Principal component analysis food data

Chemists and statisticians use the term mixture in different ways. To a chemist, any combination of several substances is a mixture. In more formal statistical terms, however, a mixture involves a series of factors whose total is a constant sum this property is often called closure and will be discussed in completely different contexts in the area of scaling data prior to principal components analysis (Chapter 4, Section 4.3.6.5 and Chapter 6, Section 6.2.3.1). Hence in statistics (and chemometrics) a solvent system in HPLC or a blend of components in products such as paints, drugs or food is considered a mixture, as each component can be expressed as a proportion and the total adds up to 1 or 100%. The response could be a chromatographic separation, the taste of a foodstuff or physical properties of a manufactured material. Often the aim of experimentation is to find an optimum blend of components that tastes best, or provide die best chromatographic separation, or die material diat is most durable. 

Chemometrics is a branch of science and technology dealing with the extraction of useful information from multidimensional measurement data using statistics and mathematics. It is applied in numerous scientific disciplines, including the analysis of food [313-315]. The most common techniques applied to multidimensional analysis include principal components analysis (PCA), factor analysis (FA), linear discriminant analysis (LDA), canonical discriminant function analysis (DA), cluster analysis (CA) and artificial neurone networks (ANN). 

Among the different chemometric methods, exploratory data analysis and pattern recognition are frequently used in the area of food analysis. Exploratory data analysis is focused on the possible relationships between samples and variables, while pattern recognition studies the behavior between samples and variables [95]. Principal component analysis (PCA) and partial least-squares discriminant analysis (PLS-DA) are the methods most commonly used for exploratory analysis and pattern recognition, respectively. The importance of these statistical tools has been demonstrated by the wide number of works in the field of food science where they have been applied. The majority of the applications are related to the characterization and authentication of olive oil, animal fats, marine and vegetable oils [95], wine [97], fruit juice [98], honey [99], cheese [100,101], and so on, although other important use of statistical tools is the detection of adulterants or frauds [96,102]. 

This book contains several different NIR applications in food analysis, and many of them use multivariate data handling. Our aim in this chapter is to discuss the aspects of latent variable decomposition in principal component analysis and partial least squares regression and to illustrate their use by an application in the NIR region. 

The types of statistieal analytical methods required in this application are often multivariate methods. These statistical procedures are called multivariate when the property being measured, for example, the location of the food, is being related to several variables (such as the signal levels in different miz channels) in the analysis. Multivariate statistical methods can be broadly divided into two types (1) unsupervised, which means that no a priori knowledge of the samples to be classified is required and (2) supervised, which requires a priori knowledge about the samples [18]. A good example of an unsupervised method is principal component analysis (PCA) [19-27], which looks for patterns in a block of data that depend on different variables. PCA provides a useful tool to explore and visualize information, and in particular to identify patterns in complex data, and it is therefore widely used. Applications of PCA in food science will be presented later in this chapter. 

J. Brahms, J. Masters, J. Labows, and M. Prencipe, Investigation of the interaction between dentifrice flavor and product base by principal component analysis of head-space-GC data, Flavor-Food Interactions (J. Leland and R. McGorrin, eds.), ACS Symposium Series 633, 1996, pp. 188—200. 

Because of peak overlappings in the first- and second-derivative spectra, conventional spectrophotometry cannot be applied satisfactorily for quantitative analysis, and the interpretation cannot be resolved by the zero-crossing technique. A chemometric approach improves precision and predictability, e.g., by the application of classical least sqnares (CLS), principal component regression (PCR), partial least squares (PLS), and iterative target transformation factor analysis (ITTFA), appropriate interpretations were found from the direct and first- and second-derivative absorption spectra. When five colorant combinations of sixteen mixtures of colorants from commercial food products were evaluated, the results were compared by the application of different chemometric approaches. The ITTFA analysis offered better precision than CLS, PCR, and PLS, and calibrations based on first-derivative data provided some advantages for all four methods. ... 

Under the Food Quality Protection Act (FQPA), the U.S. EPA evaluates the potential for people to be exposed to more than one pesticide at a time from a group of chemicals with an identified common mechanism of toxicity. As part of the examinations, to clarify whether some or all of the pyrethroids share a common mechanism of toxicity, a comparative FOB (functional observational battery) studies with 12 pyrethroids were carried out under standardized conditions [15]. The FOB was evaluated at peak effect time following oral administration of non-lethal doses of pyrethroids to rats using com oil as vehicle. Four principal components were observed in the FOB data [22], Two of these components described behaviors associated with CS syndrome (lower body temperature, excessive salivation, impaired mobility) and the others described behaviors associated with the T syndrome (elevated body temperature, tremor myoclonus). From the analysis, pyrethroids can be divided into two main groups (Type I T syndrome and Type II CS syndrome) and a third group (Mixed Type) that did not induce a clear typical response. Five other pyrethroids were also classified by an FOB study conducted in the same manner [16]. The results of these classifications are shown in Table 1. The FOB results for all non-cyano pyrethroids were classified as T syndrome, and the results of four ot-cyano pyrethroids were classified as CS syndrome however, three of the ot-cyano pyrethroids, esfenvalerate, cyphenothrin, and fenpropathrin, were classified as Mixed Type. 

Chemometrics is an essential part of NIR and Vis/NIR spectroscopy in food sector. NIR and Vis/NIR instrumentation in fact must always be complemented with chemometiic analysis to enable to extract useful information present in the sp>ectra separating it both from not useful information to solve the problem and from sp>ectral noise. Chemometric techniques most used are the princip)al component analysis (PCA) as a technique of qualitative analysis of the data and PLS regression analysis as a technique to obtain quantitative prediction of the parameters of interest (Naes et al., 2002 Wold et al., 2001 Nicolai et al., 2007 Cen He, 200 . ... 

More sophisticated statistical treatments of sensory data have been more commonly applied in studies of multiple factors of Upid oxidation on quality of foods, including Multivariate and Principal Component analyses. These procedures attempt to simplify complex relationships of several factors and sets of data into more understandable levels. Multivariate analysis is based on the fact that one measured property generally depends on more than one factor and the classical statistical univariate methods dealing with just one variable at a time are inadequate to analyse complex data. 

Mass spectrometry and chemometric methods cover very diverse fields Different origin of enzymes can be disclosed with LC-MS and multivariate analysis [45], Pyrolysis mass spectrometry and chemometrics have been applied for quality control of paints [46] and food analysis [47], Olive oils can be classified by analyzing volatile organic hydrocarbons (of benzene type) with headspace-mass spectrometry and CA as well as PC A [48], Differentiation and classification of wines can similarly be solved with headspace-mass spectrometry using unsupervised and supervised principal component analyses (SIMCA = soft independent modeling of class analogy) [49], Early prediction of wheat quality is possible using mass spectrometry and multivariate data analysis [50],... 

Heymann H, Noble AC (1989) Comparison of canonical variate and principal analyses of wine descriptive analysis component data. J Food Sci 54 1355 1358... 

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