Complex-Valued Chemometrics in Spectroscopy: Inverse Least Squares Regression

Area of Science:

• Analytical Chemistry
• Spectroscopy
• Chemometrics

Background:

• Classical least squares (CLS) regression requires prior knowledge of mixture components.
• Inverse least squares (ILS) regression overcomes this limitation.
• Complex-valued ILS further enhances ILS by utilizing complex refractive index data.

Purpose of the Study:

• To demonstrate the effectiveness of complex-valued ILS in determining component concentrations without prior knowledge.
• To showcase performance enhancements in thermodynamically ideal mixtures.
• To explore error reduction strategies using complex-valued data.

Main Methods:

• Application of complex-valued inverse least squares (ILS) regression.
• Utilizing the complex refractive index function.
• Employing leave-one-out cross-validation (LVOOCV) scheme.
• Leveraging correlations between errors and imaginary concentration components.

Main Results:

• Achieved over 50% reduction in mean absolute error for benzene-toluene and benzene-cyclohexane mixtures.
• Demonstrated significant error reduction by incorporating complex refractive index data.
• Identified additional error reduction through error-imaginary component correlations.

Conclusions:

• Complex-valued ILS offers superior performance for mixture analysis compared to traditional methods.
• The complex refractive index function, obtainable via infrared spectroscopy and Kramers-Kronig relations, is key to this improvement.
• Complex-valued machine learning holds significant potential for advancing analytical applications.