Cross Tensor Approximation Methods for Compression and Dimensionality Reduction

SALMAN AHMADI-ASL; CESAR F. CAIAFA; ANDRZEJ CICHOCKI; ANH HUY PHAN; TOSHIHISA TANAKA; IVAN OSELEDETS; JUN WANG

IEEE Access

IEEE

Lugar: New York; Año: 2021 vol. 9 p. 150809 - 150838

2169-3536

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