Spectral knowledge-based regression for laser-induced breakdown spectroscopy quantitative analysis

Laser-induced breakdown spectroscopy (LIBS) is a promising atomic emission spectroscopic technique for multi-elemental analysis and has the advantages of real-time multi-element measurement, minimal sample preparation and remote detection. However, the quality of LIBS data can be low due to matrix effects and signal uncertainty which hinders the wide application of LIBS. Recent studies attempt to improve the performance of LIBS quantitative analysis using linear and nonlinear multivariate analysis models. Linear models can easily present how important variables contribute to the prediction but suffer from performance degradation if data has a high degree of nonlinearity. Nonlinear models tend to have good performance, but lack simple and intuitive variable interpretability and are prone to overfitting. Moreover, neither linear nor nonlinear models used in LIBS quantitative analysis are originally designed to explicitly consider the domain knowledge of atomic spectroscopy. In this work, a new machine learning algorithm is proposed, namely spectral knowledge-based regression (SKR), which integrates linear and nonlinear models to improve the performance of LIBS quantitative analysis. The linear model is knowledge-driven and built on key variables correlated with analyte composition. While the nonlinear model is data-driven and transforms the input data into a kernel matrix. The proposed SKR is tested on 18 quantification tasks in 4 LIBS datasets and compared with 5 baseline methods. It yields the lowest and the second-lowest root-mean-square errors in 12/18 and 2/18 tasks, respectively. Moreover, SKR intuitively explains the contribution of key variables to prediction and has the same low computational complexity as ridge regression. These results demonstrate that SKR inherits the high accuracy of nonlinear modelling and the simple variable interpretability of linear models. Therefore, it can serve as a promising candidate for improving the accuracy and reliability of LIBS quantitative analysis.