Geometry Seminar

Date: November 13, 2020

Time: 4:00PM - 5:00PM

Location: zoom

Speaker: Joe Kileel , University of Texas Austin

Title: Fast symmetric tensor decomposition

Abstract: Tensors are higher-order matrices, and decomposing tensors can reveal structure in datasets. In recent years, tensor decomposition has found applications in statistics, computational imaging, signal processing, and quantum chemistry.

In this talk, we will present a new numerical method for low-rank symmetric tensor decomposition, building on the usual power method and ideas from classical algebraic geometry. The approach achieves a speed-up over the state-of-the-art by roughly one order of magnitude. We will also discuss an “implicit” variant of the algorithm for the case of moment tensors which avoids the explicit formation of higher-order moments, analogously to matrix-free techniques in linear algebra. Finally, we will make some quantitative statements about the non-convex optimization landscape underlying our method.

This talk is based on joint works with Joao Pereira, Tammy Kolda and Timo Klock.