This paper proposes a novel method called Low-Rank Kernel Tensor Learning for Incomplete Multiple Views Clustering (LRKT-IMVC) to address the problem of incomplete multi-view clustering. The method introduces the concept of kernel tensor to explore inter-view correlations and uses a low-rank kernel tensor constraint to capture consistency information for imputing missing kernel elements, thereby improving clustering quality. An alternative optimization method with guaranteed convergence is designed to solve the resulting optimization problem. The proposed method is evaluated on seven well-known datasets with different missing ratios, demonstrating its effectiveness and advantages over existing methods. The main contributions include introducing the kernel tensor concept, developing a versatile IMVC method with low-rank tensor constraint for imputing missing views, and proposing a novel approach for comprehensive imputation of absent kernel elements. The method also utilizes an auxiliary tensor to address the optimization problem and designs a four-step alternative optimization algorithm. Comprehensive experimental results show the effectiveness and efficiency of the proposed method. LRKT-IMVC unifies imputation and clustering into one optimization process and incorporates low-rank kernel tensor constraint to capture more consistency information for clustering. The method is theoretically guaranteed to converge to a local optimum and has been shown to perform well in experiments with various missing ratios. The algorithm is efficient and can handle large-scale datasets. The results demonstrate that LRKT-IMVC significantly outperforms other methods in terms of clustering accuracy, normalized mutual information, and purity. The method is also sensitive to the parameter λ, which balances the quality of clustering and kernel reconstruction. The results show that LRKT-IMVC can achieve excellent clustering performance even with a decrease in the number of views by adjusting the appropriate hyperparameter. The method is effective in capturing high-order correlations in incomplete multiple kernels and improves clustering performance by utilizing consistency and complementary information from other kernels. The method is also compared with various methods that do not rely on multiple kernel learning, showing its advantages in handling incomplete multi-view data. The results demonstrate the effectiveness of combining tensor constraint and kernel learning in incomplete multi-view clustering.This paper proposes a novel method called Low-Rank Kernel Tensor Learning for Incomplete Multiple Views Clustering (LRKT-IMVC) to address the problem of incomplete multi-view clustering. The method introduces the concept of kernel tensor to explore inter-view correlations and uses a low-rank kernel tensor constraint to capture consistency information for imputing missing kernel elements, thereby improving clustering quality. An alternative optimization method with guaranteed convergence is designed to solve the resulting optimization problem. The proposed method is evaluated on seven well-known datasets with different missing ratios, demonstrating its effectiveness and advantages over existing methods. The main contributions include introducing the kernel tensor concept, developing a versatile IMVC method with low-rank tensor constraint for imputing missing views, and proposing a novel approach for comprehensive imputation of absent kernel elements. The method also utilizes an auxiliary tensor to address the optimization problem and designs a four-step alternative optimization algorithm. Comprehensive experimental results show the effectiveness and efficiency of the proposed method. LRKT-IMVC unifies imputation and clustering into one optimization process and incorporates low-rank kernel tensor constraint to capture more consistency information for clustering. The method is theoretically guaranteed to converge to a local optimum and has been shown to perform well in experiments with various missing ratios. The algorithm is efficient and can handle large-scale datasets. The results demonstrate that LRKT-IMVC significantly outperforms other methods in terms of clustering accuracy, normalized mutual information, and purity. The method is also sensitive to the parameter λ, which balances the quality of clustering and kernel reconstruction. The results show that LRKT-IMVC can achieve excellent clustering performance even with a decrease in the number of views by adjusting the appropriate hyperparameter. The method is effective in capturing high-order correlations in incomplete multiple kernels and improves clustering performance by utilizing consistency and complementary information from other kernels. The method is also compared with various methods that do not rely on multiple kernel learning, showing its advantages in handling incomplete multi-view data. The results demonstrate the effectiveness of combining tensor constraint and kernel learning in incomplete multi-view clustering.