Ulfasari Rafflesia, Adhitya Ronnie Effendie, Devni Prima Sari, Dedi Rosadi
Clustering is a significant unsupervised categorization method that provides a fundamental component in data mining. It is acknowledged as a primary task in data analysis and has applications in various disciplines. Determining the optimal number of clusters is a crucial aspect of cluster analysis, often achieved through the use of cluster validity indices. Traditional internal validity indices use mean-based measures of mean tendency and dispersion, which are sensitive to outliers and non-normal data distributions. This study proposes an enhancement of internal cluster validity in the k-means algorithm by integrating robust statistical estimators—such as the median, trimmed mean, winsorized mean, Huber mean, and Minimum Covariance Determinant (MCD)—into the calculations of two classical indices, namely Fukuyama-Sugeno (FS) and Xie-Beni (XB). The proposed indices are used to determine the ideal number of clusters and improve the reliability of cluster evaluations in the presence of outliers. The evaluation was conducted on six benchmark datasets of varying complexity—namely Iris, Wine, Breast Cancer, Pima Indian Diabetes, Glass Identification, and Ecoli—as well as on a real-world dataset of daily COVID-19 cases across Indonesian provinces. The experimental results demonstrate that the MCD means consistently yields the lowest index values in most scenarios, particularly for the XB index and in high-dimensional or noisy datasets. The FS index also indicates strong performance by MCD and median estimators in several cases. In the COVID-19 dataset, both the FS and XB indices unanimously identified k = 3 as the optimal number of clusters, revealing meaningful geographic and epidemiological patterns. These findings affirm that the use of robust central estimators, particularly the MCD mean, enhances the stability and accuracy of cluster validity evaluations in complex data environments and opens new directions for developing adaptive and resilient clustering quality measures. © (2026), (International Association of Engineers), All Rights Reserved.
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Bengkulu, Indonesia; Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Yogyakarta, Indonesia; Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Padang, Padang, Indonesia; Statistics RnD, Yogyakarta, Indonesia
