Tensorized Soft Label Learning Based on Orthogonal NMF

Recently, a strong interest has been in multiview high-dimensional data collected through cross-domain or various feature extraction mechanisms. Nonnegative matrix factorization (NMF) is an effective method for clustering these high-dimensional data with clear physical significance. However, existing multiview clustering based on NMF only measures the difference between the elements of the coefficient matrix without considering the spatial structure relationship between the elements. And they often require postprocessing to achieve clustering, making the algorithms unstable. To address this issue, we propose minimizing the Schatten p-norm of the tensor, which consists of a coefficient matrix of different views. This approach considers each element's spatial structure in the coefficient matrices, crucial for effectively capturing complementary information presented in different views. Furthermore, we apply orthogonal constraints to the cluster index matrix to make it sparse and provide a strong interpretation of the clustering. This allows us to obtain the cluster label directly without any postprocessing. To distinguish the importance of different views, we utilize adaptive weights to assign varying weights to each view. We introduce an unsupervised optimization scheme to solve and analyze the computational complexity of the model. Through comprehensive evaluations of six benchmark datasets and comparisons with several multiview clustering algorithms, we empirically demonstrate the superiority of our proposed method.