Because multiple kernel learning can avoid selection of kernel functions and parameters effectively， and graph clustering can fully mine complex structural information between samples， Multiple Kernel Graph Clustering （MKGC） has received widespread attention in recent years. However， the existing MKGC methods suffer from the following problems： graph learning technique complicates the model， the high rank of graph Laplacian matrix cannot ensure the learned affinity graph to contain accurate c connected components （block diagonal property）， and most of the methods ignore the high-order structural information among the candidate affinity graphs， making it difficult to fully utilize the multiple kernel information. To tackle these problems， a novel MKGC method was proposed. First， a new graph learning method based on capped simplex projection was proposed to directly project the kernel matrices onto graph simplex， which reduced the computational complexity. Meanwhile， a new block diagonal constraint was introduced to keep the accurate block diagonal property of the learned affinity graphs. Moreover， the low-rank tensor learning was introduced in capped simplex projection space to fully mine the high-order structural information of multiple candidate affinity graphs. Compared with the existing MKGC methods on multiple datasets， the proposed method has less computational cost and high stability， and has great advantages in Accuracy （ACC） and Normalized Mutual Information （NMI）.
