Analisis Komparatif Jarak Euclidean, Manhattan, Canberra, Chebyshev, Cosine pada K-Means untuk Evaluasi Kepuasan Masyarakat
- Fakhri Fakhri Universitas Islam Negeri Sultan Syarif Kasim Riau, Pekanbaru, Indonesia
-
Iis afrianty
*
Universitas Islam Negeri Sultan Syarif Kasim Riau, Pekanbaru,
Indonesia
- Elvia Budianita Universitas Islam Negeri Sultan Syarif Kasim Riau, Pekanbaru, Indonesia
- Fadhilah Syafria Universitas Islam Negeri Sultan Syarif Kasim Riau, Pekanbaru, Indonesia
- Siska Kurnia Gusti Universitas Islam Negeri Sultan Syarif Kasim Riau, Pekanbaru, Indonesia
- Salmiyati Salmiyati Universitas Islam Negeri Sultan Syarif Kasim Riau, Pekanbaru, Indonesia (*) Corresponding Author
Abstract
The selection of distance metrics in the K-Means Clustering algorithm can affect the quality of clustering results, particularly on public satisfaction data measured using a Likert scale. This study aims to compare the performance of five distance metrics, namely Euclidean Distance, Manhattan Distance, Canberra Distance, Chebyshev Distance, and Cosine Similarity, in clustering the level of public satisfaction toward public services. The research data were obtained from 533 respondents who used the services of the Mal Pelayanan Publik (MPP) Pekanbaru through a questionnaire consisting of 23 questions based on the SERVQUAL dimensions and the Community Satisfaction Survey indicators in accordance with PERMEN PAN-RB Number 14 of 2017. After the data cleaning process, one duplicate record was removed, resulting in 532 respondent records used in the analysis stage. The number of clusters was determined using the Elbow Method, while cluster quality was evaluated using the Davies-Bouldin Index (DBI) and Silhouette Score. The results show that Manhattan Distance with k=2 produced the lowest DBI value of 0.8144, whereas Euclidean Distance with k=3 produced the highest Silhouette Score of 0.5088. The clustering results formed groups of respondents with different satisfaction levels, namely Dissatisfied, Satisfied, and Very Satisfied. This study contributes an evaluative comparison of five distance metrics in the K-Means algorithm using two evaluation approaches simultaneously, namely the Davies-Bouldin Index and Silhouette Score, on public satisfaction data based on a Likert scale. The results indicate that the performance of distance metrics may differ depending on the evaluation method used, therefore the selection of distance metrics should consider the characteristics of the data and the objectives of the analysis.The difference in evaluation results indicates that DBI and Silhouette Score assess clustering quality from different aspects. Based on the findings, Manhattan Distance and Euclidean Distance demonstrated better performance compared to other distance metrics on the dataset used, and can therefore be considered in the analysis of public satisfaction toward public services.
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Copyright (c) 2026 Fakhri Fakhri, Iis afrianty, Elvia Budianita, Fadhilah Syafria, Siska Kurnia Gusti, Salmiyati Salmiyati
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