Applied Algebra Seminar: Decomposition and unfolding of higher-order tensors

Seminar | March 9 | 5:15-6:15 p.m. | 891 Evans Hall

 Yun Song, University of Pennsylvania and UC Berkeley

 Department of Mathematics

Recently, tensors of order 3 or greater, known as higher-order tensors, have attracted increased attention in many fields across science and engineering. A common paradigm in tensor-related algorithms advocates unfolding (or flattening) the tensor into a matrix and applying classical methods developed for matrices. In this talk, I will consider all possible unfoldings of a tensor into lower order tensors and present general inequalities between their operator norms. I will then describe an application of these theoretical results to tensor decomposition and present a new algorithm built on Kruskal's uniqueness theorem. This tensor decomposition method provably handles a greater level of noise compared to previous methods and achieves a high estimation accuracy. Numerical results demonstrate that our algorithm is robust to various noise distributions and that it performs especially favorably as the order increases. If time permits, I will describe applications of our method to multi-way clustering. (Joint work with Miaoyan Wang, Khanh Dao Duc, and Jonathan Fischer.)