This paper introduces a novel unsupervised learning schema for the k-means clustering algorithm, aiming to address the limitations of traditional k-means, such as sensitivity to initializations and the need for a priori knowledge of the number of clusters. The proposed U-k-means algorithm automatically determines the optimal number of clusters without requiring any initialization or parameter selection. The authors construct a learning procedure based on entropy penalty terms to adjust biases and estimate the number of clusters. The computational complexity of the U-k-means algorithm is analyzed, and its effectiveness is demonstrated through comparisons with other clustering methods on both synthetic and real datasets. Experimental results show that the U-k-means algorithm outperforms existing methods in terms of accuracy and robustness to different cluster volumes and shapes. The paper also includes a detailed analysis of the algorithm's performance and a comparison with other clustering algorithms, highlighting the advantages of the U-k-means approach.This paper introduces a novel unsupervised learning schema for the k-means clustering algorithm, aiming to address the limitations of traditional k-means, such as sensitivity to initializations and the need for a priori knowledge of the number of clusters. The proposed U-k-means algorithm automatically determines the optimal number of clusters without requiring any initialization or parameter selection. The authors construct a learning procedure based on entropy penalty terms to adjust biases and estimate the number of clusters. The computational complexity of the U-k-means algorithm is analyzed, and its effectiveness is demonstrated through comparisons with other clustering methods on both synthetic and real datasets. Experimental results show that the U-k-means algorithm outperforms existing methods in terms of accuracy and robustness to different cluster volumes and shapes. The paper also includes a detailed analysis of the algorithm's performance and a comparison with other clustering algorithms, highlighting the advantages of the U-k-means approach.