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The Application Of K – Harmonic Means Method In District/City Grouping

PENERAPAN METODE K – HARMONIC MEANS DALAM PENGELOMPOKAN KABUPATEN/KOTA (Studi Kasus: Kemiskinan di Pulau Kalimantan Tahun 2020)

Jurnal Matematika, Statistika dan Komputasi · Vol. 19 No. 1 (2022) · pp. 51–64

DOI
10.20956/j.v19i1.21116
ISSN
2614-8811, 1858-1382
Published
2022-09-07
Publisher
Department of Mathematics, Hasanuddin University
Language
en
License
creativecommons.org/licenses/by/4.0

Abstract

English

Poverty is one of the problems that faced by every country in the world, especially in developing countries, one of them is Indonesia. Poverty alleviation that is currently planned is no longer uniform, but it is necessary to pay attention to the condition of each dimension causing poverty in an area, so it is necessary to group districts/cities on the Kalimantan Island based on poverty. Cluster analysis is classifying the data (objects) only based on the information discovered in the data that describes the objects and the relations between them. The method used in this research is K-Harmonic Means method. K-Harmonic Means is a non-hierarchical clustering algorithm that uses the average harmonic distance from each data point to the cluster center. This study aims to classify the District/City in Kalimantan Island based on poverty indicators and obtain the silhouette coefficient value from the optimal cluster analysis. Based on the results of the analysis of the K-Harmonic Means method, the optimal number of clusters is 2 clusters with parameter (p) of 4. Cluster 1 consists of 11 Districts/Cities and Cluster 2 consists of 45 Districts/Cities. Silhouette coefficient value for data validation of District/City clustering results on Kalimantan Island using the K-Harmonic Means method, namely 2 clusters with parameter (p) of 4 is 0.323 which states that the resulting cluster structure in this grouping is a weak structure.

Bahasa Indonesia

Kemiskinan merupakan salah satu permasalahan yang dihadapi oleh setiap negara di dunia, terutama pada negara yang sedang berkembang, salah satunya adalah negara Indonesia. Pengentasan kemiskinan yang direncanakan saat ini tidak lagi bersifat seragam, namun perlu memperhatikan kondisi setiap dimensi penyebab kemiskinan suatu wilayah maka perlu dilakukan pengelompokan Kabupaten/Kota di Pulau Kalimantan berdasarkan kemiskinan. Analisis klaster adalah mengelompokkan data (objek) yang didasarkan hanya pada informasi yang ditemukan dalam data yang menggambarkan objek tersebut dan hubungan di antaranya. K-Harmonic Means adalah algoritma pengelompokan non-hierarki yang menggunakan rata-rata harmonik jarak dari setiap data ke pusat klaster. Penelitian ini bertujuan untuk mengelompokkan Kabupaten/Kota di Pulau Kalimantan berdasarkan indikator kemiskinan serta memperoleh nilai silhouette coefficient hasil analisis klaster optimal. Berdasarkan hasil analisis metode K-Harmonic Means didapatkan banyak klaster optimal yaitu 2 klaster dengan parameter (p) sebesar 4. Klaster 1 beranggotakan 11 Kabupaten/Kota dan klaster 2 beranggotakan 45 Kabupaten/Kota. Nilai silhouette coefficient untuk validasi data hasil klastering Kabupaten/Kota di Pulau Kalimantan menggunakan metode K-Harmonic Means, yaitu 2 klaster dengan parameter (p) sebesar 4 adalah 0,323 yang menyatakan bahwa struktur klaster yang dihasilkan pada pengelompokan ini adalah weak structure.

Keywords

Collaboration network of the authors

15 authors · 29 co-authorship links

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Co-authorOrganisationJoint articles
Memi Nor HayatiAffiliation unknown2
Syaripuddin SyaripuddinAffiliation unknown2
Hairi SeptiyanorAffiliation unknown1
Putri Sri AstutiAffiliation unknown1
Sifriyani SifriyaniAffiliation unknown1
Muhammad Danil PasarellaAffiliation unknown1
Wasono WasonoAffiliation unknown1
Shanaz TulzahrahAffiliation unknown1
Rara SuciatiAffiliation unknown1
Nur Annisa FitriAffiliation unknown1
M. FathurahmanAffiliation unknown1
Ardiman WiranataAffiliation unknown1

Affiliations come from OpenAlex; journal OAI-PMH metadata carries none. Authors without an OpenAlex ID are matched by name, which can merge or split people.

Metadata source: OAI-PMH (metadata jurnal) https://journal.unhas.ac.id/index.php/jmsk/oai, first harvested 5 Nov 2026, last seen 5 Nov 2026.
Original metadata (oai_dc) 
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	<dc:title xml:lang="en">The Application Of K – Harmonic Means Method In District/City Grouping</dc:title>
	<dc:title xml:lang="id">PENERAPAN METODE K – HARMONIC MEANS DALAM PENGELOMPOKAN KABUPATEN/KOTA  (Studi Kasus: Kemiskinan di Pulau Kalimantan Tahun 2020)</dc:title>
	<dc:creator xml:lang="en">Yunistya, Dwi Indra </dc:creator>
	<dc:creator xml:lang="en">Goejantoro, Rito </dc:creator>
	<dc:creator xml:lang="en">Amijaya, Fidia Deny Tisna </dc:creator>
	<dc:subject xml:lang="en">Poverty</dc:subject>
	<dc:subject xml:lang="en">K-Harmonic Means</dc:subject>
	<dc:subject xml:lang="en">Silhouette Coefficient</dc:subject>
	<dc:subject xml:lang="id">Kemiskinan</dc:subject>
	<dc:subject xml:lang="id">K-Harmonic Means</dc:subject>
	<dc:subject xml:lang="id">Silhouette Coefficient</dc:subject>
	<dc:description xml:lang="en">Poverty is one of the problems that faced by every country in the world, especially in developing countries, one of them is Indonesia. Poverty alleviation that is currently planned is no longer uniform, but it is necessary to pay attention to the condition of each dimension causing poverty in an area, so it is necessary to group districts/cities on the Kalimantan Island based on poverty. Cluster analysis is classifying the data (objects) only based on the information discovered in the data that describes the objects and the relations between them. The method used in this research is K-Harmonic Means method. K-Harmonic Means is a non-hierarchical clustering algorithm that uses the average harmonic distance from each data point to the cluster center. This study aims to classify the District/City in Kalimantan Island based on poverty indicators and obtain the silhouette coefficient value from the optimal cluster analysis. Based on the results of the analysis of the K-Harmonic Means method, the optimal number of clusters is 2 clusters with parameter (p) of 4. Cluster 1 consists of 11 Districts/Cities and Cluster 2 consists of 45 Districts/Cities. Silhouette coefficient value for data validation of District/City clustering results on Kalimantan Island using the K-Harmonic Means method, namely 2 clusters with parameter (p) of 4 is 0.323 which states that the resulting cluster structure in this grouping is a weak structure.
 </dc:description>
	<dc:description xml:lang="id">Kemiskinan merupakan salah satu permasalahan yang dihadapi oleh setiap negara di dunia, terutama pada negara yang sedang berkembang, salah satunya adalah negara Indonesia. Pengentasan kemiskinan yang direncanakan saat ini tidak lagi bersifat seragam, namun perlu memperhatikan kondisi setiap dimensi penyebab kemiskinan suatu wilayah maka perlu dilakukan pengelompokan Kabupaten/Kota di Pulau Kalimantan berdasarkan kemiskinan. Analisis klaster adalah mengelompokkan data (objek) yang didasarkan hanya pada informasi yang ditemukan dalam data yang menggambarkan objek tersebut dan hubungan di antaranya. K-Harmonic Means adalah algoritma pengelompokan non-hierarki yang menggunakan rata-rata harmonik jarak dari setiap data ke pusat klaster. Penelitian ini bertujuan untuk mengelompokkan Kabupaten/Kota di Pulau Kalimantan berdasarkan indikator kemiskinan serta memperoleh nilai silhouette coefficient hasil analisis klaster optimal. Berdasarkan hasil analisis metode K-Harmonic Means didapatkan banyak klaster optimal yaitu 2 klaster dengan parameter (p) sebesar 4. Klaster 1 beranggotakan 11 Kabupaten/Kota dan klaster 2 beranggotakan 45 Kabupaten/Kota. Nilai silhouette coefficient untuk validasi data hasil klastering Kabupaten/Kota di Pulau Kalimantan menggunakan metode K-Harmonic Means, yaitu 2 klaster dengan parameter (p) sebesar 4 adalah 0,323 yang menyatakan bahwa struktur klaster yang dihasilkan pada pengelompokan ini adalah weak structure.</dc:description>
	<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
	<dc:date>2022-09-07</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
	<dc:type>info:eu-repo/semantics/publishedVersion</dc:type>
	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://journal.unhas.ac.id/index.php/jmsk/article/view/21116</dc:identifier>
	<dc:identifier>10.20956/j.v19i1.21116</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 19 No. 1 (2022): SEPTEMBER, 2022; 51-64</dc:source>
	<dc:source>2614-8811</dc:source>
	<dc:source>1858-1382</dc:source>
	<dc:language>en</dc:language>
	<dc:relation>https://journal.unhas.ac.id/index.php/jmsk/article/view/21116/8610</dc:relation>
	<dc:relation>10.20956/j.v19i1.21116.g8610</dc:relation>
	<dc:rights xml:lang="en">Copyright (c) 2022 Author and publisher</dc:rights>
	<dc:rights xml:lang="en">https://creativecommons.org/licenses/by/4.0</dc:rights>
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