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Session Overview
Session
SI(AG)^2 Early Career Prize Lecture: Elina Robeva: Orthogonal Tensor Decomposition
Time:
Wednesday, 10/Jul/2019:
5:15pm - 6:00pm

Location: vonRoll, Fabrikstr. 6, 001
468 seats, 433 m^2

Presentations

Orthogonal Tensor Decomposition

Elina Robeva

Massachusetts Institute of Technology, United States of America

Tensor decomposition has many applications. However, it is often a hard problem. In this talk we will discuss a family of tensors, called orthogonally decomposable, which retain some of the properties of matrices that general tensors don't. A symmetric tensor is orthogonally decomposable if it can be written as a linear combination of tensor powers of n orthonormal vectors. As opposed to general tensors, such tensors can be decomposed efficiently. We study the spectral properties of symmetric orthogonally decomposable tensors and give a formula for all of their eigenvectors. We also give polynomial equations defining the set of all such tensors. Analogously, we study nonsymmetric orthogonally decomposable tensors, describing their singular vector tuples and giving polynomial equations that define them. To extend the definition to a larger set of tensors, we define tight-frame decomposable tensors and study their properties. Finally, we conclude with some open questions and future research directions.