Semi-supervised correntropy-based non-negative matrix factorization with hypergraph regularization

Non-negative matrix factorization (NMF) stands as a potent technique for reducing dimensionality, renowned especially for its prowess in clustering. However, it often disregards the crucial a priori labeling information inherent in diverse datasets. In this study, we introduce a semi-supervised approach named SCNMFH, leveraging hypergraph regularization to address these aforementioned challenges. Specifically, we integrate correntropy into the loss function of SCNMFH, replacing the conventional Euclidean metric. This alteration is aimed at fortifying the robustness of our algorithm. Furthermore, we incorporate hypergraph regularization into the objective function to capture higher-order geometric relationships among data samples. Additionally, recognizing NMF's inherent operation as an unsupervised matrix factorization technique, we employ limited label information as supervision to enhance the discriminative capacity of the matrix factorization. Consequently, our algorithm enhances clustering performance without substantially increasing complexity. Through extensive experimentation across nine image datasets, we have demonstrated the effectiveness and superiority of the proposed algorithm. Comparative analyses, involving several state-of-the-art algorithms, were conducted, thereby elucidating the efficacy and superiority of our approach.