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 a...
| Autores: | , , , , , , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2021 |
| País: | Argentina |
| Recursos: | Universidad Nacional de La Plata |
| Repositorio: | SEDICI (UNLP) |
| Idioma: | inglés |
| OAI Identifier: | oai:sedici.unlp.edu.ar:10915/129981 |
| Acesso em linha: | http://sedici.unlp.edu.ar/handle/10915/129981 |
| Access Level: | acceso abierto |
| Palavra-chave: | Ingeniería CUR algorithms Cross approximation Tensor decomposition Tubal SVD Randomization |
| Resumo: | 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 state-of-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 fiber 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. |
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