Tel-Aviv University - Computer Science Colloquium

Sunday, Jan 15, 2006, 11:15-12:15

Room 309
Schreiber Building


Yosi Keller

Yale University


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, Avi Silberschatz, Amit

Zinger, Steven Zucker.