Decomposing Low-Rank Symmetric Tensors
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.