A Perspectives on Topological and Geometric Methods for High Dimensional Data Analysis

Speaker:	Dr. Yuan YAO
		Stanford University

Title:		"A Perspectives on Topological and Geometric Methods
		for High  Dimensional Data Analysis"

Date:		Tuesday, 13 January 2009

Time:		16:00pm - 17:00 pm

Venue:		Room 3501 (via lifts 25/26), HKUST

Abstract:

Modern massive data sets of high dimensionality are nowadays arising  from
various fields in science and technology, such as biology,  computer
science, finance, and statistics, etc. In spite of its rapid  evolution,
many of core challenges, e.g. the curse of dimensionality,  scalability, and
characterization of nonlinear variation or sparsity  in data, are ubiquitous
and call upon a multidisciplinary  collaboration across academia, where
Mathematics joins with its  deeper connections and far reaching novel
discoveries. In this talk,  instead of general theories, two recent examples
will be presented  which reflect the renaissance of some classical topics in
topology  and geometry in the field of high dimensional data analysis and
statistical machine learning. The first example is inspired by the
classical Morse Theory, which helps develop new data representation  in the
study of biomolecular folding. As a successful application it  provides for
the first time some structural evidence from simulations  solving the
biological debates over multiple pathways of RNA hairpin  folding. The
second example is based on combinatorial Hodge theory,  establishing a novel
approach for the statistical rank aggregation  problem. It extends the Borda
count in the social choice theory in  Economics to the modern settings with
incomplete and imbalanced data  over networks. These two examples illustrate
some perspectives of the  current development of topological and geometric
methods for  statistics and high dimensional data analysis.

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Biography:

Yuan Yao received BS/MS in Control Engineering from Harbin Institute  of
Technology in 1996/1998, respectively, MPhil from CityUHK in 2002  and PhD
from UC Berkeley in 2006, both in Mathematics. Since 2006 he  has been a
Postdoctoral Fellow at Stanford University. His research  interests have an
interdisciplinary span over Computer Science,  Statistics and Mathematics,
etc., including geometrical and  topological treatment for high dimensional
data, online learning with  stochastic algorithms, as well as applications
in biomolecular  folding and statistical machine learning.