K-means and fuzzy c-means algorithm comparison on regency/city grouping in Central Java Province


Ummu Wachidatul Latifah, Sugiyarto - Surono, Suparman suparman


The Human Development Index (HDI) is very important in measuring the country's success as an effort to build the quality of life of people in a region, including Indonesia. The government needs to make groupings based on the needs of a city/district. To facilitate data grouping based on the similarity of existing characteristics, it is necessary to have a data grouping method, namely the clustering technique. There are several algorithms that are often used in clustering techniques, namely K-Means and Fuzzy C-Means. Each algorithm has advantages and disadvantages. Therefore, in this research, the comparison of the best clustering algorithms will be discussed. The purpose of this research is to compare the K-Means and Fuzzy C-Means algorithms in the grouping of Regencies/Cities in Central Java Province in 2021 based on the Human Development Index (IPM) indicator. The method used is descriptive qualitative. The data used is obtained from the Central Java Statistics Agency, which is in the form of the Central Java Province HDI indicator in 2021 which consists of 35 Regency/City members and has 4 variables, namely Life Expectancy (AHH) (X1), Expectation of School Years (HLS) (X2), Average Length of School (RLS) (X3) and Expenditure Per Capita (X4). The results showed that after a comparative analysis with the standard deviation ratio method, the FCM clustering method was better than the K-Means method. The value of the FCM standard deviation ratio is 0.460093 and the K-Means standard deviation ratio is 0.473601.


K-Means; Fuzzy C-Means; Clustering

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Agustini, F. (2017). Implementasi algoritma fuzzy c-means studi kasus. Jurnal Ilmu Pengetahuan Dan Teknologi Komputer, 3(1), 127–132.

BPS Jateng. (2021). Indeks pembangunan manusia (metode baru) 2019-2021. https://jateng.bps.go.id/indicator/26/83/1/indeks-pembangunan-manusia-metode-baru-.html

Bunkers, M. J., Miller, J. R., & DeGaetano, A. T. (1996). Definition of climate regions in the northern plains using an objective cluster modification technique. Journal of Climate, 9(1). https://doi.org/10.1175/1520-0442(1996)009<0130:DOCRIT>2.0.CO;2

Ghazal, T. M., Hussain, M. Z., Said, R. A., Nadeem, A., Hasan, M. K., Ahmad, M., Khan, M. A., & Naseem, M. T. (2021). Performances of k-means clustering algorithm with different distance metrics. Intelligent Automation and Soft Computing, 30(2), 735–742. https://doi.org/10.32604/iasc.2021.019067

Haqiqi, B. N., & Kurniawan, R. (2015). Analisis perbandingan metode fuzzy c-means dan subtractive fuzzy c-means. Media Statistika, 8(2), 59–67. https://doi.org/10.14710/medstat.8.2.59-67

Hassan, A. A. hussian, Shah, W. M., Othman, M. F. I., & Hassan, H. A. H. (2020). Evaluate the performance of k-means and the fuzzy c-means algorithms to formation balanced clusters in wireless sensor networks. International Journal of Electrical and Computer Engineering, 10(2), 1515–1523. https://doi.org/10.11591/ijece.v10i2.pp1515-1523

Irawan, J., Handayani, A. A. A. T., & Zohri, L. H. N. (2021). Operasionalisasi ibm spss 21 untuk meningkatkan kemampuan dan keterampilan olah data penelitian mahasiswa. Jurnal Pengabdian Magister Pendidikan IPA, 4(2). https://doi.org/10.29303/jpmpi.v4i2.660

J. Mac Queen. (1967). Some methods for classification and analysis of multivariate observations. https://doi.org/10.1007/s11665-016-2173-6

Kirana, I. O., Nasution, Z. M., & Wanto, A. (2019). Proyeksi indeks pembangunan manusia di indonesia menggunakan metode statistical parabolic dalam menyongsong revolusi industri 4.0. Jurnal Pendidikan Teknologi Dan Kejuruan, 16(2), 202. https://doi.org/10.23887/jptk-undiksha.v16i2.18178

Kolay, S., Ray, K. S., & Mondal, A. C. (2017). K+ means: An enhancement over k-means clustering algorithm. In arXiv.

Le, T., & Altman, T. (2011). A new initialization method for the fuzzy c-means algorithm using fuzzy subtractive clustering. Proc. Intl’Conf. on Information and Knowledge Engineering, Las Vegas USA, 144–150.

Ningrat, D. R., Maruddani, D. A. I., & Wuryandari, T. (2016). Analisis cluster dengan algoritma k-means dan fuzzy c-means clustering untuk pengelompokan data obligasi korporasi. None, 5(4), 641–650.

Oktarina, C., Notodiputro, K. A., & Indahwati, I. (2020). Comparison of k-means clustering method and k-medoids on twitter data. Indonesian Journal of Statistics and Its Applications, 4(1), 189–202. https://doi.org/10.29244/ijsa.v4i1.599

Purba, W., Tamba, S., & Saragih, J. (2018). The effect of mining data k-means clustering toward students profile model drop out potential. Journal of Physics: Conference Series, 1007(1). https://doi.org/10.1088/1742-6596/1007/1/012049

Rahakbauw, D. L., Ilwaru, V. Y. I., & Hahury, M. H. (2017). Implementasi fuzzy c-means clustering dalam implementation of fuzzy c-means clustering in. Jurnal Ilmu Matematika Dan Terapan, 11, 1–12.

Ramadhan, A., Mustakim, & Handinata, R. (2019). Implementasi algoritma fuzzy c means dan moora untuk pengelompokan dan penentuan wilayah penanggulangan bencana banjir.

Sutoyo, M. N., & Sumpala, A. T. (2016). Penerapan fuzzy c-means untuk deteksi dini kemampuan penalaran matematis. Scientific Journal of Informatics, 2(2), 129. https://doi.org/10.15294/sji.v2i2.5080

Syakur, M. A., Khotimah, B. K., Rochman, E. M. S., & Satoto, B. D. (2018). Integration k-means clustering method and elbow method for identification of the best customer profile cluster. IOP Conference Series: Materials Science and Engineering, 336(1), 0–6. https://doi.org/10.1088/1757-899X/336/1/012017

Utomo, W. (2021). The comparison of k-means and k-medoids algorithms for clustering the spread of the covid-19 outbreak in indonesia. ILKOM Jurnal Ilmiah, 13(1), 31–35. https://doi.org/10.33096/ilkom.v13i1.763.31-35

Wakhidah, N. (2010). Clustering menggunakan k-means algorithm. Jurnal Transformatika, 8(1), 33. https://doi.org/10.26623/transformatika.v8i1.45

Wiharto, W., & Suryani, E. (2020). The comparison of clustering algorithms k-means and fuzzy c-means for segmentation retinal blood vessels. Acta Informatica Medica, 28(1), 42–47. https://doi.org/10.5455/AIM.2020.28.42-47

Winarta, A., & Kurniawan, W. J. (2021). Optimasi cluster k-means menggunakan metode elbow pada data pengguna narkoba dengan pemrograman python. Jurnal Teknik Informatika Kaputama (JTIK), 5(1), 113–119.

Windarto, A. P., Hasan Siregar, M. N., Suharso, W., Fachri, B., Supriyatna, A., Carolina, I., Efendi, Y., & Toresa, D. (2019). Analysis of the k-means algorithm on clean water customers based on the province. Journal of Physics: Conference Series, 1255(1). https://doi.org/10.1088/1742-6596/1255/1/012001

Zhou, K., & Yang, S. (2020). Effect of cluster size distribution on clustering: A comparative study of k-means and fuzzy c-means clustering. Pattern Analysis and Applications, 23(1), 455–466. https://doi.org/10.1007/s10044-019-00783-6

DOI: https://doi.org/10.24042/djm.v5i2.12204

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