Optimization landscape of Tucker decomposition

Journal Article (Journal Article)

Tucker decomposition is a popular technique for many data analysis and machine learning applications. Finding a Tucker decomposition is a nonconvex optimization problem. As the scale of the problems increases, local search algorithms such as stochastic gradient descent have become popular in practice. In this paper, we characterize the optimization landscape of the Tucker decomposition problem. In particular, we show that if the tensor has an exact Tucker decomposition, for a standard nonconvex objective of Tucker decomposition, all local minima are also globally optimal. We also give a local search algorithm that can find an approximate local (and global) optimal solution in polynomial time.

Full Text

Duke Authors

Cited Authors

  • Frandsen, A; Ge, R

Published Date

  • June 1, 2022

Published In

Volume / Issue

  • 193 / 2

Start / End Page

  • 687 - 712

Electronic International Standard Serial Number (EISSN)

  • 1436-4646

International Standard Serial Number (ISSN)

  • 0025-5610

Digital Object Identifier (DOI)

  • 10.1007/s10107-020-01531-z

Citation Source

  • Scopus