Spectral multivariate calibration with wavelength selection using variants of Tikhonov regularization

Area of Science:

• Chemometrics
• Spectroscopy
• Data Analysis

Background:

• Multivariate calibration models are essential for analyzing complex spectral data.
• Tikhonov regularization (TR) is a versatile technique for building such models.
• Existing TR variants include ridge regression (RR), utilizing full or selected wavelengths.

Purpose of the Study:

• To explore the flexibility of Tikhonov regularization (TR) in multivariate calibration.
• To evaluate TR models built using full wavelengths, individual wavelengths, or wavelength bands.
• To identify the optimal TR approach for minimizing prediction errors in spectral data analysis.

Main Methods:

• Implementation of Tikhonov regularization (TR) with three distinct wavelength selection strategies: full wavelengths (ridge regression), individually selected wavelengths, and multiple bands of selected wavelengths.
• Comparative analysis of prediction errors generated by each TR variant across near-infrared, ultraviolet-visible, and synthetic spectral datasets.
• Assessment of model vector magnitude to understand the trade-off between error reduction and prediction uncertainty.

Main Results:

• The Tikhonov regularization (TR) variant employing selected wavelength bands demonstrated the lowest prediction errors compared to full or individually selected wavelengths.
• A correlation was observed between reduced prediction error and an increased model vector magnitude, indicating a potential rise in prediction uncertainty.
• The findings were consistent across diverse spectral data types, including near-infrared, ultraviolet-visible, and synthetic datasets.

Conclusions:

• Tikhonov regularization (TR) provides a flexible framework for multivariate calibration, with wavelength band selection offering superior performance in error reduction.
• The benefits of reduced prediction error via wavelength band selection in TR models are accompanied by a potential increase in prediction uncertainty.
• The developed TR methods are broadly applicable beyond wavelength selection to other variable-selection challenges in data analysis.