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Expressions for blocks of the information Fisher matrix are presented based on factorization of the Neudecker derivative of
a transposed face-splitting matrix product.

Content uploaded by Vadym Slyusar

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All content in this area was uploaded by Vadym Slyusar on Aug 20, 2018

Content may be subject to copyright.

A preview of the PDF is not available

The article proposes ways to solve the problem of structural synthesis of neural networks architectures; based on non-traditional approaches to their analytical formalization and application of new ones data processing operations. The example of the CIFAR10 dataset proves the possibility of improving the accuracy of the solution image classification tasks within an alternative architecture with expandable input and narrowing structures of trained neural networks. The results of the application of input expanding image taken with Resizing and Conv2DTranspose layers at the input trained neural networks indicate the effectiveness of solving such classification problems by example CIFAR10 dataset. Achieved on the basis of the Xception neural network, the average classification accuracy of 10 classes CIFAR10 images are 97.3%. The side effect of pre-scaling images is leveling the accuracy of the classification of different classes, which allows us to consider such a change in size as an option data augmentation in the dataset. Tensor-matrix methods have been introduced for further development of this approach formalization of the description of neural networks on the basis of the penetrating end product of matrices and its block ones modifications. On this basis, a number of new convolution and maxpooling operations are proposed, as well as combinations on input of the narrowing segment not only symmetrically enlarged image, but also its variants obtained on the basis of a generalized penetrating product. It is about drawing images expanded by rows of pixels (horizontally) and columns (vertically), as well as a combination of several different options symmetrical image extensions on the principle of constructing a pyramidal segment of the PSPNet neural network.

The article proposes ways to solve the problem of structural synthesis of neural networks architectures; based on non-traditional approaches to their analytical formalization and application of new ones data processing operations. The example of the CIFAR10 dataset proves the possibility of improving the accuracy of the solution image classification tasks within an alternative architecture with expandable input and narrowing structures of trained neural networks. The results of the application of input expanding image taken with Resizing and Conv2DTranspose layers at the input trained neural networks indicate the effectiveness of solving such classification problems by example CIFAR10 dataset. Achieved on the basis of the Xception neural network, the average classification accuracy of 10 classes CIFAR10 images are 97.3%. The side effect of pre-scaling images is leveling the accuracy of the classification of different classes, which allows us to consider such a change in size as an option data augmentation in the dataset. Tensor-matrix methods have been introduced for further development of this approach formalization of the description of neural networks on the basis of the penetrating end product of matrices and its block ones modifications. On this basis, a number of new convolution and maxpooling operations are proposed, as well as combinations on input of the narrowing segment not only symmetrically enlarged image, but also its variants obtained on the basis of a generalized penetrating product. It is about drawing images expanded by rows of pixels (horizontally) and columns (vertically), as well as a combination of several different options symmetrical image extensions on the principle of constructing a pyramidal segment of the PSPNet neural network.

This lecture presents the basic concepts of a lot of matrix operations and related applications for digital beamforming, which was proposed by author in 1996-1998. This lecture can be used for radar system, smart antennas for wireless communications, and other systems applying digital beamforming. It's intended for individuals new to the field who wish to gain a basic understanding in this area. For additional information, check out the reference material presented at the end of this lecture.

This paper is the first publication about concept of face-splittiing product of matrices and his properties, which dated on December 1996.
In this article was used the old version of English translation the origin term "торцевое произведение", which was introduced by Vadym Slyusar. In next publications was used translation as face-splitting product.

Methods of determination of the accuracy limits in problems of estimation of unknown parameters

- P A Bakut
- V P Loginov
- Yu P Shumilov

P.A. Bakut, V. P. Loginov, and Yu. P. Shumilov, "Methods of determination of the accuracy limits in problems of
estimation of unknown parameters," Zarubezh. Radioelektr., No. 5, 3-35 (1978).

New operations of matrix multiplication in radar-tracking applications

- V I Slyusar
- V. I. Slyusar

V.I. Slyusar, "New operations of matrix multiplication in radar-tracking applications," in: Direct and Inverse Problems
of the Theory of Electromagnetic and Acoustic Waves (DIPED-97), Inst. Prikl. Probl. Mekh. Mat. NAN Ukr., L'vov
(1997), pp. 73-74.

Matrix Derivative for Multivariate Statistics

- Kollo Tynu

Kollo Tynu, Matrix Derivative for Multivariate Statistics, Tartu Univ., Tartu (1991).

Synthesis of algorithms for measuring the distance fromM sources under extra gating of readings of analog-to-digital converter

- V I Slyusar

V.I. Slyusar, "Synthesis of algorithms for measuring the distance from M sources under extra gating of readings of
analog-to-digital converter," Radioelektronika, No. 5, 55-62 (1998).

Face-splitting matrix products in radar-trac king applications

- V I Slyusar