Autors: Kountchev, R. K., Mironov, R. P., Kountcheva R.
Title: Complexity Estimation of Cubical Tensor Represented through 3D Frequency-Ordered Hierarchical KLT
Keywords: cubical tensor decomposition; 3D hierarchical adaptive PCA transform; 3D Frequency-Ordered Hierarchical KLT; computational complexity

Abstract: In this work is introduced one new hierarchical decomposition for cubical tensor of size 2n, based on the well-known orthogonal transforms Principal Component Analysis and Karhunen–Loeve Transform. The decomposition is called 3D Frequency-Ordered Hierarchical KLT (3D-FOHKLT). It is separable, and its calculation is based on the one-dimensional Frequency-Ordered Hierarchical KLT (1D-FOHKLT) applied on a sequence of matrices. The transform matrix is the product of n sparse matrices, symmetrical at the point of their main diagonal. In particular, for the case in which the angles which define the transform coecients for the couples of matrices in each hierarchical level of 1D-FOHKLT are equal to /4, the transform coincides with this of the frequency-ordered 1D Walsh–Hadamard. Compared to the hierarchical decompositions of Tucker (H-Tucker) and the Tensor-Train (TT), the o ered approach does not ensure full decorrelation between its components, but is close to the maximum.

References

    Issue

    MDPI Symmetrfy, vol. 12, issue 10, pp. 1605, 2020, Switzerland, MDPI, ISSN 2073-8994

    Вид: статия в списание, публикация в издание с импакт фактор, публикация в реферирано издание, индексирана в Scopus