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in PCA-plots. The combination of a chromatographic fingerprint with PCA and CA is a powerful tool for assessing herbal products quality, or for selecting the best cultivars, on the basis of the preferred properties. For example, HPLC-DAD in combination with PCA and CA was used for quantification of several bioactive compounds (cinnamic acids, flavonols, monoterpenes, benzoic acids, chatechins, organic acids and vitamins) from the different cultivars of raspberry’s buds [179].

      Many studies include supervised methods applied to discriminate samples from different regions or different botanical origin. Partial least squares discriminant analysis (PLS-DA) is the most used supervised method. PLS-DA is a variation of PLS regression analysis, which is a supervised method related to PCA. For example, UV-spectroscopy and ultra-fast liquid chromatography (UFLC) were used as PLS-DA input to discriminate five samples from two different parts of mushrooms [181].

      Another supervised method considered to classify similar samples is linear discriminant analysis (LDA). LDA searches for directions with maximum separation among the classes. LDA was used by Valdés et al. [181] to classify seven cultivars of almonds analyzing their skin, which is a by-product from almond manufacture. TPC, antioxidant activity and flavonoid content were used as input variables for LDA and a good classification was achieved using two factors [181].

      In addition, MVA could be applied for monitoring a process involving a change into the bioactive compounds profile. For example, FT-NIR coupled to PCA and LDA was used as a characterization method for fortified fermented milk with two sources of antioxidants (grape and olive pomaces by-products). PCA was used to eliminate outliers from the original data set and LDA was used as a classification tool and a variable selection method [182]. In another example, pork sausages were enriched with two concentrations of polyphenols and physiochemically and microbiologically monitored during 14 days of storage. In this case PCA and PLS-DA determined matches among samples [183].

      Spectroscopy could be typically coupled with MVA to monitoring different processes. For example, in commercial production of wines the use of the correct yeast strain is critical. Moore et al. [184], studied the composition of 40 yeast strains inoculated into grape must and analyzed them using FT-MIR using PCA, OPLS-DA. PCA-plot allowed discrimination of strains from laboratory and industrial strains. By OPLS-DA a better classification of the samples into the two target groups could be performed, caused by the modifications induced to cell wall structure in the selection processes of yeast domestication [184].

      The authenticity of a product or an ingredient is of outmost relevance in several industries in order to cover legal aspects and favor economic performance. PLS-DA was applied to FT-MIR spectroscopy to classify samples of adulterated rosehip oil with others lowly economical edible oils (soybean, corn and sunflower). The results show an excellent separation of the samples, including adulterations with a proportion of 5% of non-rosehip oils [185].

An emerging area of interest for analysis of the bioactive compounds could be done using metabolome studies [186]. Metabolomics comprises the quantitative determination of intracellular metabolites, for which after the separative steps mass spectrometry (MS) and/or nuclear magnetic resonance spectroscopy (NMR) [187] are frequently employed. Considering the complexity of MS and NMR data, multivariate analysis is commonly used to recognize compositional differences among samples [188]. Bhatia et al. [189], analyzed the metabolic profile from five different extracts of fruit, leaves, latex, stem and roots of Commifora wightii by means of GC-MS and NMR. 118 chemically diverse metabolites were identified and the outcomes were used in PCA and PLS-DA to discriminate and classify, respectively, the extracts from those several parts of the plant. PCA and loading analysis showed that the cluster separation could be attributed to the several different bioactive compounds [189].

Table 2.4 summarizes the multivariate methods described before.

The use of MVA is an increasing and is a useful strategy used by many authors to discriminate raw materials and products and their profile change during processes or storage of bioactive compounds. There are many choices for discrimination or classification problems, and emergent or new methods also could be performed. There are some important considerations before and after the use of a multivariate method. An appropriate selection of MVA method is crucial and this is not trivial. If the user needs only a similarity grouping, unsupervised methods are a good choice, because their simplicity and capacity to reduce the dimensionality of the data. In that case, PCA and CA are mainly the most popular methods used. In the other hand, supervised methods require a major number of samples. There is an advantage of using supervised methods over unsupervised ones, which is, the firsts use the information of the class for each sample, and in consequence would be a better separation of the data set. The second consideration is to verify that the number of components or functions chosen to group or classify the samples accounts for a large amount of data total variance. The lower the total variance accumulated, the poorest the resolution of the grouping or classification. Finally, it is useful to search for original variables correlations and the relation of these original variables with latent variables or functions.

Table 2.4 Use of multivariate analysis as a tool to discriminate bioactive compounds profiles for different fields.

Area of interest	Product	Analytical technique	Multivariate method	Refs.
Unsup.	Sup.
Geographical discrimination	Propolis	RP-HPTLC DART-MS	PCA		[177]
Botanical discrimination	Wheat grains	GC-FID TPC DPPH	PCA		[178]
Botanical discrimination	Raspeberry buds	HPLC-DAD	PCA, CA		[179]
Geographical discrimination	Mushrooms	UV–spectroscopy UFLC	HCA	PLS-DA	[180]
Botanical discrimination By-product exploitation	Almonds skin	TPC HPLC-MS		LDA	[181]
Monitoring a food process By-product exploitation	Fermented milk (fortified with olive and grape by-products)	FT-NIR	PCA	LDA	[182]
Monitoring a food process By-product exploitation	Sausage fortification with olive by-product	GC–MS		PLS-DA	[183]
Monitoring changes in yeasts during wine fermentation	Yeasts from wine fermentation	FT-MIR	PCA	PLS-DA OPLS-DA	[184]
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