Technion
 
         Computer Science Colloquium
 
Time+Place : Tuesday 17/01/2012 14:30 room 337-8 Taub  Bld.
Speaker    : Amit Singer
Affiliation: Princeton University
Host       : Nir Ailon
Title      : Vector Diffusion Maps and the Connection Laplacian
 
Abstract   :
 
Motivated by problems in structural biology, specifically cryo-electron
microscopy, we introduce vector diffusion maps (VDM), a new mathematical
framework for organizing and analyzing high dimensional data sets, 2D images
and 3D shapes. VDM is a mathematical and algorithmic generalization of
diffusion maps and other non-linear dimensionality reduction methods, such
as LLE, ISOMAP and Laplacian eigenmaps. While existing methods are either
directly or indirectly related to the heat kernel for functions over the
data, VDM is based on the heat kernel for vector fields. VDM provides tools
for organizing complex data sets, embedding them in a low dimensional space
and interpolating and regressing vector fields over the data. In particular,
it equips the data with a metric, which we refer to as the vector diffusion
distance. In the manifold learning setup, where the data set is distributed
on a low dimensional manifold M^d embedded in R^p, we prove the relationship
between VDM and the connection-Laplacian operator for vector fields over the
manifold.
Applications to structural biology (cryo-electron microscopy and NMR
spectroscopy), computer vision and shape space analysis will be discussed.
 
(Joint work with Hau-tieng Wu.)
 
Short Bio:
 
Amit Singer is an Associate Professor of Mathematics and a member of the
Executive Committee of the Program in Applied and Computational Mathematics
(PACM) at Princeton University. He joined Princeton as an Assistant
Professor in 2008. From 2005 to 2008 he was a Gibbs Assistant Professor in
Applied Mathematics at the Department of Mathematics, Yale University.
Singer received the BSc degree in Physics and Mathematics and the PhD degree
in Applied Mathematics from Tel Aviv University (Israel), in 1997 and 2005,
respectively. He served in the Israeli Defense Forces during 1997-2003. He
was awarded the Presidential Early Career Award for Scientists and Engineers
(2010), the Alfred P. Sloan Research Fellowship (2010) and the Haim Nessyahu
Prize for Best PhD in Mathematics in Israel (2007). His current research in
applied mathematics focuses on problems of massive data analysis and
structural biology.
 
Refreshments served from 14:15 on,
 	Lecture starts at 14:30
 
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