Hierarchical third‐order tensor decomposition through inverse difference pyramid based on the three‐dimensional Walsh–Hadamard transform with applications in data mining

Author(s):  
Roumen K. Kountchev ◽  
Barna L. Iantovics ◽  
Roumiana A. Kountcheva
Water ◽  
2021 ◽  
Vol 13 (18) ◽  
pp. 2578
Author(s):  
Leonid Kulikov ◽  
Natalia Inkova ◽  
Daria Cherniuk ◽  
Anton Teslyuk ◽  
Zorigto Namsaraev

Satellite research methods are [DCh]actively involvedfrequently used in observations of water bodies. One of the most important problems in satellite observations is the presence of missing data due to internal malfunction of satellite sensors and poor atmospheric conditions. We proceeded on the assumption that the use of data recovery methods based on spatial relationships in data can increase the recovery accuracy. In this paper, we present a method for missing data reconstruction from remote sensors. We refer our method to as Tensor Interpolating Empirical Orthogonal Functions (TIEOF). The method relies on the two-dimensional nature of sensor images and organizes the data into three-dimensional tensors. We use high-order tensor decomposition to interpolate missing data [ZN] on chlorophyll a concentration in lake Baikal (Russia, Siberia). Using MODIS and SeaWiFS satellite data of lake Baikal we show that the observed improvement of TIEOF was 69% on average compared to the current state-of-the-art DINEOF algorithm measured in various preprocessing data scenarios including thresholding and different interpolating schemes.


This paper refers to study of industrial robot (KUKA KR16-2), in which we have considered the matrix decomposition and tensor decomposition model in rotational motion. We have considered robotic matrix & Tensor and defined a modal product between robot rotation matrix and a tensor Further we have proposed the third order tensor for the motion of Industrial robot and tried to find out the useful result. At last we have shown that the tensor model is providing alternate way to find the solution.


2021 ◽  
Vol 11 (11) ◽  
pp. 5006
Author(s):  
Li Li ◽  
Rui Bai ◽  
Jianfeng Lu ◽  
Shanqing Zhang ◽  
Ching-Chun Chang

To protect the copyright of the color image, a color image watermarking scheme based on quaternion discrete Fourier transform (QDFT) and tensor decomposition (TD) is presented. Specifically, the cover image is partitioned into non-overlapping blocks, and then QDFT is performed on each image block. Then, the three imaginary frequency components of QDFT are used to construct a third-order tensor. The third-order tensor is decomposed by Tucker decomposition and generates a core tensor. Finally, an improved odd–even quantization technique is employed to embed a watermark in the core tensor. Moreover, pseudo-Zernike moments and multiple output least squares support vector regression (MLS–SVR) network model are used for geometric distortion correction in the watermark extraction stage. The scheme utilizes the inherent correlations among the three RGB channels of a color image, and spreads the watermark into the three channels. The experimental results indicate that the proposed scheme has better fidelity and stronger robustness for common image-processing and geometric attacks, can effectively resist each color channel exchange attack. Compared with the existing schemes, the presented scheme achieves better performance


2021 ◽  
pp. 108128652110165
Author(s):  
Yakov Itin ◽  
Shulamit Reches

Third-order tensors are widely used as a mathematical tool for modeling the physical properties of media in solid-state physics. In most cases, they arise as constitutive tensors of proportionality between basic physical quantities. The constitutive tensor can be considered the complete set of physical parameters of a medium. The algebraic features of the constitutive tensor can be used as a tool for proper identification of natural materials, such as crystals, and for designing artificial nanomaterials with prescribed properties. In this paper, we study the algebraic properties of a general asymmetric third-order tensor relative to its invariant decomposition. In correspondence with different groups acting on the basic vector space, we present the hierarchy of different types of tensor decomposition into invariant subtensors. In particular, we discuss the problem of non-uniqueness and reducibility of high-order tensor decomposition. For a general asymmetric third-order tensor, these features are described explicitly. In the case of special tensors with a prescribed symmetry, the decomposition is demonstrated to be irreducible and unique. We present the explicit results for two physically interesting models: the piezoelectric tensor as an example of pair symmetry and the Hall tensor as an example of pair skew-symmetry.


Microscopy ◽  
2020 ◽  
Author(s):  
Yuki Nomura ◽  
Kazuo Yamamoto ◽  
Satoshi Anada ◽  
Tsukasa Hirayama ◽  
Emiko Igaki ◽  
...  

Abstract In this study, a noise-reduction technique for series low-dose electron holograms using tensor decomposition is demonstrated through simulation. We treated an entire dataset of the series holograms with Poisson noise as a third-order tensor, which is a stack of 2D holograms. The third-order tensor, which is decomposed into a core tensor and three factor matrices, is approximated as a lower-rank tensor using only noise-free principal components. This technique is applied to simulated holograms by assuming a p-n junction in a semiconductor sample. The peak signal-to-noise ratios of the holograms and the reconstructed phase maps have been improved significantly using tensor decomposition. Moreover, the proposed method was applied to a more practical situation of time-resolved in situ electron holography by considering a nonuniform fringe contrast and fringe drift relative to the sample. The accuracy and precision of the reconstructed phase maps were quantitatively evaluated to demonstrate its effectiveness for in situ experiments and low-dose experiments on beam-sensitive materials.


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