# L1-norm Tucker Tensor Decomposition

arXiv: https://arxiv.org/abs/1904.06455 · HTML: https://mlsanity.com/paper/1904.06455/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Apr 2019.

## Built on by (most cited first, 5 of 5)

- [Tensor Methods in Computer Vision and Deep Learning](https://mlsanity.com/paper/2107.03436/) (2021)
- [Near-Linear Time and Fixed-Parameter Tractable Algorithms for Tensor Decompositions](https://mlsanity.com/paper/2207.07417/) (2022)
- [Spatial-temporal traffic modeling with a fusion graph reconstructed by tensor decomposition](https://mlsanity.com/paper/2212.05653/) (2022)
- [Robust Adversarial Defense by Tensor Factorization](https://mlsanity.com/paper/2309.01077/) (2023)
- [On Finite-Step Convergence of the Non-Greedy Algorithm and Proximal Alternating Minimization Method with Extrapolation for L1-Norm PCA](https://mlsanity.com/paper/2302.07712/) (2023)

## Abstract (arXiv)

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.