The Weizmann Institute of Science
Faculty of Mathematics and Computer Science
Special Guest Lecture
Yosi Keller
Department of Mathematics
Yale University
will speak on
The diffusion framework: bridging statistical
learning and signal processing
Abstract:
The diffusion framework: a computational approach to data analysis and signal
processing on data sets. The diffusion framework is a computational approach to
high dimensional data analysis and processing. Based on spectral graph theory,
we define diffusion processes on data sets. These agglomerate local transitions
reflecting the infinitesimal geometries of high-dimensional dataset, to obtain
meaningful global embeddings.
The eigenfunctions of the corresponding diffusion operator (Graph Laplacian)
provide a natural embedding of the sets into a Euclidean space, in which the
$L_2$ distance measures an intrinsic probabilistic quantity denoted the
diffusion distance. In this talk, we introduce the mathematical foundations of
our approach and apply it to high dimensional data organization and statistical
learning. Then we show that the eigenfunctions of the Laplacian form manifold
adaptive bases, which pave the way to the extension of signal processing
concepts and algorithms from $R^n$ spaces to general data sets. We exemplify
this approach by applying it to image colorization and denoising, collaborative
filtering, and extension of psychometric data.
Joint work with Ronald Coifman, Stephane Lafon, Alon Schalar, Amit Zinger and
Steven Zucker.
The lecture will take place in the
Lecture Hall, Room 1, Ziskind Building
on Thursday, January 19, 2006
at noon