Variance-k-means++: A deterministic centroid initialization method based on variance for enhanced clustering stability

Abstract

K-means++ is developed to improve the performance of k-means when choosing a starting centroid. However, both algorithms in clustering still select an initial centroid randomly. Randomly selecting initial centroids has the potential to produce unstable clusters. This paper proposes a deterministic centroid initialization method called variance-k-means++, which utilizes statistical properties—mean and variance—to generate pseudo-centroids and derive initial centroids. The method aims to improve clustering stability and reduce the number of iterations. For the initial study, we used low-dimensional data to conduct the experiment series. Then, we employed two baseline methods for benchmarking, k-means and k-means++. The results show that variance-k-means++ outperformed the baseline method on average. Evaluating in Davies-Bouldin Index (DBI) and convergence analysis, we obtained DBI values at 0.756 and 0,771 for vertical and horizontal variance k-means++ with Iris dataset. At the same time, baseline methods have 0.802 and 0.830 for k-means++ and k-means, respectively. In convergence analysis, the results are 5.158 for vertical and 5.474 for horizontal, while baseline methods are 9.000 and 8.842. The primary contribution of this study lies in its achievement of minimizing the number of iterations while enhancing cluster stability.