Robust Tensor Learning for Multi-View Spectral Clustering

Abstract

Tensor-based multi-view spectral clustering methods are promising in practical clustering applications. However, most of the existing methods adopt the ℓ2,1 norm to depict the sparsity of the error matrix, and they usually ignore the global structure embedded in each single view, compromising the clustering performance. Here, we design a robust tensor learning method for multi-view spectral clustering (RTL-MSC), which employs the weighted tensor nuclear norm to regularize the essential tensor for exploiting the high-order correlations underlying multiple views and adopts the nuclear norm to constrain each frontal slice of the essential tensor as the block diagonal matrix. Simultaneously, a novel column-wise sparse norm, namely, ℓ2,p, is defined in RTL-MSC to measure the error tensor, making it sparser than the one derived by the ℓ2,1 norm. We design an effective optimization algorithm to solve the proposed model. Experiments on three widely used datasets demonstrate the superiority of our method.