Complex-Valued Chemometrics in Spectroscopy: Partial Least Squares Regression.

Area of Science:

• Chemometrics
• Spectroscopy
• Data Analysis

Background:

• Traditional chemometrics often uses only the imaginary part of spectral data (e.g., absorbance).
• Complex-valued chemometrics utilizes both real (e.g., refractive index) and imaginary parts of spectra.
• Kramers-Kronig transformations allow extension to absorbance and Raman spectra.

Purpose of the Study:

• To extend complex-valued chemometrics by incorporating partial least squares (PLS) regression.
• To explore and compare different strategies for implementing complex-valued PLS.
• To evaluate the performance of complex-valued PLS against conventional PLS.

Main Methods:

• Developed parallel computation of real and imaginary PLS components using nonlinear iterative partial least squares (NIPALS).
• Employed a brute-force approach with nested leave-one-out (LOO) cross-validation to select optimal solutions from multiple possibilities.
• Applied singular value decomposition (SVD) directly to complex matrix products.

Main Results:

• Complex-valued PLS demonstrated significantly lower errors (over an order of magnitude) compared to conventional PLS.
• The improvement was particularly notable when high-wavenumber refractive indices differed between mixture components.
• Successful application to complex refractive index spectra of binary mixtures (benzene-toluene, benzene-cyclohexane, benzene-CCl4).

Conclusions:

• Complex-valued PLS regression is a powerful extension of chemometric methods.
• This approach offers superior accuracy for analyzing spectral data, especially for mixtures.
• The developed methods provide a more robust tool for quantitative spectral analysis.