Total Partial Least Square Regression and its application in infrared spectra quantitative analysis

The quantitative analysis model for infrared spectroscopy primarily relies on regression methods. Partial Least Squares (PLS) is proposed to overcome the small sample problem through dimensionality reduction. However, spectral data may still include orthogonal variation components. Orthogonal Signal Correction (OSC) methods are developed to remove these orthogonal components, improving analysis accuracy, but they require orthogonality assumptions. Total Least Squares (TLS) regression is introduced to suppress noise and perturbations in both predictor and response variables, yet it does not solve the small sample size issue. Therefore, we propose Total Partial Least Squares Regression (TPLS) and its extended model (TPLSE). These models address both small sample sizes and non-orthogonal noise. We present algorithms, time complexity analysis, and bounds analysis. Validation using four public datasets shows that TPLS and TPLSE outperform PLS, OSC, and TLS in prediction accuracy. We also verify the impact of regularization coefficients on model performance and robustness against noise.