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Title: Optimization landscape of Tucker decomposition
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 nd an approximate local (and global) optimal solution in polynomial time.  more » « less
Award ID(s):
1845171 1704656
NSF-PAR ID:
10161657
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Mathematical Programming
ISSN:
0025-5610
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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