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Complex-Valued Chemometrics in Spectroscopy: Principal Component Regression.

Thomas G Mayerhöfer1,2, Oleksii Ilchenko3,4, Andrii Kutsyk4

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Summary
This summary is machine-generated.

We introduce complex-valued principal component regression (PCR) for spectroscopy, allowing principal components (PCs) to cover the complex plane. A novel method combining SVD eigenvectors with Kramers-Kronig transforms consistently outperformed conventional PCR.

Keywords:
ChemometricsPCRcomplex refractive indexideal binary liquid mixturesprincipal component regression

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Area of Science:

  • Spectroscopy
  • Chemometrics
  • Data Analysis

Background:

  • Traditional spectroscopy methods are limited to real or imaginary data.
  • Complex-valued data analysis offers enhanced modeling but lacks optimal tools.
  • Principal Component Regression (PCR) is a key chemometric technique.

Purpose of the Study:

  • To introduce and evaluate complex-valued PCR for spectroscopic data.
  • To explore eigenvector computation strategies for complex-valued PCR.
  • To compare the performance of novel complex-valued PCR against conventional PCR.

Main Methods:

  • Applied Singular Value Decomposition (SVD) directly to complex refractive index spectra.
  • Developed an alternative method combining SVD-derived eigenvectors with Kramers-Kronig transforms.
  • Investigated two strategies for computing eigenvectors in complex-valued PCR.

Main Results:

  • The novel method using Kramers-Kronig transforms consistently outperformed conventional PCR.
  • Complex-valued PCR allows principal components to span the entire complex plane.
  • The proposed method enhances data analysis capabilities in spectroscopy.

Conclusions:

  • Complex-valued PCR, particularly the Kramers-Kronig transform method, offers superior performance.
  • This approach expands modeling flexibility beyond traditional real/imaginary constraints.
  • The findings suggest significant potential for advancing infrared and Raman spectroscopy data analysis.