A Calibration Method Free of Optimum Factor Number Selection for Automated Multivariate Analysis. Experimental and Theoretical Study

Liang Xu, Israel Schechter*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

82 Scopus citations

Abstract

Several analytical applications of multivariate calibration methods require human decisions, the most difficult being the number of factors involved. Thus, eliminating the optimum factor number may contribute to the improvement of automatic calibration processes. We propose a factor analysis method that does not need the factor number. It is particularly suitable for indirect calibration of a system under indirect observation. The algorithm is based on composing a subspace excluding the contribution from the component of interest and calculating its net analyte signal through an orthogonal projection to an orthogonal space. This method is applicable as long as the spectral vector dimension (i.e., the number of data points) is larger than the calibration set size. This condition readily satisfied in spectroscopic analysis. The relevant effects, including the effect of the spectral vector dimension and of the calibration set size upon prediction errors, have been investigated using extensive computer simulation. The algorithm has been exemplified by a successful application to the predictions of ethanol concentration and of octane number of gasoline samples using near-IR spectra. In this example of an indirect calibration, the proposed method, which requires no information on optimum factor number, is of particular importance. In most cases, the results obtained by this method are similar to those of the traditional PCR; however, this method does not fail when the optimal model cannot be correctly determined by automatic procedures.

Original languageEnglish
Pages (from-to)3722-3730
Number of pages9
JournalAnalytical Chemistry
Volume69
Issue number18
DOIs
StatePublished - 15 Sep 1997
Externally publishedYes

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