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class="publication_info"> class="authors3">Berger A.I., class="authors3">Guda S.A.
Optimal threshold selection algorithms for multi-label classification: property study
Computer Research and Modeling, 2022, v. 14, no. 6, pp. 1221-1238

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Multi-label classification models arise in various areas of life, which is explained by an increasing amount of information that requires prompt analysis. One of the mathematical methods for solving this problem is a plug-in approach, at the first stage of which, for each class, a certain ranking function is built, ordering all objects in some way, and at the second stage, the optimal thresholds are selected, the objects on one side of which are assigned to the current class, and on the other — to the other. Thresholds are chosen to maximize the target quality measure. The algorithms which properties are investigated in this article are devoted to the second stage of the plug-in approach which is the choice of the optimal threshold vector. This step becomes non-trivial if the $F$-measure of average precision and recall is used as the target quality assessment since it does not allow independent threshold optimization in each class. In problems of extreme multi-label classification, the number of classes can reach hundreds of thousands, so the original optimization problem is reduced to the problem of searching a fixed point of a specially introduced transformation $\boldsymbol V$, defined on a unit square on the plane of average precision $P$ and recall $R$. Using this transformation, two algorithms are proposed for optimization: the $F$-measure linearization method and the method of $\boldsymbol V$ domain analysis. The properties of algorithms are studied when applied to multi-label classification data sets of various sizes and origin, in particular, the dependence of the error on the number of classes, on the $F$-measure parameter, and on the internal parameters of methods under study. The peculiarity of both algorithms work when used for problems with the domain of $\boldsymbol V$, containing large linear boundaries, was found. In case when the optimal point is located in the vicinity of these boundaries, the errors of both methods do not decrease with an increase in the number of classes. In this case, the linearization method quite accurately determines the argument of the optimal point, while the method of $\boldsymbol V$ domain analysis — the polar radius.

class="publication_info"> class="authors3">Risnik D.V., class="authors3">Levich A.P., class="authors3">Fursova P.V., class="authors3">Goncharov I.A.
The algorithm of the method for calculating quality classes’ boundaries for quantitative systems’ characteristics and for determination of interactions between characteristics. Part 1. Calculation for two quality classes
Computer Research and Modeling, 2016, v. 8, no. 1, pp. 19-36

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A calculation method for boundaries of quality classes for quantitative systems characteristics of any nature is suggested. The method allows to determine interactions which are not detectable using correlation and regression analysis; quality classes’ boundaries of systems’ condition indicator and boundaries of the factors influencing this condition; contribution of the factors to a degree of «inadmissibility» of indicator values; sufficiency of the program observing the factors to describe the causes of «inadmissibility» of indicator values.

class="publication_info"> class="authors3">Risnik D.V., class="authors3">Levich A.P., class="authors3">Fursova P.V., class="authors3">Goncharov I.A.
The algorithm of the method for calculating quality classes’ boundaries for quantitative systems’ characteristics and for determination of interactions between characteristics. Part 2. Calculation for three or more quality classes
Computer Research and Modeling, 2016, v. 8, no. 1, pp. 37-54

class="abstract">

The method of calculation of the boundaries of quality classes for quantitative characteristics of systems with any properties is adapted to search for boundaries of three quality classes. In addition to other results, adaptation of the method allowed to determine boundaries between quality classes at simultaneous «unacceptability » of high and low values of indicator characteristic of the system condition and simultaneous «inadmissibility » of high and low values of factors affecting the system.

class="publication_info"> class="authors3">Risnik D.V., class="authors3">Levich A.P., class="authors3">Bulgakov N.G., class="authors3">Bikbulatov E.S., class="authors3">Bikbulatova E.M., class="authors3">Ershov Y.V., class="authors3">Konuhov I.V., class="authors3">Korneva L.G., class="authors3">Lazareva V.I., class="authors3">Litvinov A.S., class="authors3">Maksimov V.N., class="authors3">Mamihin S.V., class="authors3">Osipov V.A., class="authors3">Otyukova N.G., class="authors3">Poddubnii S.A., class="authors3">Pirina I.L., class="authors3">Sokolova E.A., class="authors3">Stepanova I.E., class="authors3">Fursova P.V., class="authors3">Celmovich O.L.
Searching for connections between biological and physico-chemical characteristics of Rybinsk reservoir ecosystem. Part 1. Criteria of connection nonrandomness
Computer Research and Modeling, 2013, v. 5, no. 1, pp. 83-105

class="abstract">

Based on contents of phytoplankton pigments, fluorescence samples and some physico-chemical characteristics of the Rybinsk reservoir waters, searching for connections between biological and physicalchemical characteristics is working out. The standard methods of statistical analysis (correlation, regression), methods of description of connection between qualitative classes of characteristics, based on deviation of the studied characteristics distribution from independent distribution, are studied. A method of searching for boundaries of quality classes by criterion of maximum connection coefficient is offered.

class="publication_info"> class="authors3">Levich A.P., class="authors3">Bulgakov N.G., class="authors3">Risnik D.V., class="authors3">Bikbulatov E.S., class="authors3">Bikbulatova E.M., class="authors3">Goncharov I.A., class="authors3">Ershov Y.V., class="authors3">Konuhov I.V., class="authors3">Korneva L.G., class="authors3">Lazareva V.I., class="authors3">Litvinov A.S., class="authors3">Maksimov V.N., class="authors3">Mamihin S.V., class="authors3">Osipov V.A., class="authors3">Otyukova N.G., class="authors3">Poddubnii S.A., class="authors3">Pirina I.L., class="authors3">Sokolova E.A., class="authors3">Stepanova I.E., class="authors3">Fursova P.V., class="authors3">Celmovich O.L.
Searching for connections between biological and physico-chemical characteristics of Rybinsk reservoir ecosystem. Part 3. Calculation of the boundaries of water quality classes
Computer Research and Modeling, 2013, v. 5, no. 3, pp. 451-471

class="abstract">

Approbation of calculation of borders of water quality classes for the purpose of ecological diagnosis and standardization by data of the Rybinsk reservoir is carried out. For bioindication indicators of phytoplankton fluorescence and the contents of pigments of phytoplankton are used. Chesnokov's importance coefficient proved to be the most preferred measure of connection for analyzing the effects of environmental factors on indicators. The factors important for environmental condition are identified. Comparison of borders between quality classes “valid” and “invalid” of factors values and boundaries of the classifications of water quality.

class="publication_info"> class="authors3">Borisova L.R., class="authors3">Kuznetsova A.V., class="authors3">Sergeeva N.V., class="authors3">Sen'ko O.V.
Comparison of Arctic zone RF companies with different Polar Index ratings by economic criteria with the help of machine learning tools
Computer Research and Modeling, 2020, v. 12, no. 1, pp. 201-215

class="abstract">

The paper presents a comparative analysis of the enterprises of the Arctic Zone of the Russian Federation (AZ RF) on economic indicators in accordance with the rating of the Polar index. This study includes numerical data of 193 enterprises located in the AZ RF. Machine learning methods are applied, both standard, from open source, and own original methods — the method of Optimally Reliable Partitions (ORP), the method of Statistically Weighted Syndromes (SWS). Held split, indicating the maximum value of the functional quality, this study used the simplest family of different one-dimensional partition with a single boundary point, as well as a collection of different two-dimensional partition with one boundary point on each of the two combining variables. Permutation tests allow not only to evaluate the reliability of the data of the revealed regularities, but also to exclude partitions with excessive complexity from the set of the revealed regularities. Patterns connected the class number and economic indicators are revealed using the SDT method on one-dimensional indicators. The regularities which are revealed within the framework of the simplest one-dimensional model with one boundary point and with significance not worse than p < 0.001 are also presented in the given study. The so-called sliding control method was used for reliable evaluation of such diagnostic ability. As a result of these studies, a set of methods that had sufficient effectiveness was identified. The collective method based on the results of several machine learning methods showed the high importance of economic indicators for the division of enterprises in accordance with the rating of the Polar index. Our study proved and showed that those companies that entered the top Rating of the Polar index are generally recognized by financial indicators among all companies in the Arctic Zone. However it would be useful to supplement the list of indicators with ecological and social criteria.