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部分最小二乘(PLS)算法在多元统计过程监控等领域得到了广泛应用。但常用的求解方法需要多次迭代求解残差矩阵,不利于对算法的理论分析和结论的解释。基于PLS算法的优化函数形式,该文提出一种新的PLS优化目标函数及相应简化算法。在此基础上构造了PLS算法与线性神经元网络之间的自然映射,给出了相应的训练算法及其理论分析。仿真结果验证了所提出算法的有效性,表明该算法可直接从原数据矩阵得到相应的成分及回归系数,并易于对其进行解释。
Partial Least Squares (PLS) algorithm has been widely used in many statistical process monitoring and other fields. However, the commonly used solution requires multiple iterations to solve the residual matrix, which is not conducive to the theoretical analysis of the algorithm and the interpretation of the conclusion. Based on the PLS algorithm optimization function form, this paper presents a new PLS optimization objective function and the corresponding simplified algorithm. On this basis, the natural mapping between PLS algorithm and linear neuron network is constructed, and the corresponding training algorithm and its theoretical analysis are given. The simulation results verify the validity of the proposed algorithm, which shows that the algorithm can obtain the corresponding components and regression coefficients directly from the original data matrix and easily interpret it.