METHODS OF SYNTHESIS OF MODELS OF QUANTITATIVE DEPENDENCIES IN THE BASIS OF TREES OF REGRESSION, REALIZING CLUSTER-REGGRESSION APPROXIMATION BY PRECEDENTS
DOI:
https://doi.org/10.15588/1607-3274-2019-3-9Keywords:
Modeling, cluster-regression approximation, estimation, decision trees, regression analysisAbstract
Context. To make decisions in technical applications, it is usually necessary to have a model that allows you to predict the stateof a managed object or process. The object of the study is the process of building dependency models by use cases. The subject of the
study are the methods for constructing quantitative dependencies based on cluster-regression approximation precedents.
Objective. The aim of the paper is to simplify cluster regression approximation models by indirectly implementing cluster analysis
in the process of model building.
Method. A tree-based cluster-regression approximation method is proposed which, for a given training sample, constructs a tree
for hierarchical clustering of instances whose leaf nodes correspond to clusters, for each cluster, constructs a particular model of dependence
on instances of the training sample that fall into the cluster, in order to provide the least complexity of the model and uses
the set the most informative features of the shortest length. This allows to ensure an acceptable accuracy of the model, high levels of
interpretation and generalization of data, to reduce the complexity of the model, and to simplify its implementation in the sequential
organization of calculations.
Results. The software that implements the proposed method of tree-like cluster-regression approximation is developed. The developed
method and the software implementing it are investigated in solving practical problems of prediction. The conducted experiments
confirmed the working capacity of the developed software and allow to recommend it for use in practice.
Conclusions. Unlike traditional methods of regression model constructing that build a model based on a function form that is
uniform for the entire feature space, the proposed method forms a hierarchical combination of particular models. Unlike the wellknown
methods of regression tree constructing whose leaf nodes contain averaged values of the output feature for clusters, the proposed
method forms a tree consisting of particular models for clusters, which allows to ensure greater accuracy of the model.
References
Ajvazjan S. A., Enjukov I. S., Meshalkin L. D. Prikladnaja statistika: Issledovanie zavisimostej. Moscow, Finansy i statistika,
, 487 p.
Afifi A., Jejzen S. Statisticheskij analiz: podhod s ispol’zovaniem EVM. Moscow, Mir, 1982, 488 p.
Kruse R., Borgelt C., Klawonn F. et. al. Computational intelligence:a methodological introduction. London, Springer-Verlag,
, 488 p.
Intelligent hybrid systems: fuzzy logic, neural networks, and genetic algorithms, ed. D. Ruan. Berlin, Springer, 2012, 374 p.
Ivahnenko A. G., Jurachkovskij Ju. P. Modelirovanie slozhnyh sistem po jeksperimental’nym dannym. Moscow, Radio i svjaz’,
, 118 s.
Madala H. R., Ivakhnenko A. G. Inductive Learning Algorithms for Complex Systems Modeling. Boca Raton, CRC Press, 1994,
p.
Clarke B., Fokoue E., Zhang H. H. Principles and theory for data mining and machine learning. New York, Springer, 2009,
p.
Breiman L., Friedman J. H., Stone C. J., Olshen R. A. Classification and regression trees. Boca Raton, Chapman & Hall, CRC, 1984, 368 p.
Rutkowski L. Flexible neuro-fuzzy systems : structures, learning and performance evaluation. Boston, Kluwer, 2004, 276 p.
Liu P., Li H. Fuzzy neural network theory and application. Singapore, World Scientific, 2004, 376 p. (Series in Machine Perception and Artificial Intelligence ; vol. 59).
Buckleya J. J., Hayashi Y. Fuzzy neural networks: a survey, Fuzzy sets and systems, 1994, Vol. 66, Issue 1, pp. 1–13.
Jang J. R., Sun C.-T., Mizutani E. Neuro-fuzzy and soft computing: a computational approach to learning and machine intelligence. Upple Saddle River, Prentice-Hall, 1997, 614 p.
Subbotin S. O. Algorytmy klaster-regresijnoi aproksymacii ta jih nejromerezhevi interpretacii, Radio Electronics, Computer
Science, Control, 2003, No. 1, рр. 114–121.
Subbotin S. A. Metod sinteza nejro-nechjotkih approksimatorov, Avtomatizacija i sovremennye tehnologii, 2007, No. 11,
pp. 14–18.
Subbotin S. A. Nejro-nechjotkaja klaster-regressionnaja approksimacija po obobshhjonnoj osi, Nejrokomp’jutery: razrabotka,
primenenie, 2009, No. 8, pp. 52–62.
Berkhin P., Dhillon I. S. ed. R. A. Meyers Knowledge discovery: clustering, Encyclopedia of complexity and systems science.
Berlin, Springer, 2009, pp. 5051–5064.
Abonyi J., Feil B. Cluster analysis for data mining and system identification. Basel, Birkhäuser, 2007, 303 p.
Widrow B., Lehr M. A. 30 years of adaptive neural networks: percep-tron, madaline, and backpropagation, Proceedings of the
IEEE, Vol. 78, Issue 9, pp. 1415–1442. DOI:10.1109/5.58323
Ravindran A., Ragsdell K. M, Reklaitis G. V. Engineering optimization:methods and applications. New Jersey, John Wiley
& Sons, 2006, 688 p.
Rumelhart D. E., Hinton G. E., Williams R. J. Learning representations by back-propagating errors, Nature, 1986, Vol. 323,
P. 533–536. DOI:10.1038/323533a0
Gorban A. N., Mirkes Eu. M., Tsaregorodtsev V. G. Generation of Explicit Knowledge from Empirical Data through Pruning of
Trainable Neural Networks, International Joint Conference on Neural Networks (IJCNN’99), Washington, July 1999 : proceedings.
Los Alamitos, IEEE, 1999, Vol. 6. pp. 4393–4398.
Akaike H. A new look at the statistical model identification, IEEE transactions on automatic control, 1974, Vol. 19, № 6,
pp. 716–723.
Schwarz G. E. Estimating the dimension of a model, Annals of statistics, 1978, Vol. 6, No. 2, pp. 461–464.
Hannan E. J., Quinn B. G. The determination of the order of an autore-gression, Journal of the Royal Statistical Society, 1979,
Ser. B, Vol. 41, pp. 190–195.
Subbotin S. A. Analiz svojstv i kriterii sravnenija nejrosetevyh modelej dlja reshenija zadach diagnostiki i raspoznavanija obrazov, Reestracіja, zberіgannja і obrobka danih, 2009, Vol. 11, No. 3, pp. 42–52.
Subbotin S. A. Modeli kriteriev sravnenija nejronnyh i nejronechjotkih setej v zadachah diagnostiki i klassifikacii obrazov,
Naukovі pracі Donec’kogo nacіonal’nogo tehnіchnogo unіversytetu. Serіja «Іnformatyka, kіbernetyka ta obchysljuval’na
tehnіka». Donec’k, DNTU, 2010, Vyp. 12 (165), pp. 148–151.
Subbotin S. A. Metodika i kriterii sravnenija modelej i algoritmov sinteza iskusstvennyh nejronnyh setej, Radio Electronics,
Computer Science, Control, 2003, No. 2, pp. 109–114.
Boguslaev A. V., Olejnik Al. A., Olejnik An. A., Pavlenko D. V., Subbotin S. A.; pod red. Pavlenko D. V., Subbotina
S. A. Progressivnye tehnologii modelirovaniya, optimizacii i intellektual’noj avtomatizacii etapov zhiznennogo cikla aviacionnyh dvigatelej : monografiya. Zaporozh’e, OAO «Motor Sich», 2009, 468 p.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2019 S. A. Subbotin
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Creative Commons Licensing Notifications in the Copyright Notices
The journal allows the authors to hold the copyright without restrictions and to retain publishing rights without restrictions.
The journal allows readers to read, download, copy, distribute, print, search, or link to the full texts of its articles.
The journal allows to reuse and remixing of its content, in accordance with a Creative Commons license СС BY -SA.
Authors who publish with this journal agree to the following terms:
-
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License CC BY-SA that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
-
Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
-
Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
