Cross Tensor Approximation Methods for Compression and Dimensionality Reduction

Cross Tensor Approximation (CTA) is a generalization of Cross/skeleton matrix and CUR Matrix (CMA) suitable tool for fast low-rank tensor approximation. It facilitates interpreting the underlying data tensors decomposing/compressing in such way that their structures as nonnegativity, smoothness, or sparsity can be potentially preserved. In this paper, we review extend state-of-the-art deterministic randomized algorithms CTA with intuitive graphical illustrations. We discuss several possible generalizations CMA to tensors, including CTAs: based on fiber selection, slice-tube lateral-horizontal slice selection. The main focus using Tucker t-SVD models while provide references other decompositions Train (TT), Hierarchical (HT) Canonical Polyadic Decomposition (CPD). evaluate performance by extensive computer simulations compress color medical images compare performance.