Title: Robust Tensor Completion and its Application
Abstract: In this talk, we report the results of robust tensor completion using tubal singular value decomposition, and its applications. We considers the problem of recovering multidimensional array, in particular third-order tensor, from a random subset of its arbitrarily corrupted entries. Our study is based on a recently proposed algebraic framework in which the tensor-SVD is introduced to capture the low-tubal-rank structure in tensor. We analyze the performance of a convex program, which minimizes a weighted combination of the tensor nuclear norm, a convex surrogate for the tensor tubal rank, and the tensor l1 norm. We prove that under certain incoherence conditions, this program can recover the tensor exactly with overwhelming probability, provided that its tubal rank is not too large and that the corruptions are reasonably sparse. The number of required observations is order optimal (up to a logarithm factor) when comparing with the degrees of freedom of the low-tubal-rank tensor. Numerical experiments verify our theoretical results and real world applications demonstrate the effectiveness of our algorithm.
Bio: Michael Ng is the Chair Professor in Department of Mathematics, Director of Research Division for Mathematical and Statistical Science, and Director of Big Data Research Cluster, Faculty of Science, The University of Hong Kong. He obtained his B.Sc. degree in 1990 and M.Phil. degree in 1992 at the University of Hong Kong, and Ph.D. degree in 1995 at Chinese University of Hong Kong. At 2017, Michael obtained Feng Kang Prize for his significant contributions in numerical linear algebra for solving structured linear systems, mathematical and computational methods in image processing. At 2014, Michael obtained Hong Kong Baptist University President's Awards for Outstanding Performance in Scholarly Work. Michael won the Honorable Mention of Householder Award IX , in 1996 at Switzerland, an excellent young researcher's presentation at Nanjing International Conference on Optimization and Numerical Algebra, 1999, and the Outstanding Young Researcher Award of the University of Hong Kong, 2001. Michael was the plenary speaker of SIAM Conference on Applied Linear Algebra, 2009. He is the first Chinese to be plenary speaker of SIAM LA since 1985.
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