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SUMMARY:Online Robust Principal Components Analysis - Prof. Namrata Vaswan
 i\, Iowa State University
DTSTART:20150702T133000Z
DTEND:20150702T143000Z
UID:TALK59402@talks.cam.ac.uk
CONTACT:Prof. Ramji Venkataramanan
DESCRIPTION:This work studies the problem of sequentially recovering a tim
 e sequence of sparse vectors x_t and vectors from a low-dimensional subspa
 ce l_t from knowledge of their sum (x_t + l_t) at each time t. The subspac
 e of l_t's changes slowly enough so that the matrix \nL_t = [l_1\, l_2\, .
 .. l_t] is low-rank at each time t. Clearly the matrix \nX_t = [x_1\, x_2\
 , ... x_t] is sparse. Thus this is a problem of online sparse + low-rank m
 atrix recovery from their sum. If the primary goal is to recover the low-d
 imensional subspace in which the l_t's lie\, then the problem is one of on
 line robust principal components analysis (PCA). An example of where such 
 a problem might arise is in separating a sparse foreground and a slowly ch
 anging dense background in a surveillance video. In our work\, we have dev
 eloped a novel algorithm called ReProCS to solve this problem and demonstr
 ated its significant advantage over other robust PCA based methods for the
  video layering problem.\n \nWhile there has been a large amount of recent
  work on performance guarantees for the batch robust PCA problem\, the onl
 ine problem is largely open. In recent work\, we have shown that\, with Re
 ProCS\, under mild assumptions and with high probability\, the error in re
 covering the subspace in which l_t lies decays to a small value within a s
 hort delay of a subspace change time and the support of x_t is recovered e
 xactly. Moreover\, the error made in estimating x_t and l_t is small at al
 l times. The assumptions that we need are (a) a good estimate of the initi
 al subspace is available (easy to obtain using a short sequence of backgro
 und-only frames in video surveillance)\; (b) the l_t's obey a `slow subspa
 ce change' assumption\; (c) the basis vectors for the subspace from which 
 l_t is generated are dense (non-sparse)\; and (d) the support of x_t chang
 es by at least a certain amount at least every so often.\n \n*Bi*o:\nNamra
 ta Vaswani received a B.Tech. from the Indian Institute of Technology (IIT
 )\, Delhi\, in 1999 and a Ph.D. from the University of Maryland\, College 
 Park\, in 2004\, both in Electrical Engineering. Since Fall 2005\, she has
  been with the Iowa State University where she is currently an Associate P
 rofessor of Electrical and Computer Engineering. Namrata's research intere
 sts lie at the intersection of signal and information processing and machi
 ne learning for high dimensional problems. She also works on applications 
 in big-data\, video analytics and bio-imaging. Namrata has held the Harpol
 e-Pentair Assistant Professorship at Iowa State during 2008-09 and has ser
 ved one term as an Associate Editor for the IEEE Transactions on Signal Pr
 ocessing (TSP). She is the recipient of the 2014 Iowa State Early Career E
 ngineering Faculty Research Award and the 2014 IEEE Signal Processing Soci
 ety Best Paper Award for her 2010 TSP paper on Modified-CS.
LOCATION:LR5\, Department of Engineering
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