Methods for Improving Generality of Multivariate Calibrations

We are investigating a number of variable selection methods for multivariate calibration, with the aim of producing calibrations that are more robust to interferences and better suited to transfer calibrations from one instrument to another. The aim is to find sets of variables that are the most highly related to the property being calibrated, then to find subsets from those that provide adequate performance when interferences are present in the measured spectra.

Our previous work has led to the development of stacked regression models. We showed [1] that the usual PLS regression could be broken into a series of separate calibrations, which were then stacked to gain the advantage of high-level fusion of the models. The isolation of the intervals could be done by a static window (Figure 1)or a moving window technique (Figure 2).



Figure 1 Stacked PLS with Static Window


Figure 2 Stacked PLS with Moving Window

Modeling  intervals of the spectrum, whether with a static or a moving window,  led to calibrations superior to conventional PLS or a PLS regression based on selection of the best performing interval (iPLS)   (Figure 3).


Figure 3  Predictive Performance of Stacked and Interval Regressions

The stacking also gives an advantage for  a transfer of calibration models. Stacking can be used for the usual piecewise direct standardization method ( a standard way to transfer a calibration between instruments) either in the spectral domain or in the wavelet domain, as shown in Table I [2]

Screen Shot 2016-08-26 at 09.04.18

From reference [2].

A transfer of calibration with no need for standards can be accomplished with stacking. A stacked PLS model was transferred by model update between 4 different spectrometers, giving useful calibrations.[3]

Screen Shot 2016-08-26 at 08.53.39

From  reference [3].

More recently, we showed that using a frequency domain representation with stacking and an orthogonal projection (called DDTOP) gave transfers superior to those from all other methods that we are aware of in the literature. We were able to transfer calibrations to instruments not seen, and with errors comparable to those obtained by a calibration on that instrument.

Model generalization analysis results (from top to bottom: polymer data, corn data, Swedish lake data). From reference [4].

A comprehensive review of calibration transfer with 166 references has been prepared and will appear soon [5].


[1] Ni W, Brown SD, Man. R. Stacked partial least squares regression for spectral calibration and prediction. J. Chemom. 2009; 23: 505–517.

[2] W. Ni, S.D. Brown, R. Man, Data fusion in multivariate calibration transfer, Analytica Chimica Acta. 2010; 661:133–142.

[3] W. Ni, S.D. Brown, R. Man, Stacked PLS for calibration transfer without standards, J. Chemometrics. 2011;  25: 130–137.

[4] D. Poerio and S.D. Brown, Dual-Domain Calibration Transfer Using Orthogonal Projection, Appl. Spectrosc. 2018;  72: 378–391.

[5] S.D. Brown, Transfer of Multivariate Calibration Models, In Comprehensive Chemometrics, 2nd Ed., R. Tauler, B. Walczak and S.D. Brown, Eds. Elsevier, in press, publication expected late 2019.

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Last revision: 28 April 2019


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