Implementing Partial Least Squares Regression Model Using MATLAB

Partial Least Squares Regression (PLSR) is a statistical method combining principal component analysis and multiple regression, particularly suitable for modeling high-dimensional data with multicollinearity issues. Implementing PLSR in MATLAB primarily relies on functions from the Statistics and Machine Learning Toolbox, with the following key implementation approach: Data Preprocessing Stage: First, raw data requires centering and standardization to eliminate scale differences. MATLAB's zscore function efficiently performs standardization, while the mean function aids in centering calculations. Code example: X_scaled = zscore(X) for standardization, X_centered = X - mean(X) for centering. Model Building Stage: The core implementation uses the plsregress function, which accepts predictor matrix X and response variable matrix Y as inputs. Critical attention must be paid to specifying the number of retained principal components (latent variables), which can be optimized through cross-validation. The function returns essential parameters including projection matrices and regression coefficients. Implementation code: [Xloadings,Yloadings,Xscores,Yscores,beta] = plsregress(X,Y,ncomp). Model Validation Stage: Common validation methods include hold-out validation or k-fold cross-validation to assess model performance. Metrics like prediction residuals and R-squared values should be calculated. MATLAB's crossval function facilitates cross-validation procedures. For new sample predictions, apply the trained regression coefficient matrix directly. Code example: Y_pred = [ones(size(Xnew,1),1) Xnew] * beta. Result Visualization: MATLAB's powerful plotting capabilities enable visualization of variable projection plots and regression coefficient diagrams, aiding in understanding variable relationships. Combining scatter and plot functions with PLSR results intuitively presents the reduced-dimensional data distribution. Implementation approach: use plot(Xscores(:,1),Xscores(:,2),'o') for score plots and bar(beta) for coefficient visualization. This method projects original variables into a lower-dimensional space, effectively addressing multicollinearity while preserving features most explanatory to response variables. It finds wide applications in chemometrics, bioinformatics, and related fields. During implementation, pay attention to data quality checks and outlier handling, as these significantly impact final model performance. Key considerations include using isoutlier function for outlier detection and employing robust scaling techniques when necessary.