Complex-Valued Chemometrics for Analyzing Absorbance or Raman Spectra.

Area of Science:

• Analytical Chemistry
• Spectroscopy
• Chemometrics

Background:

• Classical chemometrics utilizes real spectral components.
• Complex-valued chemometrics leverages both real and imaginary spectral data for enhanced analysis.
• Existing regression methods can be limited by solely using real spectral information.

Purpose of the Study:

• To transform conventional absorbance and Raman spectra into complex-valued forms.
• To benchmark the performance of complex-valued regression methods against classical approaches.
• To demonstrate the broad applicability and computational efficiency of complex-valued chemometrics.

Main Methods:

• Kramers-Kronig transform to derive real spectral parts from measured intensities (imaginary parts).
• Benchmarking of classical least squares (CLS), inverse least squares (ILS), principal component regression (PCR), and partial least-squares regression (PLSR) using complex-valued spectra.
• Application across diverse systems including mixtures and biological samples (blood plasma).

Main Results:

• Complex-valued chemometric approaches consistently reduce prediction errors (MAE, RMSE, R^2) compared to conventional methods.
• FFT-based routines enable rapid Kramers-Kronig transforms, making implementation computationally inexpensive.
• Complex-valued ILS demonstrated comparable or superior performance to complex-valued PLSR, challenging established regression hierarchies.

Conclusions:

• Complex-valued chemometrics is a broadly applicable and physically grounded extension of classical methods.
• This approach enhances both classical and modern regression strategies in analytical spectroscopy.
• The findings suggest a re-evaluation of regression method hierarchies when complex spectral data are utilized.