Multi-view Subspace Clustering Based on Tensor Log-Determinant Minimization Approach

Multi-view clustering aims to capture the information inherent in multiple views by identifying data clusters that reflect different characteristics of the dataset. Given the widespread agreement in research that diverse perspectives of a data collection exhibit a shared hidden structure, numerous existing techniques for multi-view subspace learning utilize the nuclear norm to uncover a low-dimensional representation of the concealed subspace. However, due to its convex nature, the nuclear norm often fails to distinguish the characteristic variance of each cluster, and the data tend to fall into multiple nonlinear subspaces of the cube. The tensor core norm scales linearly with the sum of singular values, and the tensor rank approximation using the tensor core norm can be problematic if the ratio of non-zero singular values is far from 1. In this paper, the tensor logarithmic determinant is adopted, aiming to achieve better low-rank approximation of the tensor. Not only is this possible, but it's also quite effective. This paper explores multi-view subspace clustering based on tensor Log-Determinant minimization approach (TLDM). The method is tested on six benchmark datasets and compared with four existing methods. Experimental results show that this method outperforms state-of-the-art multi-view subspace clustering methods and is robust.