**Tel-Aviv****
University**

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

**Room 309**

**Schreiber****
Building**

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**Yosi**** Keller**

**Yale**** University**

Title:

The diffusion framework: a computational approach to data
analysis and

signal processing on data sets

Abstract:

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.