Filter Learning-Based Partial Least Squares Regression and Its Application in Infrared Spectral Analysis - Yi Mou; Long Zhou; Weizhen Chen; Jianguo Liu; Teng Li (Algorithms, 2025)
Partial Least Squares (PLS) regression has been widely used to model the relationship between predictors and responses. However, PLS may be limited in its capacity to handle complex spectral data contaminated with significant noise and interferences. In this paper, we propose a novel filter learning-based PLS (FPLS) model that integrates an adaptive filter into the PLS framework. The FPLS model is designed to maximize the covariance between the filtered spectral data and the response. This modification enables FPLS to dynamically adapt to the characteristics of the data, thereby enhancing its feature extraction and noise suppression capabilities. We have developed an efficient algorithm to solve the FPLS optimization problem and provided theoretical analyses regarding the convergence of the model, the prediction variance, and the relationships among the objective functions of FPLS, PLS, and the filter length. Furthermore, we have derived bounds for the Root Mean Squared Error of Prediction (RMSEP) and the Cosine Similarity (CS) to evaluate model performance. Experimental results using spectral datasets from Corn, Octane, Mango, and Soil Nitrogen show that the FPLS model outperforms PLS, OSCPLS, VCPLS, PoPLS, LoPLS, DOSC, OPLS, MSC, SNV, SGFilter, and Lasso in terms of prediction accuracy. The theoretical analyses align with the experimental results, emphasizing the effectiveness and robustness of the FPLS model in managing complex spectral data.