In view of the limitations of existing low-rank decomposition methods in mining potential low-rank structures of high-order tensors, research on low-rank decomposition methods and algorithms for high-order tensors was carried out. Existing tensor low-rank decomposition methods, either indiscriminately matrixing tensor data, or directly acting on original high-order data that may contain a large amount of redundant information, fail to fully combine the structural information of the tensor data itself, making it difficult to efficiently obtain accurate low-rank structures, which restricts the effect of high-order tensor data processing. In order to solve the above problems, we conducted in-depth research based on the correlation theory of each order of high-order tensors, and proposed the research idea of eliminating redundant information through the collapse of tensor orders and screening the optimal collapse method from multiple perspectives. Based on this, we established a statistical model of multiview low-rank decomposition, designed a data-driven rapid estimation algorithm of model parameters, and completed the theoretical proof of the consistency of the algorithm estimators. The proposed theory and algorithm were empirically verified through experimental research. The experimental results confirmed the correctness and effectiveness of the relevant theories and algorithms. The results showed that this multiview low-rank decomposition fast algorithm provides new ideas and algorithm support for obtaining the optimal low-rank structure of high-order tensors and compressing high-order tensor data.