Метод візуалізації багатовимірних випадкових процесів

: cc. 5-10
Харківський національний автомобільно-дорожній університет, Україна
Харківський національний автомобільно-дорожній університет, Україна
Харківський національний автомобільно-дорожній університет, Україна
Державний біотехнологічний університет, Україна

The article proposes a method for visualizing multidimensional random process realizations using the example of the concentrations of harmful gases emitted into the atmosphere from a thermal power plant. The method is based on the transformation of gas concentration values in one point of multidimensional space at the same time into a two-dimensional curve, which is described by the sum of products of normalized concentrations by orthogonal Legendre functions of the corresponding order. The combination of such curves on a two-dimensional plane at discrete times creates a characteristic image that can be used
to visually detect features of gas concentrations over time by a human operator.

[1] G. Phillips-Wren. Intelligent Systems to Support Human Decision Making. In book: Artificial Intelligence, 2017, pp.3023–3036. DOI:10.4018/978-1-5225-1759-7.ch125
[2] S. Mansmann, T. Neumuth, M. H. Scholl, Multidimensional Data Modeling for Business Process Analysis, 26th Int. Conf. on Conceptual Modeling, Nov. 5-9, 2007, Auckland,
New Zealand. DOI:10.1007/978-3-540-75563-0_4
[3] J. Starck, F. Murtagh, Handbook of Astronomical Data Analysis. Elsevier, 2002. [Online] Available: https://www. academia. edu/2608657/Handbook_of_Astronomical_Data_Analysis
[4] Pak Chung Wong and R. Daniel Bergeron. 30 Years of Multidimensional Multivariate Visualization. In Sc. Visualization, Overviews, Methodologies and Techniques. IEEE Computer Society Press, pp 3–33, 1994. Available: https:// www.cs.unc.edu/xcms/courses/comp715-s10/papers/Wong97_30_years_of_multid...
[5] H. C. Purchase, N. Andrienko, T. J. Jankun-Kelly, M. Ward.Theoretical Foundations of Information Visualization. In: Inf.Visualization: Human-Centered Issues and Perspectives, 1970,
pp.46-64. DOI:10.1007/978-3-540-70956-5_3.
[6] W. Weaver, C. Shannon. The mathematical theory of communication.Physics, 2009. DOI:10.1098/rspa.2009.0063
[7] D. Asimov, “The grand tour: A tool for viewing multidimensional data”, SIAM Journ. on Sc. & Stat. Comp., pp.128-143, 1985. DOI: 10.1137/0906011

[8] R. Bergeron, W. Cody, W. Hibbard, D. Kao, K. Miceli, L.Treinish, S. Walther. Database Issues for Data Visualization:Data Model Development. In IEEE Visualization '93 Workshop, San Jose, California, USA, October 26, 1993,pp. 3-15. In Proc. Lecture Notes in Comp. Sc.ce 871,Springer 1993. [Online] Available: https://link.springer.com/book/10.1007/BFb0021138
[9] I. Romanova, "Modern Methods of Multidimensional Data Visualization: Analysis, Classification, Implementation and Applications in Technical Systems, Science and Education
of the Bauman MSTU, Vol. 3, 2016, pp. 133–167. DOI:10.7463/0316.0834876
[10] Zongben Xu, Yong Shi. Exploring Big Data Analysis: Fundamental Scientific Problems, Ann. data sci., 2 (4), 2015, pp. 363-372. DOI:10.1007/s 40745-015-00637
[11] Yau Nathan. Visualize This: The Flowing Data Guide to Design, Visualization, and Statistics s. Indianapolis, In:Wiley Publishing, 2011. [E-book] Available:
[12] H. Chernoff. The Use of Faces to Represent Points in KDimensional Space Graphically. Journ. Am. Stat. Ass., Vol.68, No. 342., pp. 361-368, 1973. DOI:10.2307/2284077
[13] J. Heer, M. Bostock, V. Ogievetsky, A Tour through the Visualization Zoo. A survey of powerful visualization techniques, from the obvious to the obscure. Communications
of the ACM. Stanford University. 2010. Vol. 53, Iss.6, pp.59-67. DOI:10.1145/1743546.1743567
[14] V. Ogievetsky, J. Heer. D3: Data Driven Documents, IEEE Trans. Visualization & Comp. Graphics, 2011. [Online], Available: http://vis.stanford.edu/files/2011-D3-InfoVis.pdf
[15] M. Marjani, F. Nasaruddin, A. Gani, A. Karim, I. Abaker, T.Hashen, A Siddiqa, I. Yaqoob. Big Data Analytics: Architecture, Opportunities, and Open Res. Challenges. IEEE
Access, vol. 5, 2017, pp. 5247–5261. DOI:10.1109/ACCESS.2017.2689040
[16] S. Koyamada, Y. Shikauchi, K. Nakae, M. Koyama, S.Ishii. Deep Learning of FMRI big data: a novel approach to subject-transfer decoding. – arXiv: 1502.00093v1 [stat ML]
31 January 2015. [Online]. Available: https://arxiv.org/pdf/1502.00093.pdf
[17] L. van der Maaten, G. Hinton. Visualizing Data using t-SNE. Journ. Mach. Learn. Res., 2008, vol. 9, pp.2579–2605. [Online]. Available: https://www.jmlr.org/papers/volume9/vandermaaten08a/vandermaaten08a.pdf
[18] A. Genender-Feltheimer. Visualizing High Dimensional and Big Data. Complex Adaptive Systems Conference with Theme: Cyber Physical Systems and Deep Learning, CAS,  2018, 5-7 Nov. 2018, Chicago, USA, pp.112–121. DOI:10.1016/j.procs.2018.10.308
[19] K. Börner, C. Chen, K. Boyack. Visualizing knowledge domains. An. Rev. of Inf. Sc. & Techn., vol. 37, 2003, Medford, NJ: Information Today, Inc./Amer. Soc. for Inf. Sc. and Techn., Ch.5, pp.179–255. DOI:10.1002/aris.1440370106
[20] J. Emerson, W. Green, B. Schloerke, J. Crowley, D. Cook, H. Hofmann, H. Wickham. The Generalized Pairs Plot.Journ Comp. and Graph. Statistics, vol. 22(1), 2013, pp. 79-91. DOI:10.1080/10618600.2012.694762
[21] J. Im, M. McGuffin, R. Leung. GPLOM: Generalized Plot Matrix for Visualizing Multidimensional Multivariate Data, IEEE Trans. on Visualization and Comp. Graphics, 19 (12),
2013, pp. 2606-2614. DOI: 10.1109/TVCG.2013.160
[22] J. van Wijk, R. van Liere. HyperSlice: Visualization of Scalar Functions of Many Variables, 1998. [Online]. Available:www.researchgate.net/publication/2660434_ HyperSlice
[23] D. Andrews. Plots of high-dimensional data, Biometrics, Vol. 28, no.1, 1972, pp. 69-97. DOI:10.2307/2528964
[24] O. Poliarus, Y. Poliakov, A. Lebedynskyi. Detection of landmarks by autonomous mobile robots using camerabased sensors in outdoor environments. IEEE Sensors
Journal, vol. 21, iss.10, 2021, pp. 11443-11450, DOI:10.1109/JSEN.2020.3010883