Generalized Partial Least Squares Regression MATLAB Implementation

Partial Least Squares Regression (PLSR) is an advanced multivariate statistical data analysis method primarily used for regression modeling between multiple dependent variables (Y) and multiple independent variables (X). This method demonstrates exceptional effectiveness when variables exhibit high internal linear correlation structures. Furthermore, PLSR effectively addresses challenges arising from situations where the number of observations is smaller than the number of variables. To better understand PLSR, we should examine its two core components: partial least squares decomposition and regression modeling. The decomposition phase involves projecting both the predictor matrix X and response matrix Y into lower-dimensional spaces through iterative calculations of latent components (T and U) and loading matrices (P and Q). In MATLAB implementations, this is typically achieved using the SIMPLS algorithm or NIPALS iterative procedure, which sequentially extracts latent vectors maximizing covariance between X and Y. The regression modeling phase utilizes the decomposition results (T, U, P, Q) to construct multivariate regression models. The final regression coefficients are derived through the relationship between latent components and original variables. MATLAB code implementations often include functions for cross-validation to determine optimal number of components, along with diagnostic plots for model validation. Thus, PLSR represents a highly flexible methodology suitable for diverse data analysis scenarios, particularly in chemometrics, bioinformatics, and multivariate calibration problems where traditional regression methods face limitations.