Instrumental data sets, multivariate methods

Beilken et al. [ 12] have applied a number of instrumental measuring methods to assess the mechanical strength of 12 different meat patties. In all, 20 different physical/chemical properties were measured. The products were tasted twice by 12 panellists divided over 4 sessions in which 6 products were evaluated for 9 textural attributes (rubberiness, chewiness, juiciness, etc.). Beilken etal. [12] subjected the two sets of data, viz. the instrumental data and the sensory data, to separate principal component analyses. The relation between the two data sets, mechanical measurements versus sensory attributes, was studied by their intercorrelations. Although useful information can be derived from such bivariate indicators, a truly multivariate regression analysis may give a simpler overall picture of the relation. 

In the resolution of any multicomponent system, the main goal is to transform the raw experimental measurements into useful information. By doing so, we aim to obtain a clear description of the contribution of each of the components present in the mixture or the process from the overall measured variation in our chemical data. Despite the diverse nature of multicomponent systems, the variation in then-related experimental measurements can, in many cases, be expressed as a simple composition-weighted linear additive model of pure responses, with a single term per component contribution. Although such a model is often known to be followed because of the nature of the instrumental responses measured (e.g., in the case of spectroscopic measurements), the information related to the individual contributions involved cannot be derived in a straightforward way from the raw measurements. The common purpose of all multivariate resolution methods is to fill in this gap and provide a linear model of individual component contributions using solely the raw experimental measurements. Resolution methods are powerful approaches that do not require a lot of prior information because neither the number nor the nature of the pure components in a system need to be known beforehand. Any information available about the system may be used, but it is not required. Actually, the only mandatory prerequisite is the inner linear structure of the data set. The mild requirements needed have promoted the use of resolution methods to tackle many chemical problems that could not be solved otherwise. 

As manufacturing processes have become increasingly instrumented in recent years, more variables are being measured and data are being recorded more frequently. This yields data overload, and most of the useful information may be hidden in large data sets. The correlated or redundant information in these process measurements must be refined to retain the essential information about the process. Process knowledge must be extracted from measurement information, and presented in a form that is easy to display and interpret. Various methods based on multivariate statistics, systems theory and artificial intelligence are presented in this chapter for data-based input-output model development. 

Multivariate data in chemistry often contain a rather large number of features. The reasons for this situation are as follows (a) a priori it is not known which features are relevant and which are irrelevant remember that systems are usually investigated by statistical methods that are not understood sufficiently (b) automated analytical instruments easily allow the production of large data sets (c) typical chemical data like for instance molecular spectra or the description of chemical structures are complex and therefore actually require many features. 

This method can be considered a calibration transfer method that involves a simple instrument-specific postprocessing of the calibration model outputs [108,113]. It requires the analysis of a subset of the calibration standards on the master and all of the slave instmments. A multivariate calibration model built using the data from the complete calibration set obtained from the master instrument is then applied to the data of the subset of samples obtained on the slave instruments. Optimal multiplicative and offset adjustments for each instrument are then calculated using linear regression of the predicted y values obtained from the slave instrument spectra versus the known y values. 

During the last two or three decades, chemists became used to the application of computers to control their instruments, develop analytical methods, analyse data and, consequently, to apply different statistical methods to explore multivariate correlations between one or more output(s) (e.g. concentration of an analyte) and a set of input variables (e.g. atomic intensities, absorbances). 

During the last two or three decades atomic spectroscopists have become used to the application of computers to control their instruments, develop analytical methods, analyse data and, consequently, to apply different statistical methods to explore multivariate correlations between one or more output(s) e.g. concentration of an analyte) and a set of input variables e.g. atomic intensities, absorbances). On the other hand, the huge efforts made by atomic spectroscopists to resolve interferences and optimise the instrumental measuring devices to increase accuracy and precision have led to a point where many of the difficulties that have to be solved nowadays cannot be described by simple univariate linear regression methods (Chapter 1 gives an extensive review of some typical problems shown by several atomic techniques). Sometimes such problems cannot even be addressed by multivariate regression methods based on linear relationships, as is the case for the regression methods described in the previous two chapters. 

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