Increasing the Accuracy of Solving Discrete Ill-Posed Problems by the Random Projection Method

Revunova, E. G.

doi:10.1007/s10559-018-0086-0

Cited by 6 publications

(8 citation statements)

References 18 publications

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“…An experimental study [33] showed that the proposed estimate of the input vector provides a solution accuracy that is very close to the accuracy of the truncated singular value decomposition method. However the dependence of the error on k is smoother than for the truncated singular value decomposition.…”

Section: Distributed Representations Based On Random Projections For mentioning

confidence: 71%

“…The use of distributed representations formed by random projection allows increasing the computational efficiency and accuracy of information technologies based on solving discrete ill-posed problems [41], [42]. The solution accuracy of discrete ill-posed problems was investigated analytically, [25], [26], [33]. These developments are protected by three patents.…”

Section: Discussionmentioning

confidence: 99%

“…One of the approaches to ensuring the stability of solving ill-posed problems is the use of an integer regularization parameter, which is the number of summands in the model (linear with respect to parameters) approximating the original data. To obtain a stable solution (estimation x*), such methods as truncated singular value decomposition [32], truncated QR decomposition, and the method based on random projection [25], [26], [33] can be used.…”

Section: Distributed Representations Based On Random Projections For mentioning

confidence: 99%

“…The bias and variance of error that appear due to averaging over the realizations of the random matrix are not explicitly presented and therefore cannot be analyzed. In [33] expressions for the error were obtained in a form that allows us to propose a method for solving the DIP with a reduced error with respect to the random projection method [23], [25]. By analogy with the works that studied bias and variance of the error arising due to the presence of additive noise in the output vector, we call as the variance of the vector x (input) recovery when averaged over random matrices R k .…”

Section: Distributed Representations Based On Random Projections For mentioning

confidence: 99%

“…By analogy with the works that studied bias and variance of the error arising due to the presence of additive noise in the output vector, we call as the variance of the vector x (input) recovery when averaged over random matrices R k . In [33], the bias and variance components were obtained by averaging the error e x over the realizations of the random matrix R k . Bias and variance of the input vector recovery error are…”

Section: Distributed Representations Based On Random Projections For mentioning

confidence: 99%

See 4 more Smart Citations

Neural Distributed Representations of Vector Data in Intelligent Information Technologies

Gritsenko¹,

Revunova²,

Rachkovskij³

2018

Kibern. vyčisl. teh.

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Introduction. Distributed representation (DR) of data is a form of a vector representation,where each object is represented by a set of vector components, and each vector component can belong to representations of many objects. In ordinary vector representations, the meaning of each component is defined, which cannot be said about DR. However, the similarity of RP vectors reflects the similarity of the objects they represent.DR is a neural network approach based on modeling the representation of information in the brain, resulted from ideas about a "distributed" or "holographic" representations. DRs have a large information capacity, allow the use of a rich arsenal of methods developed for vector data, scale well for processing large amounts of data, and have a number of other advantages. Methods for data transformation to DRs have been developed for data of various types -from scalar and vector to graphs.The purpose of the article is to provide an overview of a part of the work of the Department of Neural Information Processing Technologies (International Center) in the field of neural network distributed representations. The approach is a development of the ideas of Nikolai Mikhailovich Amosov and his scientific school of modeling the structure and functions of the brain.Scope. The formation of distributed representations from the original vector representations of objects using random projection is considered. With the help of the DR, it is possible to efficiently estimate the similarity of the original objects represented by numerical vectors. Gritsenko V.I., Rachkovskij D.A., Revunova E.G. ISSN 2519-2205 (Online), ISSN 0454-9910 (Print). Киб. и выч. техн. 2018. № 4 (194) 8The use of DR allows developing regularization methods for obtaining a stable solution of discrete ill-posed inverse problems, increasing the computational efficiency and accuracy of their solution, analyzing analytically the accuracy of the solution. Thus DRs allow for increasing the efficiency of information technologies applying them.Conclusions. DRs of various data types can be used to improve the efficiency and intelligence level of information technologies. DRs have been developed for both weakly structured data, such as vectors, and for complex structured representations of objects, such as sequences, graphs of knowledge-base situations (episodes), etc. Transformation of different types of data into the DR vector format allows unifying the basic information technologies of their processing and achieving good scalability with an increase in the amount of data processed.In future, distributed representations will naturally combine information on structure and semantics to create computationally efficient and qualitatively new information technologies in which the processing of relational structures from knowledge bases is performed by the similarity of their DRs. The neurobiological relevance of distributed representations opens up the possibility of creating intelligent information technologies based on them that function similarly to...

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Section: Distributed Representations Based On Random Projections For mentioning

confidence: 71%

Section: Discussionmentioning

confidence: 99%

Section: Distributed Representations Based On Random Projections For mentioning

confidence: 99%

Section: Distributed Representations Based On Random Projections For mentioning

confidence: 99%

Section: Distributed Representations Based On Random Projections For mentioning

confidence: 99%

See 3 more Smart Citations

Neural Distributed Representations of Vector Data in Intelligent Information Technologies

Gritsenko¹,

Revunova²,

Rachkovskij³

2018

Kibern. vyčisl. teh.

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A Linear System Output Transformation for Sparse Approximation*

Tyshchuk¹,

Desiateryk

Volkov³

et al. 2022

Cybern Syst Anal

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Random Projection and Truncated SVD for Estimating Direction of Arrival in Antenna Array

Revunova¹,

Rachkovskij²

2018

Kibern. vyčisl. teh.

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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 P ratio 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 P ratio 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 P ratio by 3

show abstract

Increasing the Accuracy of Solving Discrete Ill-Posed Problems by the Random Projection Method

Cited by 6 publications

References 18 publications

Neural Distributed Representations of Vector Data in Intelligent Information Technologies

Neural Distributed Representations of Vector Data in Intelligent Information Technologies

A Linear System Output Transformation for Sparse Approximation*

Random Projection and Truncated SVD for Estimating Direction of Arrival in Antenna Array

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