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Generalized Visual Information Analysis Via Tensorial Algebra.
- Source :
- Journal of Mathematical Imaging & Vision; May2020, Vol. 62 Issue 4, p560-584, 25p
- Publication Year :
- 2020
-
Abstract
- High-order data are modeled using matrices whose entries are numerical arrays of a fixed size. These arrays, called t-scalars, form a commutative ring under the convolution product. Matrices with elements in the ring of t-scalars are referred to as t-matrices. The t-matrices can be scaled, added and multiplied in the usual way. There are t-matrix generalizations of positive matrices, orthogonal matrices and Hermitian symmetric matrices. With the t-matrix model, it is possible to generalize many well-known matrix algorithms. In particular, the t-matrices are used to generalize the singular value decomposition (SVD), high-order SVD (HOSVD), principal component analysis (PCA), two-dimensional PCA (2DPCA) and Grassmannian component analysis (GCA). The generalized t-matrix algorithms, namely TSVD, THOSVD, TPCA, T2DPCA and TGCA, are applied to low-rank approximation, reconstruction and supervised classification of images. Experiments show that the t-matrix algorithms compare favorably with standard matrix algorithms. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09249907
- Volume :
- 62
- Issue :
- 4
- Database :
- Complementary Index
- Journal :
- Journal of Mathematical Imaging & Vision
- Publication Type :
- Academic Journal
- Accession number :
- 142794681
- Full Text :
- https://doi.org/10.1007/s10851-020-00946-9