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.