USE OF LENGTH-BASED SIMILARITY MEASURE IN CLUSTERING PROBLEMS

N. E. Kondruk

Abstract


Context. The study is devoted to the development of a flexible mathematical apparatus, which should have a sufficiently wide range of
means for grouping objects into different types of similarity measures. This makes it possible, within the framework of the developed approach, to efficiently solve sufficiently broad classes of applied problems from different subject areas and to partition objects with clusters of different geometric forms.
Objective. The aim of the study is improvement of the efficiency of solving cluster problems by applying a similar measure of the vector
characteristics of objects.
Method. A fuzzy binary relation and its membership function describing the similarity of objects according to the level of similarity of
their vector attributes are described. The method of single-level clustering, based on fuzzy binary relations for the use of a similarity measure, is modified. In this case, certain values are set – the thresholds of clusterization that characterize the similarity degree of objects within the cluster. By changing the thresholds of clusterization, one can analyze the dynamics of cluster formation, investigate their structure and interrelationships between objects, determine the ultimate objects, and make a thorough analysis of the obtained results. The proposed approach does not require a preliminary determination of the number of clusters and allows clustering of data in concentric spheres in the absence of additional a priori information, so it can be used at the stage of preliminary data analysis.
Results. The developed approach is implemented in the form of a software system on the basis of which the actual applied problem of
investigating the intensity of population migration by regions of Ukraine is solved.
Conclusions. The conducted experimental researches show the convenience and efficiency of using the similarity measure for solving
applied problems requiring clustering in the form of concentric spheres. The presented approach provides an opportunity to conduct new
meaningful studies of input data. Prospects for further research are development of a decision support system, to solve the problems of
grouping objects into clusters by concentric spheres, cones, ellipses and their intersections; implementation of parallel multi-level clustering
carried out simultaneously by several criteria of similarity of objects and their application; study of the partitioning of objects by different
geometric forms of clusters for a single sample of input data and carrying out a meaningful interpretation of the obtained results

Keywords


fuzzy clustering; cluster; measure of similarity; automatic grouping of objects; clustering.

References


Kondruk N. Clustering method based on fuzzy binary relation, Eastern-European Journal of Enterprise Technologies, 2017, No. 2(4), pp. 10–16. DOI: 10.15587/1729-4061.2017.94961

Kondruk N. E., Маlyar М. М. Algorytm klasteryzacii’ kryterial’nogo prostoru dlja zadach vyboru, Visnyk Kyi’vs’kogo universytetu, 2006, Issue. 3, pp. 225–229.

Kondruk, N. E. Dejaki metody avtomatychnogo grupuvannja

ob’jektiv, Eastern-European Journal of Enterprise Technologies,

, Vol. 2, No. 4 (68), pp. 20–24.

Kondruk N. E. Systemy pidtrymky pryjnjattja rishen’ dlja avtomatyzovanogo skladannja dijet, Management of Development of Complex Systems, 2015, Issue. 23(1), pp. 110–114.

Peters, G. Soft clustering-fuzzy and rough approaches and their extensions and derivatives, International Journal of Approximate Reasoning, 2013, Vol. 54, No. 2, pp. 307–322. DOI:10.1016/j.ijar.2012.10.003

Banu P. K. N., Andrews S. Performance analysis of hard and soft clustering approaches for gene expression data, International Journal of Rough Sets and Data Analysis (IJRSDA), 2015, Vol. 2, No. 1, pp. 58–69. DOI: 10.4018/ijrsda.2015010104 7. Bora D. J., Gupta D., Kumar A. A. Comparative study between fuzzy clustering algorithm and hard clustering algorithm, International Journal of Computer Trends and Technology (IJCTT), 2014, Vol. 10(2), pp. 108–113. DOI: 10.14445/22312803/IJCTTV10P119

Jipkate B. R., Gohokar V. V. A comparative analysis of fuzzy cmeans clustering and k means clustering algorithms, International Journal Of Computational Engineering Research, 2012, Vol. 2, No. 3, pp. 737–739.

Shokouhifar M., Jalali A. Optimized sugeno fuzzy clustering algorithm for wireless sensor networks, Engineering applications of artificial intelligence, 2017, Vol. 60, pp. 16–25. DOI:10.1016/j.engappai.2017.01.007

Toz G., Yücedağ İ., Erdoğmuş P. A Fuzzy Image Clustering

Method Based on an Improved Backtracking Search Optimization Algorithm with an Inertia Weight Parameter, Journal of King Saud University-Computer and Information Sciences, 2018. In press. DOI: 10.1016/j.jksuci.2018.02.011

Izakian H., Pedrycz W., Jamal I. Fuzzy clustering of time series data using dynamic time warping distance, Engineering Applications of Artificial Intelligence, 2015, Vol. 39, pp. 235–244. DOI:10.1016/j.engappai.2014.12.015

Chen S., Zhang D. Robust image segmentation using FCM with spatial constraints based on new kernel-induced distance measure, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics),

, Vol. 34, No. 4, pp. 1907–1916. DOI:10.1109/TSMCB.2004.831165

Heidarzade A., Mahdavi I., Mahdavi-Amiri N. Supplier selection using a clustering method based on a new distance for interval type-2 fuzzy sets: A case study, Applied Soft Computing, 2016, Vol. 38, pp. 213–231. DOI: 10.1016/j.asoc.2015.09.029

Ye J. Clustering methods using distance-based similarity measures of single-valued neutrosophic sets, Journal of Intelligent Systems, 2014, Vol. 23, No. 4, pp. 379–389. DOI: 10.1515/jisys-2013-0091


GOST Style Citations


1. Kondruk N. Clustering method based on fuzzy binary relation
/ N. Kondruk // Eastern-European Journal of Enterprise Technologies.
– 2017. – No. 2(4). – P. 10–16. DOI:
10.15587/1729–4061.2017.94961
2. Кондрук Н. Е. Алгоритм кластеризації критеріального
простору для задач вибору / Н. Е. Кондрук, М. М. Маляр
//Вісник Київського університету. Серія: фіз.-мат. наук. –
2006. – Вип. 3. – С. 225–229.
3. Кондрук Н. Е. Деякі методи автоматичного групування
об’єктів / Н. Е. Кондрук // Південно-Європейський журнал
передових технологій. – 2014. – Т. 2, № 4 (68). – С. 20–24.
4. Кондрук Н. Е. Системи підтримки прийняття рішень для
автоматизованого складання дієт / Н. Е. Кондрук //
Управління розвитком складних систем. – 2015. –
Вип. 23(1). – С. 110–114.
5. Peters G. Soft clustering–fuzzy and rough approaches and
their extensions and derivatives / G. Peters // International
Journal of Approximate Reasoning. – 2013. – Vol. 54, № 2. –
P. 307–322. DOI: 10.1016/j.ijar.2012.10.003
6. Banu P. K. N. Performance analysis of hard and soft clustering
approaches for gene expression data / P. K. N. Banu, S. Andrews
//International Journal of Rough Sets and Data Analysis
(IJRSDA). – 2015. – Vol. 2, № 1. – P. 58–69. DOI:
10.4018/ijrsda.2015010104
7. Bora D. J. Comparative study between fuzzy clustering algorithm
and hard clustering algorithm / D. J. Bora, D. Gupta,
A. A. Kumar // International Journal of Computer Trends and
Technology (IJCTT). – 2014. – Vol. 10(2). – C. 108–113.
DOI: 10.14445/22312803/IJCTT-V10P119
8. Jipkate B. R. A comparative analysis of fuzzy c-means clustering
and k means clustering algorithms / B. R. Jipkate,
V. V. Gohokar // International Journal Of Computational Engineering
Research. – 2012. – Vol. 2. – № 3. – P. 737–739.
9. Shokouhifar M. Optimized sugeno fuzzy clustering algorithm
for wireless sensor networks / M. Shokouhifar, A. Jalali
//Engineering applications of artificial intelligence. – 2017. –
Vol. 60. – P. 16–25. DOI: 10.1016/j.engappai.2017.01.007
10. Toz G. A Fuzzy Image Clustering Method Based on an Improved
Backtracking Search Optimization Algorithm with an
Inertia Weight Parameter / G. Toz, İ. Yücedağ, P. Erdoğmuş //
Journal of King Saud University–Computer and Information
Sciences. – 2018. In press. DOI: 10.1016/j.jksuci.2018.02.011
11. Izakian H. Fuzzy clustering of time series data using dynamic
time warping distance / H. Izakian, W. Pedrycz, I. Jamal // Engineering
Applications of Artificial Intelligence. – 2015. – Vol.
39. – P. 235–244. DOI: 10.1016/j.engappai.2014.12.015
12. Chen, S. Robust image segmentation using FCM with spatial
constraints based on new kernel-induced distance measure /
S. Chen, D. Zhang //IEEE Transactions on Systems, Man, and
Cybernetics, Part B (Cybernetics). – 2004. – Vol. 34, № 4. –
P. 1907–1916. DOI: 10.1109/TSMCB.2004.831165
13. Heidarzade A. Supplier selection using a clustering method
based on a new distance for interval type-2 fuzzy sets: A case
study / A. Heidarzade, I. Mahdavi, N. Mahdavi-Amiri // Applied
Soft Computing. – 2016. – Vol. 38. – P. 213–231. DOI:
10.1016/j.asoc.2015.09.029
14. Ye J. Clustering methods using distance-based similarity
measures of single-valued neutrosophic sets / J. Ye // Journal
of Intelligent Systems. – 2014. – Vol. 23, № 4. – P. 379–389.
DOI: 10.1515/jisys-2013-0091






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