Fused adaptive tensor log-determinant and local smoothness regularizer for multi-view clustering

The prevailing techniques for multi-view subspace clustering (MVC) methods often depend on the assumption of low-rankness, which asserts that data can be effectively represented in a low-dimensional subspace. While these approaches capture the structure of the data globally and remove noise and redundancy, they all neglect local smoothness prior, which has been extensively used to reduce noise in the image field. Besides, existing techniques often depend on the tensor nuclear norm (TNN)to approximate the intrinsically non-convex tensor rank function. However, the TNN approach equates all singular values, which gives rise to excessive penalization of the principal rank components and ultimately leads to sub-optimal tensor representations. In response to these challenges, we introduce an innovative method called fused adaptive tensor Log-determinant and local smoothness regularizer (FATLLSR) for multi-view clustering. Specifically, we initially derive the self-expressive matrix for each view and subsequently integrate these matrices into a tensor. Then in order to simultaneously explore low-rankness and local smoothness prior, FATLLSR is designed and is used to constrain the obtained tensor. By using FATLLSR, we can not only relax tensor multi-rank constraint better than TNN but also utilize the local smoothness information hidden in multi-view data, making our method more robust to noise and redundancy. These techniques are integrated to constitute a unified model that is effectively handled using the augmented Lagrange multiplier (ALM). As demonstrated by its performance on different datasets, FATLLSR achieves outstanding clustering performance compared to the most advanced methods. The code is publicly available at https://github.com/wangfii/FATLLSR.