Regularization to orthogonal-polynomials fitting with application to magnetization data
For researchers fitting magnetization data, it provides a quantitative overfitting assessment, but the method is incremental and domain-specific.
The paper proposes a regularization method with cross-validation for two-variable orthogonal-polynomials fitting to address overfitting, achieving satisfactory precision on magnetization data, enabling reliable analysis of magnetocaloric and phase-transition properties.
An obstacle encountered in applying orthogonal-polynomials fitting is how to select out the proper fitting expression. By adding a Laplace term to the error expression and introducing the concept of overfitting degree, a regularization and corresponding cross validation scheme is proposed for two-variable polynomials fitting. While the Fortran implementation of above scheme is applied to magnetization data, a satisfactory fitting precision is reached, and overfitting problem can be quantitatively assessed, which therefore offers the quite reliable base for future comprehensive investigations of magnetocaloric and phase-transition properties of magnetic functional materials.