<ul data-eligibleForWebStory="false">Clustering is crucial in data-driven fields, but accuracy is challenging especially in large datasets.A new method, CAS (Condensed and Accelerated Silhouette), aims to find the optimal k in K-Means clustering efficiently.The approach combines multiple techniques and statistical methods for better performance in text and image data clustering.Experimental results indicate significant improvements in computational efficiency and cluster validity compared to traditional methods.