Implementation of Minkowski-Chebyshev Distance in Fuzzy Subtractive Clustering

Annisa Eka Haryati; Sugiyarto Surono; Suparman Suparman

doi:10.20885/EKSAKTA.vol2.iss2.art1

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April 19, 2021

Accepted

June 11, 2021

Published

June 23, 2021

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Abstract

Clustering is a method of the grouping which is done by looking at the similarities between data in a data set. Fuzzy clustering is a clustering method that uses fuzzy set membership values as the basis for grouping data. Fuzzy Subtractive Clutering (FSC) is a fuzzy clustering method where the number of clusters to be formed is unknown. The concept of FSC is to determine the highest data density and the data with the most number of neighbors will be selected as the center of the cluster. Thus, the size of the proximity or distance between points is needed to determine the members of each cluster. The distance used in this study is a combination of the Minkowski and Chebyshev distances. The number of clusters formed will be evaluated using the Partition Coefficient (PC) value where the highest PC value indicates the best number of clusters. The results obtained indicate that the best clusters are three clusters with a PC value of 0.7422

Keywords

Clustering Fuzzy clustering Fuzzy subtractive clustering

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How to Cite

Haryati, A. E., Surono, S., & Suparman, S. (2021). Implementation of Minkowski-Chebyshev Distance in Fuzzy Subtractive Clustering. EKSAKTA: Journal of Sciences and Data Analysis, 2(2), 82–87. https://doi.org/10.20885/EKSAKTA.vol2.iss2.art1

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References

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S. Surono and R. D. A. Putri, Optimization of fuzzy c-means clustering algorithm with combination of minkowski and chebyshev distance using principal component analysis, Int. J. Fuzzy Syst., (2020) .
J. C. Bezdek, Pattern recognition with fuzzy objective function algorithms. New York: Plenum Press, 1981.
S. Kusumadewi and H. Purnomo, Aplikasi logika fuzzy untuk pendukung keputusan. Yogyakarta: Graha Ilmu, 2010.
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P. Noviyanti, Fuzzy c-Means Combination of Minkowski and Chebyshev Based for Categorical Data Clustering. Yogyakarta: Universitas Ahmad Dahlan, 2018.
N. Azizah, D. Yuniarti, and R. Goejantoro, Penerapan Metode Fuzzy Subtractive Clustering (Studi Kasus: Pengelompokkan Kecamatan di Provinsi Kalimantan Timur Berdasarkan Luas Daerah dan Jumlah Penduduk Tahun 2015), J. EKSPONENSIAL, 9 (2) (2018) 197–206.
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References

K. M. Bataineh, M. Naji, and M. Saqer, A comparison study between various fuzzy clustering algorithms, Jordan J. Mech. Ind. Eng., 5 (4) (2011) 335–343.

A. C. Rencher and W. F. Christensen, Methods of Multivariate Analysis. Wiley, 2012.

R. Sharma and K. Verma, Fuzzy shared nearest neighbor clustering, Int. J. Fuzzy Syst., 21 (8) (2019) 2667–2678.

J. S. R. Jang, C. T. Sun, and E. Mizutani, Neuro-Fuzzy and Soft Computing-A Computational Approach to Learning and Machine Intelligence [Book Review], IEEE Trans. Automat. Contr., 42 (10) (1997) 1482–1484.

K. Benmouiza and A. Cheknane, Clustered ANFIS network using fuzzy c-means, subtractive clustering, and grid partitioning for hourly solar radiation forecasting, Theor. Appl. Climatol., 137 (1–2) (2019) 31–43.

S. Zeng, S. M. Chen, and M. O. Teng, Fuzzy forecasting based on linear combinations of independent variables, subtractive clustering algorithm and artificial bee colony algorithm, Inf. Sci. (Ny)., 484 (2019) 350–366.

M. Ghane’i Ostad, H. Vahdat Nejad, and M. Abdolrazzagh Nezhad, Detecting overlapping communities in LBSNs by fuzzy subtractive clustering, Soc. Netw. Anal. Min., 8 (1) (2018) 1–11.

R. S. Kamath and R. K. Kamat, Earthquake magnitude prediction for andaman-nicobar Islands: adaptive neuro fuzzy modeling with fuzzy subtractive clustering approach, J. Chem. Pharm. Sci., 10 (3) (2017) 1228–1233.

T. Sonamani Singh, P. Verma, and R. D. S. Yadava, Fuzzy subtractive clustering for polymer data mining for saw sensor array based electronic nose, Adv. Intell. Syst. Comput., 546 (2017) 245–253.

H. Salah, M. Nemissi, H. Seridi, and H. Akdag, Subtractive Clustering and Particle Swarm Optimization Based Fuzzy Classifier, Int. J. Fuzzy Syst. Appl., 8 (3) (2019) 108–122.

X. Zhao and G. Yang, An entropy-based online multi-model identification algorithm and generalized predictive control, J. Intell. Fuzzy Syst., 32 (3) (2017) 2339–2349.

S. K. Chandar, Stock market prediction using subtractive clustering for a neuro fuzzy hybrid approach, Cluster Comput., 22 (s6) (2019) 13159–13166.

I. Sangadji, Y. Arvio, and Indrianto, Dynamic segmentation of behavior patterns based on quantity value movement using fuzzy subtractive clustering method, J. Phys. Conf. Ser., 974 (1) (2018) 0–7.

O. Rodrigues, Combining minkowski and cheyshev: new distance proposal and survey of distance metrics using k-nearest neighbours classifier, Pattern Recognit. Lett., 110 (2018) 66–71.

S. Surono and R. D. A. Putri, Optimization of fuzzy c-means clustering algorithm with combination of minkowski and chebyshev distance using principal component analysis, Int. J. Fuzzy Syst., (2020) .

J. C. Bezdek, Pattern recognition with fuzzy objective function algorithms. New York: Plenum Press, 1981.

S. Kusumadewi and H. Purnomo, Aplikasi logika fuzzy untuk pendukung keputusan. Yogyakarta: Graha Ilmu, 2010.

K. Rezaei and H. Rezaei, New distance and similarity measures for hesitant fuzzy soft sets, 16 (6) (2019) 159–176.

P. Noviyanti, Fuzzy c-Means Combination of Minkowski and Chebyshev Based for Categorical Data Clustering. Yogyakarta: Universitas Ahmad Dahlan, 2018.

N. Azizah, D. Yuniarti, and R. Goejantoro, Penerapan Metode Fuzzy Subtractive Clustering (Studi Kasus: Pengelompokkan Kecamatan di Provinsi Kalimantan Timur Berdasarkan Luas Daerah dan Jumlah Penduduk Tahun 2015), J. EKSPONENSIAL, 9 (2) (2018) 197–206.

V. Utomo and D. Marutho, Measuring hybrid sc-fcm clustering with cluster validity index, 2018 Int. Semin. Res. Inf. Technol. Intell. Syst. ISRITI 2018, (C) (2018) 322–326

Implementation of Minkowski-Chebyshev Distance in Fuzzy Subtractive Clustering

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