Mathematical Methods for Reducing the Space of Analyzed States when Processing Big Data
This paper addresses the problem of creating mathematical methods to optimize time and computing resources when processing Big Data. These methods are based on the proposed data organizational structure called “m-tuples based on ordered sets of arbitrary cardinality”. We formulated certain properties of the given data organizational structure as a consequence of the logical rules applied for the formation of m-tuples. A set of functional dependencies was also derived between m-tuples based on their location in the structure. A graphical interpretation was presented to illustrate the change of dynamics in fractions of operand combinations for which one tuple is a subset of the other. It takes into account the variation in the lengths of operand tuples. We also obtained logical conclusions about the influence of the properties studied and mathematical methods of working with the given structure to minimize the computing resources involved.
A. Gaur, “Search techniques to contain combinatorial explosion in artificial intelligence,” International Journal of Engineering Research & Technology, vol. 1, issue 7, pp. 1−7, September 2012.
S. Yadav, A. Phulre, M. Pradesh, “A literature review on Big Data reduction methods,” International Journal of Electrical, Electronics and Computer Engineering, pp. 92−99,
H. Hashem, D. Ranc, “An integrative modeling of Big Data processing,” International Journal of Computer Science and Applications, ©Technomathematics Research Foundation, vol. 12, pp. 1–15, January 2015.
K. Tadist, S. Najah, N. Nikolov, F. Mrabti, A. Zahi, “Feature selection methods and genomic Big Data: a systematic review,” Journal of Big Data, pp. 1–24, August 2019.
N. Shakhovska, O. Veres, M. Hirnyak, “Generalized formal model of Big Data,” Econtechmod. An International Quarterly Journal, vol. 5, pp. 33–38, February 2016.
B. Suvarnamukhi, M. Seshashayee, “Big Data concepts and techniques in data processing,” International Journal of Computer Sciences and Engineering, vol. 6, Issue-10, pp. 712–714, Oct 2018.
Y. Ishizuka, W. Chen, I. Paik, “Workflow transformation for real-time Big Data processing,” IEEE International Congress on Big Data, pp. 31–318, 2016.
I. Bifulco, S.Cirillo, “Discovery multiple data structures in Big Data through global optimization and clustering Methods,” IEEE 22nd International Conference Information Visualization, pp. 117–121, 2018.
K. Tasdemir, E. Merenyi, “Exploiting data topology in visualization and clustering of self-organizing maps,” IEEE Transactions on Neural Networks, vol. 20, pp. 549–562, April 2009.
O. Syrotkina, M. Alekseyev, V. Asotskyi, and I. Udovyk, “Analysis of how the properties of structured data can influence the way these data are processed,” Naukovyi Visnyk NHU, Dnipro, vol. 3 (171), 2019, pp. 119–129.
Syrotkina O. Graphical and Analytical Methods for Processing “Big Data” Based on the Analysis of Their Properties Model / O. Syrotkina, M. Alekseyev, I. Udovyk // Системні технології. Регіональний міжвузівський збірник наукових праць. – Випуск 3 (122). – Дніпро, 2019. – С. 78-90.
O. Syrotkina, M. Alekseyev, L. Meshcheriakov, and B. Moroz, “Methods of working with “big data” based on the application of “m-tuple” theory,.” Computer-Integrated Technologies: Education, Science, Production, Lutsk, vol. 36, 2019, pp. 140–152.