Analisis Metode Elbow SSE, Silhouette Score, dan Jaccard Stability dalam Pemilihan Jumlah Klaster Data yang Optimal
-
Budi Hartono
*
Universitas Stikubank, Semarang,
Indonesia
- Veronica Lusiana Universitas Stikubank, Semarang, Indonesia (*) Corresponding Author
Abstract
This study discusses the selection of the optimal number of clusters (K) in the K-Means algorithm by utilizing a combination of the Elbow method with the SSE (Sum of Squared Errors) and Silhouette Score metrics. The main problem is that the optimal K value is unknown. Choosing K that is too small can combine different patterns (under-clustering), and choosing K that is too large can break the same pattern into several clusters (over-clustering). The experiment used two-dimensional test data with variations in the number of data 20, 30, 40, 50, and 60. K-Means was run in the range of K = 2 to K = 8, then the SSE value was calculated to form the Elbow curve and the average Silhouette value to evaluate the quality of the cluster. This study added a cluster stability test using the Jaccard Stability value. The highest Silhouette value of 0.4619 was obtained from the data 20 for K = 2. The highest Jaccard stability value of 0.9507 was obtained from 60 data sets for K = 2. The experimental results show that the Elbow method, Silhouette value, and Jaccard stability can be used complementarily in determining the optimal K. In some test data, both metrics produce consistent K recommendations, while in certain test data, Elbow can provide several candidates, so that validation using the Silhouette value is needed to select the optimal K.
Downloads
References
Ashari, I. F., Nugroho, E. D., Baraku, R., Yanda, I. N., & Liwardana, R. (2023). Analysis of Elbow, Silhouette, Davies-Bouldin, Calinski-Harabasz, and Rand-Index Evaluation on K-Means Algorithm for Classifying Flood-Affected Areas in Jakarta. Journal of Applied Informatics and Computing, 7(1), 95–103. https://doi.org/10.30871/jaic.v7i1.4947
Chrisamudra, R. W., & Abdurrahman, S. (2025). Pemanfaatan Algoritma K-Means untuk Klastering Spasial Beban Kasus Pneumonia pada Kelompok Balita di Wilayah dengan Kepadatan Populasi Tinggi. TIN: Terapan Informatika Nusantara, 6(6), 761–768. https://doi.org/10.47065/tin.v6i6.8598
Diantika, M. W., Rusgiyono, A., & Saputra, B. A. (2025). Perbandingan Metode Optimasi Silhouette, Elbow, Dan Gap Statistics Dalam Menentukan Nilai K Terbaik Pada Analisis K-Means Clustering. Jurnal Gaussian, 14(2), 335–344. https://doi.org/10.14710/j.gauss.14.2.335-344
Guntara, M., & Lutfi, N. (2023). Optimasi Cacah Klaster pada Klasterisasi dengan Algoritma KMeans Menggunakan Silhouette Coeficient dan Elbow Method. Jurnal Teknologi Informasi, 2(1), 43–52. https://doi.org/10.26798/juti.v2i1.944
Han, J., Pei, J., & Tong, H. (2023). Data Mining: Concepts and Techniques. Morgan Kaufmann.
Hartono, B., Eniyati, S., & Hadiono, K. (2023). Perbandingan Metode Perhitungan Jarak pada Nilai Centroid dan Pengelompokan Data Menggunakan K-Means Clustering. Jurnal Sistem Komputer Dan Informatika (JSON), 4(3), 503−509. https://doi.org/10.30865/json.v4i3.6021
Hasan, Y. (2024). Pengukuran Silhouette Score dan Davies-Bouldin Index pada Hasil Cluster K-Means dan DBSCAN. KAKIFIKOM, 6(1), 60–74. https://ejournal.ust.ac.id/index.php/KAKIFIKOM/article/view/3938
Juanita, S., & Cahyono, R. D. (2024). K-Means Clustering With Comparison Of Elbow And Silhouette Methods For Medicines Clustering Based On User Reviews. Jurnal Teknik Informatika (Jutif), 5(1), 283–289. https://doi.org/10.52436/1.jutif.2024.5.1.1349
Kurniawan, Y. I., Anugrah, P. R., Sugihono, R. M., Abimanyu, F. A., & Afuan, L. (2023). Pengelompokan Prioritas Negara Yang Membutuhkan Bantuan Menggunakan Clustering K-Means dengan Elbow Dan Silhouette. Jurnal Pendidikan dan Teknologi Indonesia, 3(10), 455–463. https://doi.org/10.52436/1.jpti.343
Kuswardana, D. A., Prasetya, D. A., Trimono, T., & Diyasa, I. G. S. M. (2025). Comparison of Elbow and Silhouette Methods in Optimizing K-Prototype Clustering for Customer Transactions. Jurnal Ilmiah Edutic : Pendidikan Dan Informatika, 12(1), 43–48. https://doi.org/10.21107/edutic.v12i1.29744
Lusiana, V., Amin, I. H. A., & Hartono, B. (2024). Pengaruh Ekstraksi Fitur Tekstur Pada Hasil Klastering Data Citra Buah Menggunakan Metode K-Means Cluster. Journal of Computer System and Informatics (JoSYC), 5(4), 933–941. https://doi.org/10.47065/josyc.v5i4.5770
Maori, N. A., & Evanita, E. (2023). Metode Elbow dalam Optimasi Jumlah Cluster pada K-Means Clustering. Simetris: Jurnal Teknik Mesin, Elektro dan Ilmu Komputer, 14(2), 277–288. https://doi.org/10.24176/simet.v14i2.9630
Rahmawati, T., Wilandari, Y., & Kartikasari, P. (2024). Analisis Perbandingan Silhouette Coefficient Dan Metode Elbow Pada Pengelompokkan Provinsi Di Indonesia Berdasarkan Indikator Ipm Dengan K-Medoids. Jurnal Gaussian, 13(1), 13–24. https://doi.org/10.14710/j.gauss.13.1.13-24
Ritonga, P. K., & Hasibuan, M. S. (2025). Analisis Perbandingan Silhouette dengan Elbow pada Algoritma K-Means dan DBSCAN. METIK JURNAL, 9(1), 64–71. https://doi.org/10.47002/metik.v9i1.1027
Shi, C., Wei, B., Wei, S., Wang, W., Liu, H., & Liu, J. (2021). A quantitative discriminant method of elbow point for the optimal number of clusters in clustering algorithm. EURASIP Journal on Wireless Communications and Networking, 2021(1), 31. https://doi.org/10.1186/s13638-021-01910-w
Sholeh, M., & Aeni, K. (2023). Perbandingan Evaluasi Metode Davies Bouldin, Elbow dan Silhouette pada Model Clustering dengan Menggunakan Algoritma K-Means. STRING (Satuan Tulisan Riset dan Inovasi Teknologi), 8(1), 56–65. https://doi.org/10.30998/string.v8i1.16388
Shutaywi, M., & Kachouie, N. N. (2021). Silhouette Analysis for Performance Evaluation in Machine Learning with Applications to Clustering. Entropy, 23(6), 759. https://doi.org/10.3390/e23060759
Syahkur, M. R., Hartama, D., & Solikhun, S. (2024). Evaluasi Jumlah Cluster pada Algoritma K-Means++ Menggunakan Silhouette dan Elbow dengan Validasi Nilai DBI dalam Mengelompokkan Gizi Balita. JST (Jurnal Sains Dan Teknologi), 13(3), 487–496. https://doi.org/10.23887/jstundiksha.v13i3.86419
Tan, P.-N., Steinbach, M., & Kumar, V. (2019). Introduction to Data Mining. Pearson.
Vania, P., & Sari, B. N. (2023). Perbandingan Metode Elbow dan Silhouette untuk Penentuan Jumlah Klaster yang Optimal pada Clustering Produksi Padi menggunakan Algoritma K-Means. Jurnal Ilmiah Wahana Pendidikan, 9(21), 547–558. https://doi.org/10.5281/zenodo.10081332
Wicaksono, A. P., Widjaja, S., Nugroho, M. F., & Putri, C. P. (2024). Elbow and Silhouette Methods for K Value Analysis of Ticket Sales Grouping on K-Means. Sistemasi: Jurnal Sistem Informasi, 13(1), 28–38. https://doi.org/10.32520/stmsi.v13i1.2889
Bila bermanfaat silahkan share artikel ini
Berikan Komentar Anda terhadap artikel Analisis Metode Elbow SSE, Silhouette Score, dan Jaccard Stability dalam Pemilihan Jumlah Klaster Data yang Optimal
Pages: 1521-1532
Copyright (c) 2026 Budi Hartono, Veronica Lusiana
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under Creative Commons Attribution 4.0 International License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (Refer to The Effect of Open Access).
