High-dimensional Data Processing Based On HOPLS-SVM And Global Sensitivity Analysis With HOPLS-PCE

HOPLS extends the Partial Least Squares(PLS)algorithm to a higher order and becomes a new generalized multilinear regression method.The orthogonal Tucker model used in HOPLS has better performance than the CP decomposition in terms of both adaptability and flexibility,and provides a better balance between adaptability and computational complexity.By introducing the HOSVD,this thesis makes the computational process of the new algorithm more efficient than the traditionally used iterative process through a closed form solution.By compressing the large-scale tensor,HOSVD can reduce the storage capacity of the original tensor while maintaining a certain degree of accuracy,making the storage,transmission and analysis of the data more convenient and efficient.In addition,we can also reconstruct a small-scale dataset using HOSVD according to the accuracy required for practical work,making analysis on a laptop of ordinary configuration possible.In this thesis,in the field of global sensitivity analysis of high-dimensional models,the Sobol' global sensitivity analysis method based on Sparse PCE is combined with HOPLS,and the method is verified by several arithmetic examples.The main research of this thesis consists of the following points.(1)The HOPLS-SVM algorithm for high-dimensional data analysis is proposed,and the correctness and applicability of the method are verified by analyzing the census data.(2)The HOSVD algorithm for compression analysis of large-scale tensor is proposed,and the accuracy of the HOSVD algorithm is verified by a randomized tensor seismic dataset.Different tolerance errors are explored,and the HOSVD algorithm works differently under different compression rate conditions.(3)The algorithm of HOPLS-PCE for global sensitivity analysis is proposed,and the effectiveness of the algorithm is verified by performing global sensitivity analysis on the Ishigami equation,Morris equation,and 100-dimensional high-dimensional equation,and comparing with Monte Carlo simulation and low-rank approximation(LRA).