Model Selection Criteria for a Linear Model to Solve Discrete Ill-Posed Problems on the Basis of Singular Decomposition and Random Projection

Revunova, E. G.

doi:10.1007/s10559-016-9868-4

Cited by 14 publications

(23 citation statements)

References 24 publications

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“…Later other researchers began to explore the regularizing properties of random projection, for example, for classification problems and machine learning [20], and, more recently, for solving inverse problems [21]. Since the approach of random projection, along with improving the accuracy of the solution by regularization, reduces the computational complexity of the solution, we have managed to develop algorithms that provide an accurate and fast solution for discrete inverse problems [22], [23], [24], [25], [26], [27], [28].…”

Section: Distributed Representations Based On Random Projections For mentioning

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%

“…Therefore, the dependence of the error of the DIP solution on the number of rows of the random matrix has a minimum at k < N (at certain noise levels). In order to make the dependence of the error on the number of the random matrix rows more smooth and thereby facilitate the search for the minimum, in [22], [23], [24], [25], [26] we performed averaging over noise in the output vector. Experimental studies [23], [26] showed that averaging over random matrices leads to a smoothing of the e R (k) dependence and a decrease in the number of local minima.…”

Section: Distributed Representations Based On Random Projections For mentioning

confidence: 99%

“…In order to make the dependence of the error on the number of the random matrix rows more smooth and thereby facilitate the search for the minimum, in [22], [23], [24], [25], [26] we performed averaging over noise in the output vector. Experimental studies [23], [26] showed that averaging over random matrices leads to a smoothing of the e R (k) dependence and a decrease in the number of local minima. Analytic averaging over random matrices can lead to simpler expressions for e R (k), facilitate further analytical research and improve the accuracy of the method of DIP solving based on random projection.…”

Section: Distributed Representations Based On Random Projections For mentioning

confidence: 99%

“…Averaging over random matrices leads to further smoothing the dependence of the error on the size k of the random matrix [23], [26].…”

Section: Distributed Representations Based On Random Projections For mentioning

confidence: 99%

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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: 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%

“…Averaging over random matrices leads to further smoothing the dependence of the error on the size k of the random matrix [23], [26].…”

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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show abstract

Solution of the Discrete Ill-Posed Problem on the Basis of Singular Value Decomposition and Random Projection

Revunova

2017

Advances in Intelligent Systems and Computing II

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

Revunova

2018

Cybern Syst Anal

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Model Selection Criteria for a Linear Model to Solve Discrete Ill-Posed Problems on the Basis of Singular Decomposition and Random Projection

Cited by 14 publications

References 24 publications

Neural Distributed Representations of Vector Data in Intelligent Information Technologies

Neural Distributed Representations of Vector Data in Intelligent Information Technologies

Solution of the Discrete Ill-Posed Problem on the Basis of Singular Value Decomposition and Random Projection

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

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