Abstract
In this work, we present a new hierarchical decomposition aimed at the decorrelation of a cubical tensor of size 2n, based on the 3D Frequency-Ordered Hierarchical KLT (3D FO-HKLT). The decomposition is executed in three consecutive stages. In the first stage, after adaptive directional vectorization (ADV) of the input tensor, the vectors are processed through one-dimensional FO-Adaptive HKLT (FO-AHKLT), and after folding, the first intermediate tensor is calculated. In the second stage, on the vectors obtained after ADV of the first intermediate tensor, FO-AHKLT is applied, and after folding, the second intermediate tensor is calculated. In the third stage, on the vectors obtained from the second intermediate tensor, ADV is applied, followed by FO-AHKLT, and the output tensor is obtained. The orientation of the vectors, calculated from each tensor, could be horizontal, vertical or lateral. The best orientation is chosen through analysis of their covariance matrix, based on its symmetry properties. The kernel of FO-AHKLT is the optimal decorrelating KLT with a matrix of size 2 × 2. To achieve higher decorrelation of the decomposition components, the direction of the vectors obtained after unfolding of the input tensor in each of the three consecutive stages, is chosen adaptively. The achieved lower computational complexity of FO-AHKLT is compared with that of the Hierarchical Tucker and Tensor Train decompositions.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.