Semi-supervised clustering has gained significant attention from researchers due to its advantages over unsupervised clustering. However, existing studies have predominantly focused on discrete data. This paper pioneers the application of semi-supervised clustering to probability density functions. The proposed algorithm encompasses detailed implementation steps, a convergence proof, and the ability to address computational challenges. The algorithm has been effectively implemented on image data, resulting in the transformation of each image into a probability density function that is representative. In comparison to existing unsupervised algorithms, the efficacy of the proposed algorithm in partitioning and reducing computational costs is demonstrated through numerical examples and applications.