一种构造正则化矩阵的新方法

在系数矩阵病态时进行参数求解,合理地选择正则化参数和正则化矩阵可以提高参数估计的可靠性。针对正则化矩阵如何构造的问题,提出一种新的正则化矩阵构造方法。通过法矩阵较小奇异值对应的特征向量构造出一个对称矩阵,用该矩阵的主对角线元素构造出对角矩阵,然后与单位矩阵组合得出一种新的正则化矩阵。实验表明,当正则化参数小于1时,新算法的参数估值优于岭估计。

A New Method of Constructing Regularized Matrix

In parameter solving under the conditions of coefficient matrix, the rational selection of regularization parameters and regularization matrix can improve the reliability of parameter estimation. The symmetric matrix is constructed by the eigenvectors corresponding to the smaller singular values of the matrix. The diagonal matrix is constructed by the main diagonal elements of the matrix, and then a new regularization matrix is obtained by combining with the unit matrix. The experimental results show that when the regularization parameter is less than 1, the parameter estimation of this algorithm is better than the ridge estimation.