Decomposing Low-Rank Symmetric Tensors

Joe Kileel (The University of Texas at Austin)

In this talk, I will discuss low-rank decompositions of symmetric tensors (a.k.a. higher-order symmetric matrices).  I will start by sketching how results in algebraic geometry imply uniqueness guarantees for tensor decompositions, and also lead to fast and numerically stable algorithms for calculating the decompositions.  Then I will quantify the associated non-convex optimization landscapes.  Finally, I will present applications to Gaussian mixture models in data science, and rigid motion segmentation in computer vision.  Based on joint works with João M. Pereira, Timo Klock and Tammy Kolda.