Abstract
Some approach to multidimensional information scaling of the characteristics features based on results of theory of perturbation of pseudo-inverse and projective matrices and solutions of systems of linear algebraic equations is proposed. The method and algorithm of a piecewise hyperplane clusters creating with the verification of a given criterion for effectiveness of the proposed method of clustering is developed. The problem of stability of main indicators of the classifier in presence disturbances in source information is investigated. The proposed method for determining influence of source data errors on main indicators of the classifier provides presentation of undisturbed information matrix in form of splitting matrices of special kind. Advantages of the proposed approach are demonstrated, an example of using the method of scaling characteristic features for recognizing fingerspelling alphabet of sign language is given.
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REFERENCES
M. Jambu, Hierarchical Cluster Analysis and Matching (Finansy i Statistika, Moscow, 1988) [in Russian].
V. N. Vapnik, Statistical Learning Theory (Wiley, New York, 1998).
Yu. I. Zhuravlev, Yu. P. Laptin, and A. P. Vinogradov, “A comparison of some approaches to classification problems, and possibilities to construct optimal solutions efficiently,” Pattern Recogn. Image Anal. 24 (2), 189–195 (2014).
C.-W. Hsu and C.-J. Lin, “A comparison of methods for multiclass support vector machines,” IEEE Trans. Neural Networks 13 (2), 415–425 (2002).
M. L. Davison, Multidimensional Scaling (Wiley, Chichester, 1983; Finansy i Statistika, Moscow, 1988).
T. F. Cox and M. A. A. Cox, Multidimensional Scaling, 2nd ed. (Chapman and Hall/CRC, 2001).
K. V. Vorontsov, “Lectures on algorithms of clustering and multidimensional scaling,” URL: http:// www.ccas.ru/voron/download/Clustering.pdf (Accessed January 5, 2020).
P. Mair, I. Borg, and T. Rusch, “Goodness-of-fit assessment in multidimensional scaling and unfolding,” Multivar. Behav. Res. 51 (6), 772–789 (2016)
Iu. V. Krak, G. I. Kudin, and A. I. Kulyas, “Multidimensional scaling by means of pseudo inverse operations,” Cybern. Syst. Anal. 55 (1), 22–29 (2019).
N. F. Kirichenko, “Analytical representation of perturbations of pseudoinverse matrices,” Cybern. Syst. Anal. 33 (2), 230–238 (1997).
N. F. Kirichenko, Yu. V. Krak, and A. A. Polishchuk, “Pseudo inverse and projection matrices in problems of synthesis of functional transformers,” Cybern. Syst. Anal. 40 (3), 407–419 (2004).
I. V. Sergienko, A. N. Khimich, and M. F. Yakovlev, “Methods for obtaining reliable solutions to systems of linear algebraic equations,” Cybern. Syst. Anal. 47 (1), 62–73 (2011).
R. Penrose, “A generalized inverse for matrices,” Math. Proc. Cambridge Philos. Soc. 51 (3), 406–413 (1955).
R. E. Cline, “Representation for the generalized inverse of a partitioned matrix,” J. Soc. Ind. Appl. Math. 12 (3), 588–600 (1964).
A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory and Applications, 2nd ed., CMS Books in Mathematics (Springer, New York, 2003).
Iu. V. Krak, Iu. G. Kryvonos, O. V. Barmak, and A. S. Ternov, “An approach to the determination of efficient features and synthesis of an optimal band-separating classifier of dactyl elements of sign language,” Cybern. Syst. Anal. 52 (2), 173–180 (2016).
Yu. V. Krak, A. A. Golik, and V. S. Kasianiuk, “Recognition of dactylemes of Ukrainian sign language based on the geometric characteristics of hand contours defects,” J. Autom. Inf. Sci. 48 (4), 90–98 (2016).
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Iurii Krak is Professor, head of the Theoretical Cybernetics Department at Taras Shevchenko National University of Kyiv, Ukraine. He received a M.Sc. in Applied Mathematics in 1980 and a Doctor of Sc. (Math. and Phys.) on Computer Science in 1999. His scientific interest is in the fields of data and image processing, information classification and recognition, robotics, intelligent decision-making systems with applications to mathematical modeling of physical processes, face emotion and mimics modeling, lipsreading, speech signals processing, speech synthesis and recognition, sign language modeling and recognition, etc. He is author of numerous papers, monographs and is an active participant of international cooperation projects. IEEE member, Corresponding member by Informatics of NAS of Ukraine.
Veda Kasianiuk received a M.Sc. in Applied Mathematics in 1983 and a PhD on Computational Mathematics in 1988 at Taras Shevchenko National University of Kyiv, Ukraine. Since 2005 she is the Head of the Research Laboratory of Theoretical Cybernetics on Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv. Her research interests include analysis and processing of information data, research of problems of artificial intelligence.
Hrygoriy Kudin received a M.Sc. in Mathematics in 1968 and a PhD on Applied Mathematics in 1975 at Taras Shevchenko National University of Kyiv, Ukraine. Since 1971 he has been working at the Faculty of Computer Science and Cybernetics of the University in teaching and research. His interests include dynamic systems analysis, data clustering and classification based on the theory of perturbations of pseudo-inverse and projection operators.
Оlexander Barmak received M.Sc. in Mathematics in 1985 at Odessa State University, Ukraine, and Doctor of Sc.(Tech) from V.M. Glushkov Cybernetics Institute in 2013. He is a Professor at the Department of Computer Science and Information Technology at Khmelnitsky National University, Ukraine. His research interests include alternative communication information technology, information classification methods (textual, visual) for applied problems.
Eduard Manziuk received M.Sc. in Mechanics in 1998 and PhD (Tech.) in 2004 at Khmelnytskyi National University, the Ukraine. He is associate professor, Department of Computer Science and Information Technology at Khmelnytskyi National University. His research interests include using visual analytics for machine learning, model ensembles, small data set classification.
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Krak, I.V., Kasianiuk, V.S., Kudin, H.I. et al. Multivariate Scaling of the Characteristic Features Based on Pseudo-Inverse Operations for Recognition Problems Solving. Pattern Recognit. Image Anal. 30, 184–191 (2020). https://doi.org/10.1134/S1054661820020078
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DOI: https://doi.org/10.1134/S1054661820020078