Imaging and Computing Seminar
Shuchin Aeron, ECE, Tufts
Title:
Methods for Multilinear Data Analytics
Abstract:
In this talk we will focus on statistical signal processing methods
for multilinear data (tensors) analytics and consider several problems
- (a) Tensor completion from missing entries (b) Unsupervised
clustering of tensor data and (c) Collaborative filtering of
multilinear data for online learning and prediction. Most approaches
for multilinear data analytics are based on tensor factorizations and
the performance depends on the particular factorization used. In this
context, we exploit a recently proposed tensor factorization, by
Kilmer and Martin, referred to as the t-SVD, which is an operator
theoretic approach for tensor analysis. We apply the resulting notion
of tensor multi-rank and its convex relaxation to derive globally
optimal algorithms with provable performance guarantees. We show the
performance of these algorithms on 5-D and 4-D pre-stack seismic data
completion, video completion/prediction from missing pixels, and
tensor robust PCA for separating low rank tensors from sparse
corruptions. In addition to t-SVD we exploit the linear algebraic
structure arising from this tensor analysis, namely that the set of
oriented matrices forms a free module over a commutative ring (of
oriented vectors or tubes) with identity, and propose a robust method
for clustering images treated as 2-D tensors.
Bio: Shuchin Aeron is currently an assistant professor in the
department of ECE at Tufts University. He received his PhD in ECE from
Boston University in 2009. From 2009 to 2011 he was a post-doctoral
research fellow at Schlumberger-Doll Research (SDR), Cambridge, MA
where he worked on signal processing answer products for borehole
acoustics. He has several patents and the proposed workflows are
currently implemented in logging while drilling tools. He is the
recipient of the best thesis award from both the college of
engineering and the department of ECE in 2009. He received the Center
of Information and Systems Engineering (CISE) award from Boston
University in 2006 and an Schlumberger-Doll Research grant in 2007.
