Optimizing weighted k-means clustering with gradient-based methods

Clustering methods are essential in medical and data-centric research, helping to reveal underlying patterns without the need for labelled data. This study introduces a gradient-based K-means framework that jointly refines centroids, sample weights, and covariance matrices. In contrast to traditional weighted K-means, which treats these components separately, the proposed method enables a more cohesive and adaptive optimization strategy. By incorporating Mahalanobis distance to account for feature correlations and applying dynamic weighting, the approach is well-suited for complex clinical datasets. Tests on real-world medical data show that this method outperforms standard clustering algorithms, offering improved accuracy and more clearly defined cluster structures.