Centric graph regularized log-norm sparse non-negative matrix factorization for multi-view clustering

Multi-view non-negative matrix factorization (NMF) provides a reliable method to analyze multiple views of data for low-dimensional representation. A variety of multi-view learning methods have been developed in recent years, demonstrating successful applications in clustering. However, existing methods in multi-view learning often tend to overlook the non-linear relationships among data and the significance of the similarity of internal views, both of which are essential in multi-view tasks. Meanwhile, the mapping between the obtained representation and the original data typically contains complex hidden information that deserves to be thoroughly explored. In this paper, a novel multi-view NMF is proposed that explores the local geometric structure among multi-dimensional data and learns the hidden representation of different attributes through centric graph regularization and pairwise co-regularization of the coefficient matrix. In addition, the proposed model is further sparsified with 𝑙2,𝑙𝑜𝑔-(pseudo) norm to efficiently generate sparse solutions. As a result, the model obtains a better part-based representation, enhancing its robustness and applicability in complex noisy scenarios. An effective iterative update algorithm is designed to solve the proposed model, and the convergence of the algorithm is proven to be theoretically guaranteed. The effectiveness of the proposed method is verified by comparing it with nine state-of-the-art methods in clustering tasks of eight public datasets.