Invertible linear transforms based adaptive multi-view subspace clustering

Abstract

Constructing tensor with low-rank prior is the crucial issue of tensor based multi-view subspace clustering methods, but there are still some shortcomings. First, they cannot adaptively allocate the contribution of different views, resulting in the learned tensor being suboptimal. Second, they pursue low-rank tensor for different data through Discrete Fourier Transform based tensor nuclear norm, which lacks generality. To overcome these problems, we propose an invertible linear transforms based adaptive multi-view subspace clustering method, named ILTMSC. Firstly, we mine the potential low-order representation of each view through self-representation subspace learning. Then, we capture high-order representation by integrating low-order representations with adaptive weights into a tensor and then rotated. This strategy can integrate tensor adaptively and handle the noise effectively. Finally, we approximate the low-rank tensor with a recently proposed invertible linear transforms based tensor nuclear norm. Such a new tensor nuclear norm makes our model more general because it can use different invertible linear transforms for different tensor data. Moreover, an adaptive weighted tensor singular value thresholding operator is proposed for capturing the new tensor nuclear norm. Our model could be solved by convex optimization efficiently. Extensive experiments on multi-view datasets validate the effectiveness and robustness of our method.