Application of Cluster Analysis Using Agglomerative Method

Muhammad Rais Ridwan; Heri Retnawati

doi:10.25217/numerical.v5i1.1538

Authors

Muhammad Rais Ridwan STKIP YPUP Makassar
Heri Retnawati Universitas Negeri Yogyakarta

DOI:

https://doi.org/10.25217/numerical.v5i1.1538

Keywords:

Cluster Analysis; Agglomerative Method; Average Linkage Method; Ward Method; Standard Deviation Average Ratio

Abstract

Improving the quality of human resources is the main supporting factor in increasing national productivity in various fields and development sectors. The government's productive investment activities that spur the nation's competitiveness in the global era prioritize Indonesia's education development. This study aims to cluster provinces in Indonesia based on educational indicators using the Agglomerative method consisting of the Average Linkage and Ward methods. Data collection is based on documentation techniques obtained from Statistics Indonesia in 2018. Data analysis used hierarchical cluster analysis consisting of data standardization, determining the size of the similarity or dissimilarity between data, the clustering process with a distance matrix, and seeing the characteristics of the cluster results formed. The second clustering method is by doing the initial grouping and determining the excellent cluster based on the average standard deviation ratio to the standard deviation between groups. Clustering results show the Ward method with the number of collections as many as 4 clusters and produces a ratio with a value of 0.01 smaller than the Average Linkage method. It shows that the cluster analysis method using the Ward method has better group accuracy quality than the Average Linkage method.

References

Badan Pusat Statistik, Potret Pendidikan Indonesia Statistik Pendidikan 2018. Indonesia: Badan Pusat Statistik, 2018.

Y. Kartakusumah, “Analisis Faktor yang Mempengaruhi Angka Partisipasi Kasar (APK) pada Pendidikan Anak Usia Dini Taman Kanak-Kanak,” S2 Thesis, 2018.

N. A. Lestari and A. Adji, “Analisis faktor-faktor yang mempengaruhi angka partisipasi sekolah serta angka putus sekolah tingkat Sekolah Dasar dan Sekolah Menengah Pertama,” S2 Thesis, 2014.

H. R. Rahmatika, “Faktor-faktor yang mempengaruhi Angka Partisipasi Kasar (APK) jenjang pendidikan Sekolah Menengah Pertama pada masyarakat pesisir di Kecamatan Sarang Kabupaten Rembang tahun 2015,” S1 Thesis, 2016.

S. Habibah, Y. P. Putra, and Y. M. Putra, “Faktor-Faktor yang mempengaruhi angka partisipasi perguruan tinggi pada 32 provinsi di Indonesia tahun 2013-2016,” J. Anggar. dan Keuang. Negara Indones., pp. 15–34, 2019.

R. A. Johnson and D. W. Winchern, Applied multivariate statistical analysis. New Jersey: Prentice Hall Inc., 1982.

B. Everitt, Cluster analysis. London: Heinemann Education Books, 1974.

L. Rahmawati, “Analisis kelompok dengan menggunakan metode hierarki untuk pengelompokan Kabupaten/Kota di Jawa Timur berdasarkan indikator kesehatan,” S1 Thesis, 2013.

S. Yulianto and K. H. Hidayatullah, “Analisis klaster untuk pengelompokan Kabupaten/Kota di Provinsi Jawa Tengah berdasarkan indikator kesejahteraan rakyat,” J. Stat., pp. 56–63, 2014.

A. N. Fathia, “Analisis klaster kecamatan di kabupaten Semarang berdasarkan potensi desa menggunakan metode ward dan single linkage,” J. Gaussian, pp. 801–810, 2016.

Sukmawati, “Analisis cluster dengan metode hierarki untuk pengelompokkan Kabupaten/Kota di Provinsi Sulawesi Selatan berdasarkan indikator makro ekonomi,” S1 Thesis, 2017.

W. A. Talakua, Z. A. Leleury, and A. W. Taluta, “Analisis cluster dengan menggunakan metode k-means untuk pengelompokkan Kabupaten/Kota di provinsi maluku berdasarkan indikator indeks pembangunan manusia tahun 2014,” J. Ilmu Mat. dan Terap., pp. 119–128, 2017.

R. Silvi, “Analisis cluster dengan data outlier menggunakan centroid linkage dan k-means clustering untuk pengelompokan indikator HIV/AIDS di Indonesia,” MANTIK J. Mat., pp. 22–31, 2018.

M. Paramadina, Sudarmin, and M. K. Aidid, “Perbandingan Analisis Cluster Metode Average Linkage dan Metode Ward (Kasus: IPM Provinsi Sulawesi Selatan),” VARIANSI J. Stat. Its Appl. Teach. Res., pp. 22–31, 2019.

S. Laeli, “Analisis cluster dengan average linkage method dan ward’s method untuk data responden nasabah asuransi jiwa unit link,” S1 Thesis, 2016.

J. E. Jackson, A user’s guide to principal components. New York: John Wiley & Sons Inc., 1991.

A. Farahani, H. Rahiminezhed, A. L. Same, and K. Immannezhed, “A Comparison of Partial Least Square (PLS) and Ordinary Least Square (OLS) regressions in predicting of couples mental health based on their communicational patterns,” Procedia Soc. Behav. Sci., pp. 1459–1463, 2010.

I. Ghozali, Analisis multivariate dengan program SPSS Edisi Ke 4. Semarang: Badan Penerbit Universitas Diponegoro, 2006.

I. Ghozali, Aplikasi analisis multivariate dengan program SPSS. Semarang: Badan Penerbit Universitas Diponegoro, 2011.

D. N. Gujarati and D. C. Porter, Dasar–dasar ekonometrika. Jakarta: Salemba Empat, 2012.

T. P. Ryan, Modern regression methods. New York: John Wiley & Sons, 1997.

T. Naes and H. Martens, “Comparison of prediction methods for multicollinearity data,” Commun. Stat. Comput., pp. 545–576, 1985.

S. Santoso, Buku latihan SPSS statistik multivariat. Jakarta: PT Elex Media Komputindo, 2002.

D. Rachmatin, “Aplikasi metode-metode agglomerative dalam analisis klaster pada data tingkat polusi udara,” Infin. J. Ilm. Progr. Stud. Mat. STKIP Siliwangi Bandung, pp. 133–149, 2014.

R. A. Johnson and D. W. Winchern, Applied multivariate statistical analysis, Fifth Ed. New Jersey: Prentice Hall International Inc., 2002.

W. R. Dillon and M. Goldstein, Multivariate analysis. New York: John Wiley & Sons, 1984.

W. J. Bunkers, J. R. Miller, and A. T. DeGaetano, “Definition of climate regions in the nothern plains using an objective cluster modification technique,” J. Clim., pp. 130–146, 1996.

H. T. Clifford and W. Stepenson, An Introduction to Numerical Classification. New York: Academic Press, 1975.

C. J. Krebs, Ecological Methodology. New York: Harper and Row Publishers, 1989.

J. F. Hair, R. E. Anderson, R. Thatam, and W. Black, Multivariate data analysis with readings. New Jersey: Pearson New International Edition, 1995.

M. Kent and P. Coker, Vegetation description and analysis: A Practical approach. London: CRC Press & Belhaven Press, 1997.