CAS Condensed and Accelerated Silhouette: An Efficient Method for Determining the Optimal K in K-Means Clustering

--Clustering is a critical component of decision-making in today's data-driven environments. Clustering has been widely used in a variety of fields, such as bioinformatics, social network analysis, and image processing. However, clustering accuracy remains a major challenge in large datasets. This paper presents a comprehensive overview of strategies for selecting optimal k in clustering, with a focus on achieving a balance between clustering precision and computational efficiency in complex data environments. In addition, this paper introduces improvements to clustering techniques relating to text and image data to provide insights into better computational performance and cluster validity. The proposed approach is based on the Condensed Silhouette method, a statistical methods like Local Structures, Gap Statistics, Class-Consistency Ratio and Cluster Overlap Index(CCR-COI) based algorithm to calculate the best value of K for K-Means Clustering the data. The results of comparative experiments show that the proposed approach achieves up to 99% faster execution times on high-dimensional datasets while retaining both precision and scalability, making it highly suitable for real-time clustering needs or scenarios demanding efficient clustering with minimal resource utilization. Clustering is a critical component of unsupervised machine learning, with the K -means algorithm being particularly favored due to its straightforwardness, speed, and ability to be easily understood. Nonetheless, a major difficulty lies in accurately identifying the best number of clusters, K, especially with expansive and high-dimensional datasets where it is crucial to strike an effective balance between computational efficiency and accuracy.