ANIMC: A Soft Approach for Autoweighted Noisy and Incomplete Multiview Clustering

Multiview clustering has wide real-world applications because it can process data from multiple sources. However, these data often contain missing instances and noises, which are ignored by most multiview clustering methods. Missing instances may make these methods difficult to use directly, and noises will lead to unreliable clustering results. In this article, we propose a novel autoweighted noisy and incomplete multiview clustering (ANIMC) approach via a <italic>soft</italic> autoweighted strategy and a doubly <italic>soft</italic> regular regression model. First, by designing adaptive semiregularized nonnegative matrix factorization, the soft autoweighted strategy assigns a <italic>proper</italic> weight to each view and adds a soft boundary to balance the influence of noises and incompleteness. Second, by proposing <inline-formula><tex-math notation="LaTeX">$\theta$</tex-math></inline-formula>-norm, the doubly soft regularized regression model adjusts the sparsity of our model by choosing different <inline-formula><tex-math notation="LaTeX">$\theta$</tex-math></inline-formula>. Compared with previous methods, ANIMC has three unique advantages: 1) it is a soft algorithm to adjust our approach in different scenarios, thereby improving its generalization ability; 2) it automatically learns a proper weight for each view, thereby reducing the influence of noises; 3) it performs doubly soft regularized regression that aligns the same instances in different views, thereby decreasing the impact of missing instances. Extensive experimental results show its superior advantages over other state-of-the-art works.