  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.

Numerical Analysis;Data Structures and Algorithms;Signal Processing