Multivariate statistics variable-directed

At-line PAT data nsed directly without conversion back to the original variables space - e.g., MVI (Mnltivariate Identification), MSPC (multivariate statistical process control). 

The results of measurements carried out on surface samples collected during two oceanographic expeditions at the Terra Nova Bay were analyzed by a multivariate statistical approach. The Principal Components Analysis was used to observe association between variables and it showed an opposition between the Cd concentration (total and labile) and the ligand that complexes it (134). These results show that the metal speciation could affect its distribution. It, in particular, could emphasize the direct involvement of complexation in the transfer of Cd from the dissolved phase to the particulate affecting the total dissolved distribution. 

PCA is a method based on the Karhunen-Loeve transformation (KL transformation) of the data points in the feature space. In KL transformation, the data points in the feature space are rotated such that the new coordinates of the sample points become the linear combination of the original coordinates. And the first principal component is chosen to be the direction with largest variation of the distribution of sample points. After the KL transformation and the neglect of the components with minor variation of coordinates of sample points, we can make dimension reduction without significant loss of the information about the distribution of sample points in the feature space. Up to now PCA is probably the most widespread multivariate statistical technique used in chemometrics. Within the chemical community the first major application of PCA was reported in 1970s, and form the foundation of many modem chemometric methods. Conventional approaches are univariate in which only one independent variable is used per sample, but this misses much information for the multivariate problem of SAR, in which many descriptors are available on a number of candidate compounds. PCA is one of several multivariate methods that allow us to explore patterns in multivariate data, answering questions about similarity and classification of samples on the basis of projection based on principal components. 

Unlike other classification methods, the PLS-DA method explicitly determines relevant multivariate directions in the data (the PLS latent variables) that optimize the separation of known classes. Second, unlike KNN, the classification rule for PLS-DA is based on statistical analysis of the prediction values, which allows one to apply prior knowledge regarding the expected analytical response distributions of the different classes. Furthermore, PLS-DA can handle cases where an unknown sample belongs to more than one class, or to no class at all. 

Schlich et al. (1987) proposed a new approach to selecting variables in principal component analysis (PCA) and getting correlations between sensory and instrumental data. Among other studies, Wada et al. (1987a,b) evaluated 39 trade varieties of coffee by coupling gas chromatographic data with two kinds of multivariate analysis. The objective classification was compared with the sensory data (cup test), directly or after statistical treatment. The results were concordant. Murota (1993) used qualitative sensory data to interpret further the results of GC data and canonical discriminant analysis. He could thus suggest which were the components responsible for the flavor characteristics in different coffee cultivars. 

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