K-Means Optimization with Kernel Gaussian Radial Basis Function in C# (Contemporary Mathematics, 2025)
K-Means is an iterative clustering technique that relies on centroids to organize data into distinct clusters until convergence is achieved. Despite its effectiveness, K-Means struggles with non-linearly separable data and is sensitive to initial centroid selection, as data points are assigned to clusters based on proximity to centroids. Moreover, the algorithm's performance hinges on the predetermined number of clusters (K), with suboptimal K selection leading to inferior clustering outcomes. To address these limitations, this study proposes the use of Kernel K-Means, employing the Kernel Gaussian Radial Basis Function to handle non-linearly separable datasets in high-dimensional feature spaces. The Elbow method is employed to determine the optimal K value, and the Sum of Squares Error (SSE) method aids in identifying initial centroids. Subsequent analysis of clustering results utilizes the Davies Bouldin Index and Silhouette coefficient techniques. Implementation is conducted using the C# programming language to expand machine learning applications across different programming languages. Our findings indicate that Kernel K-Means consistently outperforms traditional K-Means, with the Silhouette coefficient's effectiveness varying depending on dataset characteristics and size.
Keywords: elbow; K-Means; Kernel Gaussian; Sum of Squares Error (SSE)