104 research outputs found
Cross Tensor Approximation Methods for Compression and Dimensionality Reduction
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.Fil: Ahmadi Asl, Salman. Skoltech - Skolkovo Institute Of Science And Technology; RusiaFil: Caiafa, César Federico. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones CientÃficas. Instituto Argentino de RadioastronomÃa. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - La Plata. Instituto Argentino de RadioastronomÃa; ArgentinaFil: Cichocki, Andrzej. Skolkovo Institute of Science and Technology; RusiaFil: Phan, Anh Huy. Skolkovo Institute of Science and Technology; RusiaFil: Tanaka, Toshihisa. Agricultural University Of Tokyo; JapónFil: Oseledets, Ivan. Skolkovo Institute of Science and Technology; RusiaFil: Wang, Jun. Skolkovo Institute of Science and Technology; Rusi
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