Quantitative Analysis Using PLS and PCR Regression Methods

Partial Least Squares (PLS) regression and Principal Component Regression (PCR) are widely used multivariate statistical modeling methods in chemical quantitative analysis, particularly effective for handling high-dimensional spectral data. Both techniques effectively address limitations of traditional linear regression when dealing with multicollinearity among variables. In code implementations, these methods typically utilize matrix decomposition operations and eigenvalue computations through libraries like NumPy or specialized packages such as scikit-learn's PLSRegression and PCR modules.

In quantitative determination using PLS and PCR, the core objective involves establishing mathematical models between spectral data (e.g., NIR, Raman spectra) and target substance concentrations for rapid quantitative analysis of unknown samples. PLS simultaneously decomposes both independent and dependent variable matrices to identify latent variables maximizing covariance between them, typically implemented through iterative NIPALS algorithms. PCR first reduces spectral data dimensionality via Principal Component Analysis (PCA) - extracting components with maximum variance - before performing regression modeling, which can be computationally optimized using Singular Value Decomposition (SVD).

Practical characteristics include: - Strong anti-interference capability: Can process spectral data with significant noise or baseline drift through preprocessing pipelines - Suitable for small sample sizes: Model optimization possible with limited training sets via cross-validation techniques like k-fold or leave-one-out - Visualization support: Loading plots and score plots facilitate interpretation of variable contributions, implementable using matplotlib visualization libraries

Key considerations: - Preprocessing (SNV, MSC, derivatives) required to eliminate physical interferences using data normalization functions - Selection of principal components/latent variables significantly impacts model generalization, determined through scree plots or explained variance metrics - Independent validation sets essential for evaluating actual prediction performance using metrics like RMSE and R²

These methods have been extensively applied in quality monitoring across pharmaceutical, food, and petroleum industries, constituting core tools in chemometrics with robust open-source implementation frameworks available.