UTCS/WNCG Seminar - Raman Arora/University of Washington, "Exploiting geometric and algebraic structure in data", ACES 3.408

Contact Name: 
Jenna Whitney
Date: 
Apr 22, 2011 11:00am - 12:00pm

There is a sign-up schedule for this event that can be found at

http://www.cs.utexas.edu/department/webevent/utcs/events/cgi/list_event

s.cgi

Type of Talk: UTCS/WNCG Seminar

Speaker/Affiliation: Raman

Arora/University of Washington

Talk Audience: UTCS Faculty and Grad St

udents, ECE

Date/Time: Friday, April 22, 2011, 11:00 a.m.

Loc

ation: ACES 3.408

Host: Pradeep Ravikumar and Sriram Vishwanath

T

alk Title: Exploiting geometric and algebraic structure in data

Talk A

bstract:
As signal acquisition systems become increasingly interconnected

, complex and diverse, new methods of data analysis and processing have b

ecome crucial. Often, the development of such methods benefits from modeli

ng the inherent structure present in data. The structure may come from (a)

low intrinsic complexity of high-dimensional data, as captured by the low-

rank assumption in many problems in machine learning; (b) the physics of t

he signal acquisition as in distributed video sensor networks; or (c) the

very nature of the process we are trying to study, for instance genome evo

lution via rearrangements. In this talk I will describe how we can leverage
techniques from group representation theory and differential geometry to u

tilize structure in data and develop efficient machine learning and signal

processing solutions for a wide set of problems.

The first half of th

e talk will focus on the problem of optimal estimation and detection in hom

ogeneous spaces, i.e. signal spaces where a transformation group acts tran

sitively on a set (or manifold). I will discuss the problem of recovering t

ransformations from pairs of datasets in homogeneous spaces and specialize

the discussion to the rotation group acting on the unit sphere (with applic

ation to super-resolution of omni-directional images and visual homing of r

obots) and the permutation group (with application to genome rearrangements
and multi-object tracking). In the second half of the talk I will discuss

a group theoretical approach for learning rotations in an online fashion. T

he proposed algorithm involves multiplicative updates that are matrix expo

nentials of skew-symmetric matrices comprising the Lie algebra of the rotat

ion group. I will discuss the stability and convergence of the proposed alg

orithm and application to left-stochastic decomposition (LSD) of similarity
matrices. LSD is a variant of non-negative matrix factorization and is equ

ivalent to soft kernel k-means clustering. I will give conditions for exist

ence and uniqueness of LSD factorization and clustering, present error bou

nds for noisy settings and discuss experimental results on simulated and re

al similarity datasets.

Speaker Bio:
Raman Arora received the B. Eng

g. degree in Electronics and Communication Engineering from Netaji Subhas I

nstitute of Technology, Delhi, India, and M.S. and Ph.D. degrees in Elec

trical Engineering from University of Wisconsin-Madison in 2005 and 2009,

respectively. He is currently a postdoctoral research associate at Universi

ty of Washington. His research interests include statistical signal process

ing, machine learning, bioinformatics and distributed camera networks.