K-MEANS Clustering Algorithm and Its Enhancement Using PSO and QPSO Algorithms

K-MEANS clustering is a classical unsupervised learning algorithm that iteratively assigns data points to K clusters, maximizing intra-cluster similarity while maximizing inter-cluster differences. The core mechanism involves calculating distances between samples and cluster centroids, then iteratively updating centroid positions until convergence. However, K-MEANS exhibits sensitivity to initial centroid selection, potentially leading to local optima. Code implementation typically requires initial random centroid initialization and Euclidean distance calculations for point assignment.

To enhance K-MEANS performance, Particle Swarm Optimization (PSO) algorithm can be integrated. PSO is a swarm intelligence optimization technique that mimics bird flock foraging behavior by adjusting particle velocities and positions to locate global optima. When improving K-MEANS, PSO optimizes initial centroid selection through population-based search, where each particle represents a potential centroid configuration. The algorithm combines global exploration (following the swarm's best solution) and local exploitation (following individual particle's best solution) to improve clustering stability and accuracy. Implementation involves defining fitness functions based on within-cluster sum of squares (WCSS).

Quantum-behaved Particle Swarm Optimization (QPSO) enhances traditional PSO by incorporating quantum mechanics principles, particularly probability-based state transitions. QPSO improves global search capability through quantum-inspired position updates using probability density functions, reducing premature convergence risks. When applied to K-MEANS optimization, QPSO employs quantum state probability distributions to guide particle movement, resulting in more robust clustering outcomes. Code implementation typically involves replacing classical position updates with quantum-inspired delta potential field models.

Experimental validation on breast cancer datasets demonstrates that enhanced K-MEANS algorithms (PSO-KMEANS and QPSO-KMEANS) achieve superior classification accuracy and stability. Compared to conventional K-MEANS, these optimized algorithms better handle complex data distributions through intelligent centroid initialization, improving model generalization. The validation confirms that swarm intelligence-enhanced K-MEANS clustering holds significant application value in medical data analysis and similar domains requiring robust pattern recognition.