A non-linear partial least squares based on monotonic inner relation.

A novel regression model, monotonic inner relation-based non-linear partial least squares (MIR-PLS), is proposed to address complex issues like limited observations, multicollinearity, and nonlinearity in Chinese Medicine (CM) dose-effect relationship experimental data. MIR-PLS uses a piecewise mapping function based on monotonic cubic splines to model the non-linear inner relations between input and output score vectors. Additionally, a new weight updating strategy (WUS) is developed by leveraging the properties of monotonic functions. The proposed MIR-PLS method was compared with five well-known PLS variants: standard PLS, quadratic PLS (QPLS), error-based QPLS (EB-QPLS), neural network PLS (NNPLS), and spline PLS (SPL-PLS), using CM dose-effect relationship datasets and near-infrared (NIR) spectroscopy datasets. Experimental results demonstrate that MIR-PLS exhibits general applicability, achieving excellent predictive performances in the presence or absence of significant non-linear relationships. Furthermore, the model is not limited to CM dose-effect relationship research and can be applied to other regression tasks.