Uncertainty-aware PLS regression via neutrosophic representation: Achieving robustness and interpretability in NIR spectroscopy

Abstract

Classical partial least squares (PLS) regression treats all observations and features as equally reliable, making it vulnerable to spike artifacts, detector malfunctions, and heteroscedastic noise commonly encountered in spectroscopic and sensor data. This limitation forces practitioners to choose between applying methods that ignore data quality, risking biased predictions, or manually excluding suspect observations, sacrificing statistical power. This study introduces a neutrosophic framework for PLS regression that explicitly decomposes each observation into Truth, Indeterminacy, and Falsity (T/I/F) channels, enabling uncertainty-aware latent variable modelling. Three variants were developed: NPLS with sample-level reliability weighting, NPLSW incorporating weighted estimation, and PNPLS with element-wise precision weighting through an EM-style procedure. The methods were evaluated using controlled design-of-experiments on IDRC 2016 NIR spectroscopy datasets (MA_A2, A3, B1), with spike corruption ranging from 5% to 30%. Under clean conditions, all methods performed equivalently (RMSEP = 0.963), confirming that neutrosophic encoding imposes no penalty when data integrity is maintained. Under severe corruption (30% spikes), neutrosophic variants achieved RMSEP improvements of 32-40% over classical PLS, while maintaining positive R2 values where PLS collapsed to negative values, indicating complete loss of explanatory power. The falsity-channel VIP exhibited a 3.5-fold detection ratio between corrupted and clean wavelength regions, enabling practitioners to identify problematic spectral regions without distorting genuine predictor importance. This channel-decomposed interpretability provides traceable quality control diagnostics alongside robust predictive calibration, addressing the long-standing robustness-interpretability trade-off in chemometric modelling.