Incomplete Multiview Clustering Using Normalizing Alignment Strategy With Graph Regularization

Matrix factorization has demonstrated promising performance in the incomplete multiview clustering (IMC) tasks. However, many algorithms require feature normalization operations to ensure the stability of model results, so either the convergence is unstable, or the objective function cannot fit the data well. Addressing these issues, we propose a novel IMC algorithm using a normalizing alignment strategy (IMCNAS) based on nonnegative matrix factorization. Specifically, the columns of the basis matrices are constrained into unit vector space, which integrates the feature normalization and the optimizing process, and makes the model converge fast and stable. On the other hand, this enables the model to fit the data better and produce more reasonable factorization results. Further, we develop a novel pairwise co-regularization to align incomplete multiple views more directly, without introducing a common consensus matrix like traditional centroid-based co-regularization. Graph regularization is also incorporated in the proposed model to utilize the geometrical information of data. We implement IMCNAS with a centroid-based regularization and a pairwise co-regularization respectively, and leads to two variants, i.e., IMCNAS-1 and IMCNAS-2. Both variants are optimized with multiplicative updating rules. Extensive experiments conducted on various real-world datasets comparing several state-of-the-art IMC methods verified the effectiveness of the proposed methods. The source code is available at: https://github.com/GuoshengCui/IMCNAS .