**1. Introduction**

48 Principal Component Analysis

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PCA is one of the most widely employed and useful tools in the field of exploratory analysis. It offers a general overview of the subject in question, showing the relationship that exists among objects as well as between objects and variables.

An important application of PCA consists of the characterization and subsequent differentiation of products in relation to their origin (known as traceability). PCA is often applied in order to characterize some products obtained via a manufacturing process and the transformation of some raw materials. In this case, there are two kinds of elements linkable to the differentiation of products in relation to their origin: the variability associated to the raw material and the differences in various production techniques used around the world. In this study, two examples of PCA application to some products obtained via a manufacturing process are presented. These products, belonging to completely different fields (foodstuffs and petroleum based fuel) show one element in common: their traceability is correlated to the raw material and the production process.

The strength of PCA is that it provides the opportunity to visualize data in reference to objects described by more than 3 variables. Indeed, PCA allows us to study and understand such systems, helping the human eye to see in two or three dimension systems that otherwise would necessarily have to be seen in more than three dimensions in order to be studied. PCA allows data to maintain their original structure, making only an orthogonal rotation of variables, which helps to simplify the visualization of all the information already contained in the data. Consequently, PCA can be considered the best technique to begin to approach any qualitative multivariate problem, be it unsupervised or supervised. Needless to say, supervised problems - following a primary study by PCA - require the application of either a classification or a class modeling method. In this study, three cases regarding supervised problems which involved the preliminary application of PCA are put forward. Results from PCA have been compared to those obtained from classification or class modeling tools.

Principal Component Analysis: A Powerful

Fig. 1. Score plot of PC2 versus PC1 for milk samples.

and 83% of variance for mozzarella samples.

samples.

Interpretative Tool at the Service of Analytical Methodology 51

Tables 1 and 2 show variances and cumulative variances associated to the principal components with eigenvalues greater than 1 for milk and mozzarella samples respectively. 4 PCs were extracted for both data set, which explain 86% of the variance for milk samples

PC Variance % Cumulative %

Table 1. PCs with eigenvalues greater than 1, extracted applying PCA to milk samples.

PC Variance % Cumulative %

1 35.95 35.95

2 20.45 56.40 3 15.10 71.50

4 11.83 83.33

Table 2. PCs with eigenvalues greater than 1, extracted applying PCA to mozzarella

1 40.23 40.23 2 20.93 61.16 3 13.57 74.73 4 11.33 86.06
