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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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2021 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/149081 |
| Acceso en línea: | http://hdl.handle.net/11336/149081 |
| Access Level: | acceso abierto |
| Palabra clave: | CUR algorithms cross approximations tensor decomposition randomization https://purl.org/becyt/ford/1.2 https://purl.org/becyt/ford/1 |
| Sumario: | 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. |
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