Multivariate calibration problem

T. Naes and E. Risvik (Editors), Multivariate Analysis of Data in Sensory Science, Data Handling in Science and Technology Series. Elsevier, Amsterdam, 1996 P.K. Hopke and X.-H. Song, The chemical mass balance as a multivariate calibration problem. Chemom. Intell. Lab. Assist., 37 (1997) 5-14. 

M. Sjostrom, S. Wold, W. Lindberg, J.A. Persson and H. Martens, A multivariate calibration problem in analytical chemistry solved by partial least squares models in latent variables. Anal. Chim. Acta, 150, 61-70 (1983). 

Wold, S., Martens, H., Wold, H. The multivariate calibration problem in chemistry solved by the PLS method. Lecture notes in mathematics . Springer Verlag, Heidelberg, in press... 

Sjoestroem, M., Wold, S., Lindberg, W., Persson, J.A. and Martens, H., A Multivariate Calibration Problem in Analytical Chemistry Solved by Partial Least Squares Models in Latent Variables Anal. Chim. Acta 1983, 150, 61-70. 

Partial chemical information in the form of known pure response profiles, such as pure-component reference spectra or pure-component concentration profiles for one or more species, can also be introduced in the optimization problem as additional equality constraints [5, 42, 62, 63, 64], The known profiles can be set to be invariant along the iterative process. The known profile does not need to be complete to be used. When only selected regions of profiles are known, they can also be set to be invariant, whereas the unknown parts can be left loose. This opens up the possibility of using resolution methods for quantitative purposes, for instance. Thus, data sets analogous to those used in multivariate calibration problems, formed by signals recorded from a series of calibration and unknown samples, can be analyzed. Quantitative information is obtained by resolving the system by fixing the known concentration values of the analyte(s) in the calibration samples in the related concentration prohle(s) [65],... 

Chemometrics is an interdisciplinary field that combines statistics and chemistry. From its earliest days, chemometrics has always been a practically oriented subdiscipline of analytical chemistry aimed at solving problems often overlooked by mainstream statisticians. An important example is solving multivariate calibration problems at reduced rank. The method of partial least-squares (PLS) was quickly recognized and embraced by the chemistry community long before many practitioners in statistics considered it worthy of a second look. ... 

A solution can only be revisited in the next iteration if it is a neighbor N x) of the current solution. Here we consider the selection of wavelength in a multivariate calibration problem (cf. Section 6.2) ... 

In certain applications one must reduce the number of variables in order to speed up the analysis. Multivariate calibration problems require handling and inverting matrices with many entries. It takes a lot of computer memory and time. By means... 

Many other subjects are important to achieve successful pattern recognition. To name only two, it should be investigated to what extent outliers are present, because these can have a profound influence on the quality of a model and to what extent clusters occur in a class (e.g. using the index of clustering tendency of Section 30.4.1). When clusters occur, we must wonder whether we should not consider two (or more) classes instead of a single class. These problems also affect multivariate calibration (Chapter 36) and we have discussed them to a somewhat greater extent in that chapter. 

The question of how many components to include in the final model forms a rather general problem that also occurs with the other techniques discussed in this chapter. We will discuss this important issue in the chapter on multivariate calibration. 

Several approaches have been investigated recently to achieve this multivariate calibration transfer. All of these require that a small set of transfer samples is measured on all instruments involved. Usually, this is a small subset of the larger calibration set that has been measured on the parent instrument A. Let Z indicate the set of spectra for the transfer set, X the full set of spectra measured on the parent instrument and a suffix Aor B the instrument on which the spectra were obtained. The oldest approach to the calibration transfer problem is to apply the calibration model, b, developed for the parent instrument A using a large calibration set (X ), to the spectra of the transfer set obtained on each instrument, i.e. and Zg. One then regresses the predictions (=Z b ) obtained for the parent instrument on those for the child instrument yg (=Z b ), giving... 

So, overall the chemometrics bridge between the lands of the overly simplistic and severely complex is well under construction one may find at least a single lane open by which to pass. So why another series Well, it is still our labor of love to deal with specific issues that plague ourselves and our colleagues involved in the practice of multivariate qualitative and quantitative spectroscopic calibration. Having collectively worked with hundreds of instrument users over 25 combined years of calibration problems, we are compelled, like bees loaded with pollen, to disseminate the problems, answers, and questions brought about by these experiences. Then what would a series named Chemometrics in Spectroscopy hope to cover which is of interest to the readers of Spectroscopy ... 

The aim of multivariate calibration methods is to determine the relationships between a response y-variable and several x-variables. In some applications also y is multivariate. In this chapter we discussed many different methods, and their applicability depends on the problem (Table 4.6). For example, if the number m of x-variables is higher than the number n of objects, OLS regression (Section 4.3) or robust regression (Section 4.4) cannot be applied directly, but only to a selection... 

Multivariate calibrations are powerful tools, but the number and type of calibration samples required often is prohibitive. To overcome this problem, Pelletier employed a powerful but relatively uncommon tool, spectral stripping. This technique takes advantage of existing system knowledge to use spectra of fewer, more easily generated samples. More applications of this approach can be expected. 

Problems like overlapping and interfering of fluorophores is overcome by the BioView sensor, which offers a comprehensive monitoring of the wide spectral range. Multivariate calibration models (e.g., partially least squares (PLS), principal component analysis (PCA), and neuronal networks) are used to filter information out of the huge data base, to combine different regions in the matrix, and to correlate different bioprocess variables with the courses of fluorescence intensities. 

Although following discussion centers around the type of multivariate calibration psafalems found in Chapter 5. the concepts are applicable to a much broader range of problems. The following three questions can be used to initiate theefiscussions. 

Raw Measurement Plot In multivariate calibration, it is normally not necessary to plot the prediction data if the outlier detection technique has not flagged the sample as an outlier. However, with MLR, the outlier detection methods are not as robust as with the full-spectrum techniques (e.g., CLS, PLS, PCR) because few variables are considered. Figure 5.75 shows all of the prediction data with the variables used in the modeling noted by vertical lines. One sample appears to be unusual, with an extra peak centered at variable 140. The prediction of this sample might be acceptable because the peak is not located on the variables used for the models. However, it is still suspect because the new peak is not expected and can be an indication of other problems. 

The PLS approach to multivariate linear regression modeling is relatively new and not yet fully investigated from a theoretical point of view. The results with calibrating complex samples in food analysis 122,123) j y jnfj-ared reflectance spectroscopy, suggest that PLS could solve the general calibration problem in analytical chemistry. 

In ICP-OES, it has been observed that analyte lines with high excitation potentials are much more susceptible to suffer matrix effects than those with low excitation potentials. The effect seems to be related to the ionisation of the matrix element in the plasma, but in fact it is a rather complicated and far from fully characterised effect [8,9]. Therefore, calibration strategies must be carefully designed to avoid problems of varying sensitivity resulting from matrix effects. A possible approach may be to combine experimental designs and multivariate calibration, in much the same way as in the case study presented in the multivariate calibration chapters. 

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