Diffusion Maps, Spectral Clustering and Reaction Coordinates of Dynamical Systems

author: Boaz Nadler, Weizmann Institute of Science
published: Feb. 25, 2007,   recorded: May 2005,   views: 10874

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A central problem in data analysis is the low dimensional representation of high dimensional data, and the concise description of its underlying geometry and density. In the analysis of large scale simulations of complex dynamical systems, where the notion of time evolution comes into play, important problems are the identification of the slow variables and the representation of the reaction coordinates that parameterize them.

In this paper we provide a unifying view of these apparently different tasks, by considering a family of diffusion maps, defined as the embedding of complex data onto a low dimensional Euclidian space, via the eigenvectors of suitably normalized random walks defined on the given datasets. We show, both theoretically and by examples how this embedding can be used for dimensionality reduction, manifold learning, geometric analysis of complex data sets and fast simulations of stochastic dynamical systems. Joint work with R.R. Coifman, S. Lafon, M. Maggioni and I.G. Kevrekidis

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Reviews and comments:

Comment1 Richard, November 17, 2007 at 4:04 p.m.:


where is this video?

Thanks :)


Comment2 peter (staff), November 22, 2007 at 9:12 p.m.:

As usual: Gremlins ate the video so we cooked another one ;)
(Yeah, really, the video was recovered.)

Comment3 Aaron, September 12, 2008 at 6:02 p.m.:

This is a great lecture. Unfortunately, the camera work is so distracting as to make it unwatchable - are the original slides available anywhere?

Comment4 Yevgeni, May 14, 2009 at 7:39 a.m.:

Lecture slides can be found here:


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