Seminars & Colloquia Calendar

Abstract:

Tensors (aka multiway arrays) can be instrumental in revealing latent correlations residing in high dimensional spaces. Despite their applicability to a broad range of applications in machine learning, data compression, and imaging, inconsistencies between tensor and matrix algebra have been complicating their broader utility.  Researchers seeking to overcome those discrepancies have introduced several different candidate extensions, each introducing unique advantages and challenges. In this talk, we review some of the common tensor definitions, discuss their limitations, and introduce our tensor product framework which permits the elegant extension of linear algebraic concepts and algorithms to tensors.  Following introduction of fundamental tensor operations, we discuss tensor decompositions in further depth, including tensor SVDs, based on the tensor product framework which can be computed efficiently in parallel.  We present theoretical results regarding compressibility and provide demonstrations of the applicability of our theory and algorithms on examples such as model reduction and image representation.