In:
Journal of Mathematical Imaging and Vision, Springer Science and Business Media LLC, Vol. 62, No. 4 ( 2020-05), p. 560-584
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.
Type of Medium:
Online Resource
ISSN:
0924-9907
,
1573-7683
DOI:
10.1007/s10851-020-00946-9
Language:
English
Publisher:
Springer Science and Business Media LLC
Publication Date:
2020
detail.hit.zdb_id:
1479363-5
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