Dmitry S. Shalymov

Speed Gradient and MaxEnt Principles for Shannon and Tsallis Entropies

In this paper we consider dynamics of non-stationary processes that follow the MaxEnt principle. We derive a set of equations describing dynamics of a system for Shannon and Tsallis entropies. Systems with discrete probability distribution are considered under mass conservation and energy conservation constraints. The existence and uniqueness of solution are established and asymptotic stability of the equilibrium is proved. Equations are derived based on the speed-gradient principle originated in control theory.

Dynamics of non-stationary processes that follow the maximum of the Rényi entropy principle.

We propose dynamics equations which describe the behaviour of non-stationary processes that follow the maximum Rényi entropy principle. The equations are derived on the basis of the speed-gradient principle originated in the control theory. The maximum of the Rényi entropy principle is analysed for discrete and continuous cases, and both a discrete random variable and probability density function (PDF) are used. We consider mass conservation and energy conservation constraints and demonstrate the uniqueness of the limit distribution and asymptotic convergence of the PDF for both cases. The coincidence of the limit distribution of the proposed equations with the Rényi distribution is examined.

Modelling non-equilibrium thermodynamic systems from the speed-gradient principle

The application of the speed-gradient (SG) principle to the non-equilibrium distribution systems far away from thermodynamic equilibrium is investigated. The options for applying the SG principle to describe the non-equilibrium transport processes in real-world environments are discussed. Investigation of a non-equilibrium systems evolution at different scale levels via the SG principle allows for a fresh look at the thermodynamics problems associated with the behaviour of the system entropy. Generalized dynamic equations for finite and infinite number of constraints are proposed. It is shown that the stationary solution to the equations, resulting from the SG principle, entirely coincides with the locally equilibrium distribution function obtained by Zubarev. A new approach to describe time evolution of systems far from equilibrium is proposed based on application of the SG principle at the intermediate scale level of the systems internal structure. The problem of the high-rate shear flow of viscous fluid near the rigid plane plate is discussed. It is shown that the SG principle allows closed mathematical models of non-equilibrium processes to be constructed. This article is part of the themed issue ‘Horizons of cybernetical physics’.

Randomized Algorithm of Finding the True Number of Clusters Based on Chebychev Polynomial Approximation

One of the important problems arising in cluster analysis is the estimation of the appropriate number of clusters. In the case when the expected number of clusters is sufficiently large, the majority of the existing methods involve high complexity computations. This difficulty can be avoided by using a suitable confidence interval to estimate the number of clusters. Such a method is proposed in the current chapter.

Writing style determination using the KNN text model

The aim of the paper is writing style investigation. The method used is based on re-sampling approach. We present the text as a series of characters generated by distinct probability sources. A re-sampling procedure is applied in order to simulate samples from the texts. To check if samples are generated from the same population we use a KNN-based two-sample test. The proposed method shows high ability to distinguish variety of different texts.

Arabic handwritten texts clusterization based on Feature Relation Graph (FRG)

Text clustering is known as the problem of grouping texts so that all texts within a group share a similar measure (similar author, similar genre, etc.) This task became very important for the last two decades because of increased number of text documents in digital form which needs to be organized and processed. We investigate a new metric based on the Feature Relation Graph (FRG) for Arabic handwritten texts clustering. This metric has proved to be effective for the text independent Persian writer identification. We have used it to solve more general problem of texts clustering. Pattern based features are extracted from handwritten texts using Gabor and XGabor filters. The extracted features are represented for each cluster by using the FRG. We apply several clustering algorithms in a space of FRGs. Numerical experiments to demonstrate effectiveness of proposed metric and compare effectiveness of different algorithms are provided.

A randomized algorithm for estimating the number of clusters

Clustering is actively studied in such fields as statistics, pattern recognition, machine training, et al. A new randomized algorithm is suggested and established for finding the number of clusters in the set of data, the efficiency of which is demonstrated by examples of simulation modeling on synthetic data with thousands of clusters.

N-Gram Based Approach for Text Authorship Classification: Metric Selection

Automatedauthorshipattributionisactualtoidentifytheauthorofananonymoustexts,ortextswhose authorshipisindoubt.Itcanbeusedinvariousapplicationsincludingauthorverification,plagiarism detection,computerforensicsandothers.Inthisarticle,theauthorsanalyzeanapproachbasedon frequencycombinationoflettersisinvestigatedforsolvingsuchataskasclassificationofdocuments byauthorship.Thistechniquecouldbeusedtoidentifytheauthorofacomputerprogramfroma predefinedsetofpossibleauthors.Theeffectivenessofthisapproachissignificantlydeterminedby thechoiceofmetric.Theresearchexaminesandcomparesfourdifferentdistancemeasuresbetween atextofunknownauthorshipandanauthors’profile:L1measure,Kullback-Leiblerdivergence,base metricofCommonN-grammethod(CNG)andacertainvariationofdissimilaritymeasureofCNG method.Comparisonoutlinescaseswhensomemetricoutperformsotherswithaspecificparameter combination.ExperimentsareconductedondifferentRussianandEnglishcorpora. KEywoRdS Authorship Attribution Problem, Common N-grams, Document Classification, N-grams

Dynamics of the f-divergence minimization processes based on the speed-gradient principle

The maximum and minimum entropy states are intensively investigated nowadays because of numerous applications in a various fields of science. Nevertheless the dynamics of a system that tends to minimize its relative entropy is still not well investigated. We propose a new equations describing dynamics of non-stationary processes that minimize f-divergence which is a class of generalized information distances. We use the Speed-Gradient principle originated in the control theory. The uniqueness of the limit probability distribution under the mass conservation and energy conservation constraints is examined. The proposed equations allow to forecast the dynamics of complex non-equilibrium systems. New dynamic equations for the Kullback-Liebler relative entropy, the Tsallis relative entropy, the Burg entropy, the Cressie-Read entropy and other are obtained as a special cases of provided general results.

Dynamics of differential entropy maximization process via the Speed Gradient principle

Dynamics of non-stationary processes that follow the MaxEnt principle for differential entropy is considered. A set of equations describing the dynamics of probability density function (pdf) for such processes is proposed. Equations are derived based on the Speed-Gradient principle originated in the control theory. The uniqueness of the limit pdf and asymptotic convergence of pdf are examined under the mass and energy conservation constraints.