Benchmarking Hybrid Trigonometric–RBF Kernels Against Classical KMeans for Structured Clustering

The accuracy of clustering algorithms is heavily impacted by the choice of kernel function and kernel function parameters. We propose a hybrid approach that combines trigonometric feature encodings and a classical (Gaussian) radial basis function (RBF) kernel inside a kernel KMeans algorithm. Experiments are done on both finance and health care contexts. A finance dataset with 8,950 samples each having 18 numerical features and a dataset in the health care context with 768 samples and 9 clinical biomarkers. Clustering quality is evaluated using three well-known quality metrics: Silhouette Score, Davies-Bouldin Index, and Calinski-Harabasz Index, while runtime is recorded. On the finance data, the proposed hybrid algorithm outperforms KMeans at k = 2 using the Silhouette Score (0.298 versus 0.242) and Davies-Bouldin Index (1.182 versus 1.560). On the health care data, the hybrid algorithm shows worse performance in comparison to KMeans at k = 2 using the Silhouette Score (0.745 versus 0.792). Additionally, the proposed algorithm shows numerical instability in terms of both quality metric performance and runtime across all k. Classical KMeans outperforms the hybrid kernel especially on the clinical biomarker normalized data. The presented results elaborate on the possibilities, challenges, and observed behaviour in the usage and performance of kernelized quantum-inspired kernels. The results indicate that the proposed hybrid algorithm does not universally outperform classical kernel kMeans, but that it depends more on the similarity of the underlying data set.