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Calibration maintenance and transfer using Tikhonov regularization approaches.

John H Kalivas1, Gabriel G Siano, Erik Andries

  • 1Department of Chemistry, Idaho State University, Pocatello, Idaho 83209, USA. kalijohn@isu.edu

Applied Spectroscopy
|July 11, 2009
PubMed
Summary
This summary is machine-generated.

This study presents a Tikhonov regularization (TR) method for maintaining multivariate calibrations and enabling calibration transfer between instruments. The approach ensures model applicability over time and across different instruments.

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Area of Science:

  • Analytical Chemistry
  • Chemometrics
  • Spectroscopy

Background:

  • Maintaining multivariate calibration models over time is crucial for accurate predictions.
  • Calibration transfer, predicting samples on secondary instruments using a primary instrument model, presents unique challenges.
  • Existing methods may not always be directly applicable to calibration maintenance and transfer scenarios.

Purpose of the Study:

  • To develop and evaluate a Tikhonov regularization (TR) based method for both calibration maintenance and calibration transfer.
  • To address the limitations of basic TR theory in these specific applications.
  • To compare TR with partial least squares (PLS) for these tasks.

Main Methods:

  • A Tikhonov regularization (TR) based method was applied to calibration maintenance and transfer.
  • A specific weighting scheme was designed for new (transfer/standardization) samples augmented to existing calibration samples.
  • A generic solution was developed to enable TR application in all cases.
  • TR was compared with partial least squares (PLS) using harmonious (bias/variance tradeoff) and parsimonious (effective rank) considerations.

Main Results:

  • The Tikhonov regularization method proved effective for both calibration maintenance and transfer.
  • The developed weighting scheme and generic solution facilitated TR application.
  • Both TR and PLS, when formatted similarly, demonstrated viability for these problems.
  • The comparison highlighted the effectiveness of harmonious and parsimonious considerations within TR.

Conclusions:

  • Tikhonov regularization offers a robust solution for maintaining multivariate calibrations and achieving calibration transfer.
  • The proposed TR method, with its specific design for new samples, overcomes limitations of basic TR theory.
  • Both TR and PLS are viable for calibration maintenance and transfer, with TR offering specific advantages in managing bias-variance and model complexity.