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## Cross-Entropy Reduction of Data Matrix with Restriction on Information Capacity of the Projectors and Their Norms

Mathematical Models and Computer Simulations. 2021. Vol. 13. No. 3. P. 382-394.

© 2021, Pleiades Publishing, Ltd.Abstract: We develop/propose the method reducing the dimension of a data matrix, based on its direct and inverse projection, and the calculation of projectors that minimize the cross-entropy functional, remove. We introduce the concept of information capacity of a matrix, which is used as a constraint in the optimal reduction problem, is introduced. The proposed method is compared with known methods in the problem of binary classification.

Dubnov Y. A., Scientific and Technical Information Processing 2021 Vol. 48 No. 6 P. 430-435

This paper considers the problem of feature selection in the classification problem. A method for selecting informative features based on a probabilistic approach and cross-entropy metrics is proposed. Several variants of the information criterion for selecting features for a binary classification problem are considered, as well as its generalization to the case of a multiclass ...

Added: October 28, 2022

Popkov Y., Dubnov Y. A., Volkovich Z. et al., Entropy 2017 Vol. 19(4) No. 178 P. 1-14

A proposal for a new method of classification of objects of various nature, named “2”-soft classification, which allows for referring objects to one of two types with optimal entropy probability for available collection of learning data with consideration of additive errors therein. A decision rule of randomized parameters and probability density function (PDF) is formed, ...

Added: May 26, 2017

Dubnov Y. A., Информационные технологии и вычислительные системы 2018 № 2 С. 60-69

The paper considers the problem of reducing the dimension of the feature space for describing objects
in data analysis problems using the example of binary classification. The article provides a detailed
overview of existing approaches to solving this problem and proposes several modifications. In which
the dimensionality reduction is considered as the problem of extracting the most relevant ...

Added: July 4, 2018

Popkov Y., Popkov A., Dubnov Y. A., Автоматика и телемеханика 2020 № 7 С. 148-172

A randomized forecasting method based on the generation of ensembles of entropy-optimal forecasting trajectories is developed. The latter are generated by randomized dynamic regression models containing random parameters, measurement noises, and a random input. The probability density functions of random parameters and measurement noises are estimated using real data within the randomized machine learning procedure. ...

Added: October 31, 2020

Yu. A. Dubnov, Automation and Remote Control 2019 Vol. 80 No. 3 P. 502-512

The problem of binary classification is considered, an algorithm for its solution is proposed, based on the method of entropy-based estimation of the decision rule parameters. A detailed description of the entropy-based estimation method and the classification algorithm is given, the advantages and disadvantages of this approach are described, the results of numerical experiments and ...

Added: November 19, 2019

Popkov Y., Dubnov Y. A., Popkov A. Y., Automation and Remote Control 2018 Vol. 79 No. 11 P. 2038-2051

The direct and inverse projections (DIP) method was proposed to reduce the feature space to the given dimensions oriented to the problems of randomized machine learning and based on the procedure of “direct” and “inverse” design. The “projector” matrices are determined by maximizing the relative entropy. It is suggested to estimate the information losses by ...

Added: February 12, 2019

Gromov V., Мазайшвили К. В., Заикин П. В. et al., Вестник кибернетики 2022 Т. 45 № 1 С. 72-82

The prevalence of chronic kidney disease is growing every year and is already comparable to such socially significant diseases as hypertension and diabetes mellitus, as well as obesity and metabolic syndrome [1,2]. The standard solution for hemodialysis patients is to create a permanent vascular access in the form of an arteriovenous fistula. However, its use ...

Added: November 14, 2022

Popkov Y., Dubnov Y. A., Попков А. Ю., Информатика и автоматизация (Труды СПИИРАН) 2021 Т. 20 № 5 С. 1010-1033

© St. Petersburg Federal Research Center of the Russian Academy of Sciences.The paper is devoted to the forecasting of the COVID-19 epidemic by the novel method of randomized machine learning. This method is based on the idea of estimation of probability distributions of model parameters and noises on real data. Entropy-optimal distributions correspond to the ...

Added: October 28, 2022

Dubnov Y. A., Искусственный интеллект и принятие решений 2020 № 2 С. 78-85

The paper considers the problem of feature selection in the classification problem. A method for selecting informative features based on a probabilistic approach and cross-entropy metrics is proposed. Several variants of the information criterion for selecting features for a binary classification problem are considered, as well as its generalization to the case of a multiclass ...

Added: October 31, 2020

Kuznetsov S., Serdyukov P., Segalovich I. et al., L. : Springer, 2013

Higher School of Economics (HSE) and supported by the Information Retrieval Specialist Group at the British Computer Society (BCS–IRSG). The conference was held during March 24–27, 2013, in Moscow, Russia – the easternmost location in the history of the ECIR series. ECIR 2013 received a total of 287 submissions in three categories: 191 full papers, ...

Added: April 15, 2013

Башмаков А. И., Белоозеров В. Н., Starykh V., Информационные системы и технологии 2013 № 6(80) С. 88-102

In article process of construction formal ontology of information resources system for an education, that pursues the aim to reflect representation about this sphere in the automated systems intended for creation, account, ordering, storage, search and use of these resources in educational institutions of various level is stated. The system of information resources is set ...

Added: January 16, 2014

Popkov Y., Popkov A., Dubnov Y. A., Математическое моделирование 2020 Т. 32 № 9 С. 35-52

We develop a new method of dimensionality reduction based on direct and inverse projection of data matrix and calculation of projectors minimizing cross-entropy functional. Concept of information capacity of matrix which is used as a restriction in a problem of optimal reduction is introduced. We conduct a comparison of proposed method with known ones based ...

Added: October 31, 2020

Zhuk R., Ignatov D. I., Konstantinova N., Procedia Computer Science 2014 Vol. 31 P. 928-938

We propose extensions of the classical JSM-method and the Na ̈ıve Bayesian classifier for the case of triadic relational data. We performed a series of experiments on various types of data (both real and synthetic) to estimate quality of classification techniques and compare them with other classification algorithms that generate hypotheses, e.g. ID3 and Random ...

Added: June 9, 2014

Gromov V., Zvorykina E., Beschastnov Y. et al., Working papers by Cornell University. Series math "arxiv.org" 2023 Article 14399

The paper explores mathematical methods that differentiate regular and chaotic time series, specifically for identifying pathological fistulas. It proposes a noise-resistant method for classifying responding rows of normally and pathologically functioning fistulas. This approach is grounded in the hypothesis that laminar blood flow signifies normal function, while turbulent flow indicates pathology. The study explores two ...

Added: September 27, 2023

Lerman L., Gubina E., Discrete and Continuous Dynamical Systems - Series S 2020 Vol. 13 No. 4 P. 1341-1367

We study a class of scalar differential equations on the circle S1. This class is characterized mainly by the property that any solution of such an equation possesses an exponential dichotomy both on the semi-axes R+ and R+. Also we impose some other assumptions on the structure of the foliation into integral curves for such the equation. Differential equations ...

Added: September 16, 2020

Akopov A. S., Beklaryan A., Искусственные общества 2021 Т. 16 № 1 С. 1-23

This article presents a model of the ground autonomous vehicles (AVs) motion in the Artificial Road Network (ARN) belonging to the "Manhattan Lattice" type with the implementation of the large-scale agent-based modeling framework FLAME GPU. The most important scenarios of the traffic situation development are investigated, in particular, which are associated with reducing visibility on ...

Added: April 1, 2021

Yasnitsky L., Ваулева С. В., Сафонова Д. Н. et al., Всероссийский криминологический журнал 2015 Т. 9 № 3 С. 423-430

Modern criminalists do not share a common opinion regarding the choice of parameters which could be used to work out a system of characteristics to differentiate a maniac killer from an ordinary person. This hinders the development of efficient software for investigation purposes. The paper describes the experience of developing a neural network that can ...

Added: October 1, 2015

Lanham : University Press of America, 2012

The history of logic and analytic philosophy in Central and Eastern Europe is still known to very few people. As an exception to the rule, only two scientific schools became internationally popular: the Vienna Circle and the Lvov-Warsaw School. Nevertheless, the countries included in this region have not only joint history, but also joint cultural ...

Added: February 13, 2013

Malyshev D., Journal of Applied and Industrial Mathematics (перевод журналов "Сибирский журнал индустриальной математики" и "Дискретный анализ и исследование операций") 2020 Vol. 14 No. 4 P. 706-721

The edge coloring problem for a graph is to minimize the number of colors that are sufficient to color all edges of the graph so that all adjacent edges receive distinct colors. The computational complexity of the problem is known for all graph classes defined by forbidden subgraphs with at most 6 edges. We improve ...

Added: January 30, 2021

Пермь : Пермский государственный национальный исследовательский университет, 2020

В сборнике представлены статьи участников Всероссийской научно-практической конференции молодых ученых с международным участием «Математика и междисциплинарные исследования – 2020». На конференцию было прислано более ста статей из различных регионов России, а также из ближнего
и дальнего зарубежья. По итогам работы экспертной комиссии для публикации было отобрано шестьдесят две статьи. Каждая статья оценивалась группой экспертов в той области, которая рассматривается автором.
Представленные ...

Added: December 10, 2020

Koldanov A. P., Koldanov P., Semenov D., Журнал Новой экономической ассоциации 2021 Т. 2 № 50 С. 12-34

. The problem of analysis of pairwise connections between stocks of financial market by observations on stock returns is considered. Such problem arise in stock market network analysis. It is assumed that joint distribution of stock returns belongs to the wide class of elliptical distributions. Classical Pearson correlation, Fechner correlation and Kendall correlation are used ...

Added: June 17, 2021

Marshirov V. V., Marshirova L. E., Сибирский журнал индустриальной математики 2013 Т. XVI № 4 С. 111-120

The paper considers the problem of determining the rate of cooling of metal during solidification at the intersection of the liquidus temperature under intense heat sink from the surface. The solution to this problem it is necessary to determine the process conditions, the boundary and initial conditions for which it is possible to get new ...

Added: November 17, 2013

Dordrecht, L., Heidelberg, NY : Springer, 2014

This book constitutes the thoroughly refereed proceedings of the Third International Conference on Belief Functions, BELIEF 2014, held in Oxford, UK, in September 2014. The 47 revised full papers presented in this book were carefully selected and reviewed from 56 submissions. The papers are organized in topical sections on belief combination; machine learning; applications; theory; ...

Added: October 1, 2014

Vyalyi M., Дискретная математика 1991 Т. 3 № 3 С. 35-45

Added: October 17, 2014