L1-norm Tucker Tensor Decomposition
Abstract
Tucker decomposition is a common method for the analysis of multi-way/tensor data. Standard Tucker has been shown to be sensitive against heavy corruptions, due to its L2-norm-based formulation which places squared emphasis to peripheral entries. In this work, we explore L1-Tucker, an L1-norm based reformulation of standard Tucker decomposition. After formulating the problem, we present two algorithms for its solution, namely L1-norm Higher-Order Singular Value Decomposition (L1-HOSVD) and L1-norm Higher-Order Orthogonal Iterations (L1-HOOI). The presented algorithms are accompanied by complexity and convergence analysis. Our numerical studies on tensor reconstruction and classification corroborate that L1-Tucker, implemented by means of the proposed methods, attains similar performance to standard Tucker when the processed data are corruption-free, while it exhibits sturdy resistance against heavily corrupted entries.
Cite
@article{arxiv.1904.06455,
title = {L1-norm Tucker Tensor Decomposition},
author = {Dimitris G. Chachlakis and Ashley Prater-Bennette and Panos P. Markopoulos},
journal= {arXiv preprint arXiv:1904.06455},
year = {2019}
}