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An improved successive projections algorithm version to variable selection in multiple linear regression.

Luciana Dos Santos Canova1, Federico Danilo Vallese2, Marcelo Fabian Pistonesi2

  • 1Instituto de Química, IQ, Universidade Federal do Rio Grande do Sul, Av. Bento Gonçalves, 9500 Agronomia, 91501970, Porto Alegre, RS, Brazil.

Analytica Chimica Acta
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Summary

The filtered successive projections algorithm (fSPA-MLR) improves multiple linear regression accuracy by reducing uninformative variables. This enhanced method shows comparable or superior predictive performance to existing techniques in near-infrared spectrometric analysis.

Keywords:
Multilinear regressionNIR spectrometryPartial least squaresSuccessive projections algorithmVariable selection

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Area of Science:

  • Chemometrics
  • Analytical Chemistry
  • Spectroscopy

Background:

  • Multiple linear regression (MLR) models can be affected by collinearity in calibration data.
  • The successive projections algorithm (SPA) combined with MLR (SPA-MLR) is a variable selection method known for good prediction ability.
  • Conventional full-spectrum models like partial least squares (PLS) are often used for comparison.

Purpose of the Study:

  • To introduce a modified SPA algorithm with an added filter step (fSPA-MLR).
  • To enhance variable selection by removing uninformative variables before projection.
  • To evaluate the performance of fSPA-MLR in near-infrared (NIR) spectrometric analysis.

Main Methods:

  • Implementation of a filter step prior to the projection phase in the SPA algorithm.
  • Application of the proposed fSPA-MLR algorithm to two case studies: pharmaceutical tablets and diesel/biodiesel mixtures.
  • Comparison of fSPA-MLR performance against PLS and the original SPA-MLR, using various spectral pre-processing techniques (raw, Savitzky-Golay, SNV).

Main Results:

  • The fSPA-MLR models achieved similar or better performance compared to PLS models.
  • fSPA-MLR demonstrated superior performance over the original SPA-MLR in both cross-validation and external prediction.
  • The effectiveness of fSPA-MLR was consistent across different spectral pre-processing methods.

Conclusions:

  • The addition of a filter step to SPA-MLR (fSPA-MLR) is an effective strategy for improving variable selection and model accuracy.
  • fSPA-MLR offers a robust alternative to PLS and the original SPA-MLR for NIR spectroscopic data analysis.
  • The proposed method enhances predictive capabilities regardless of spectral pre-processing techniques employed.