The Weizmann Institute of Science
Faculty of Mathematics and Computer Science
Vision and Robotics Seminar
Boaz Nadler
will speak on
Diffusion Maps, Spectral Clustering, Dimensionality Reduction
and Eigenfunctions of Fokker-Planck operators
Abstract:
Two central problems in data analysis are clustering and dimensionality
reduction. In this talk we present a diffusion based probabilistic
interpretation of spectral clustering and dimensionality reduction algorithms
that use the eigenvectors of the normalized graph Laplacian. Given the pairwise
adjacency matrix on the data, we define a diffusion distance between any two
points and show that dimensionality reduction with the first few eigenvectors
is optimal under a certain mean squared error criteria. Furthermore, we show
that these eigenvectors are discrete approximations of eigenfunctions of
Fokker-Planck diffusion operators. Applying known results from diffusion theory
regarding the eigenvalues and eigenfunctions of these operators provides a
mathematical justification for the success of spectral clustering and
dimensionality reduction algorithms. Finally, we show how some of these methods
can also be used for dimensionality reduction and fast simulations of
stochastic dynamical systems.
Joint work with R.R. Coifman, S. Lafon, M. Maggioni and I.G. Kevrekidis.
The lecture will take place in the
Lecture Hall, Room 1, Ziskind Building
on Thursday, April 6, 2006
noon - 13:00