Partial Tubal Nuclear Norm-Regularized Multiview Subspace Learning

In this article, a unified multiview subspace learning model, called partial tubal nuclear norm-regularized multiview subspace learning (PTN $<^>{2}$ MSL), was proposed for unsupervised multiview subspace clustering (MVSC), semisupervised MVSC, and multiview dimension reduction. Unlike most of the existing methods which treat the above three related tasks independently, PTN $<^>{2}$ MSL integrates the projection learning and the low-rank tensor representation to promote each other and mine their underlying correlations. Moreover, instead of minimizing the tensor nuclear norm which treats all singular values equally and neglects their differences, PTN $<^>{2}$ MSL develops the partial tubal nuclear norm (PTNN) as a better alternative solution by minimizing the partial sum of tubal singular values. The PTN $<^>{2}$ MSL method was applied to the above three multiview subspace learning tasks. It demonstrated that these tasks organically benefited from each other and PTN $<^>{2}$ MSL has achieved better performance in comparison to state-of-the-art methods.