Issue 3 (193), article 1

DOI:https://doi.org/10.15407/kvt192.03.005

Kibern. vyčisl. teh., 2018, Issue 2 (192), pp.

Revunova E.G., Ph.D. (Engineering),
Senior Researcher Department of Neural Information Processing Technologies
e-mail: egrevunova@gmail.com

Rachkovskij D.A., DSc. (Engineering),
Leading Researcher, Department of Neural Information Processing Technologies
e-mail: dar@infrm.kiev.ua

International Research and Training Center for Information Technologies
and Systems of the National Academy of Sciences of Ukraine
and Ministry of Education and Science of Ukraine,
Acad. Glushkova av., 40, Kiev, 03187, Ukraine

RANDOM PROJECTION AND TRUNCATED SVD FOR ESTIMATING DIRECTION OF ARRIVAL IN ANTENNA ARRAY

Introduction. The need to solve inverse problems arises in many areas of science and technology in connection with the recovery of the object signal based on the results of indirect remote measurements. In the case where the transformation matrix has a high conditional number, the sequence of its singular numbers falls to zero, and the output of the measuring system contains noise, the problem of estimating the input vector is called discrete ill-posed problem (DIP). It is known that the DIP solution using pseudoinverse of the input-output transformation matrix is unstable. To overcome the instability and to improve the accuracy of the solution, regularization methods are used.

Our approaches to ensuring the stability of the DIP solution (truncated singular decomposition (TSVD) and random projection (RP)) use the integer regularization parameter, which is the number of terms of the linear model. Regularization with an integer parameter makes it possible to provide a model close to the best in terms of the accuracy of the input vector recovery, and also to reduce the computational complexity by reducing the dimensionality of the problem.

The purpose of the article is to develop an approach to estimating the direction of arrival of signals in the antenna array using the DIP solution, to compare the results with the well-known MUSIC method, to reveal the advantages and disadvantages of the methods.

Results. Comparison of TSVD and MUSIC (implemented in real numbers) when working with correlated sources and five snapshots showed the advantage of TSVD in terms of the power of the useful signal Pratio by 2.2 times with the number of antenna elements K = 15 and by 4.7 times with K = 90. The advantage of TSVD in Pratio is by 3.7 times for K = 15 and by 4.2 times for K = 90. Comparison of RP and MUSIC (implemented in real numbers), when working with correlated sources and five snapshots, showed the advantage of RP in Pratio by 3 times at K = 15 and by 4.4 times at K = 90. When working with 100 snapshots, the advantage of RP in Pratio is by 3.8 times for K = 15 and by 4.2 times for K = 90.

Conclusions. The approach to determining the direction of arrival based on the l2-regularization methods provides a stable solution in the case of a small number of snapshots, high noise and correlated source signals. Methods of determining the direction of arrival based on l2-regularization, in contrast to l1-regularization, do not impose restrictions on the properties of the input-output transformation matrix, do not require a priori information on the number of signal sources, allow constructing efficient hardware implementations.

Keywords: Direction of arrival estimation, truncated singular value decomposition, random projection, MUSIC.

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Received 15.05.2018

Issue 2 (188), article 1

DOI:https://doi.org/10.15407/kvt188.02.005

Kibern. vyčisl. teh., 2017, Issue 2 (188), pp.

Grytsenko V.I., Corresponding Member of NAS of Ukraine, Director
e-mail: vig@irtc.org.ua
International Research and Training Center for Information Technologies and Systems of the NAS of Ukraine and of Ministry of Education and Science of Ukraine,
av. Acad. Glushkova, 40, Kiev, 03680, Ukraine

Rachkovskij D.A., Doctor of Engineering, Leading Researcher,
Dept. of Neural Information Processing Technologies,
e-mail: dar@infrm.kiev.ua
International Research and Training Center for Information Technologies and Systems of the NAS of Ukraine and of Ministry of Education and Science of Ukraine,
av. Acad. Glushkova, 40, Kiev, 03680, Ukraine

Frolov A.A., Doctor of Biology, Professor,
Faculty of Electrical Engineering and Computer Science FEI,
e-mail: docfact@gmail.com
Technical University of Ostrava, 17 listopadu 15, 708 33 Ostrava-Poruba, Czech Republic

Gayler R., PhD,
Independent Researcher,
r.gayler@gmail.com
Melbourne, VIC, Australia

Kleyko D., PhD post graduated,
Department of Computer Science, Electrical and Space Engineering,
denis.kleyko@ltu.se
Lulea University of Technology, 971 87 Lulea, Sweden

Osipov E., PhD, Professor,
Department of Computer Science, Electrical and Space Engineering,
evgeny.osipov@ltu.se
Lulea University of Technology, 971 87 Lulea, Sweden

NEURAL DISTRIBUTED AUTOASSOCIATIVE MEMORIES: A SURVEY.

Introduction. Neural network models of autoassociative, distributed memory allow storage and retrieval of many items (vectors) where the number of stored items can exceed the vector dimension (the number of neurons in the network). This opens the possibility of a sublinear time search (in the number of stored items) for approximate nearest neighbors among vectors of high dimension.

The purpose of the paper is to review models of autoassociative, distributed memory that can be naturally implemented by neural networks (mainly with local learning rules and iterative dynamics based on information locally available to neurons).

Scope. The survey is focused mainly on the networks of Hopfield, Willshaw, and Potts, that have connections between pairs of neurons and operate on sparse binary vectors. We discuss not only autoassociative memory, but also the generalization properties of these networks. We also consider neural networks with higher-order connections, and networks with a bipartite graph structure for non-binary data with linear constraints.

Conclusions. In conclusion we discuss the relations to similarity search, advantages and drawbacks of these techniques, and topics for further research. An interesting and still not completely resolved question is whether neural autoassociative memories can search for approximate nearest neighbors faster than other index structures for similarity search, in particular for the case of very high dimensional vectors.

Keywords: distributed associative memory, sparse binary vector, Hopfield network, Willshaw memory, Potts model, nearest neighbor, similarity search

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