Abstract: The existing multi-view clustering algorithms exhibit limitations in accurately capturing the high-order information and complementary information embedded in multi-view data during the low-dimensional representations learning process. Meanwhile, these algorithms fail to capture the local information of data, and their information extraction methods lack robustness to noise and outliers. To address these challenges, an adaptive tensor singular value shrinkage multi-view clustering algorithm named ATSVS is proposed. ATSVS proposes a novel tensor log-determinant function to enforce the low-rank constraint on the representation tensor, which can adaptively enable adaptive shrinkage of singular values based on their magnitude. Consequently, ATSVS effectively captures high-order information and complementary information within multi-view data from the global perspective. Then, ATSVS captures the local information of the data by using the l_1,2 norm that combines the advantages of sparse representation and manifold regularization technology, while improving the robustness of the algorithm to noisy points by combining with l_2,1 norms to impose sparse constraints on the noise. The experimental results with eleven comparison algorithms on nine different types of datasets show that our proposed algorithm ATSVS has the superior clustering performance, outperforming state-of-the-art baselines significantly. Consequently, ATSVS is an excellent algorithm that can effectively handle the task of clustering multi-view data.