belongs to some low dimensional manifold. However, this manifold is unknown. Recent ideas based on Laplacian eigenmaps (equivalently, diffusion kernel) focus on a representation of the geometrical features of the data set. The talk will present our own recent research going beyond such representation problems to the problem of modeling of functions on the unknown, data defined manifold. The applications include image analysis, pattern recognition, analysis of chemical structures, prediction of time series, etc.

Davidson Lecture Hall, Claremont McKenna College
Seminar-Mhaskar.pdf46.65 KB