Multivariate discriminative model

Two fundamentally different statistical approaches to biomarker selection are possible. With the first, experimental data can be used to construct multivariate statistical models of increasing complexity and predictive power - well-known examples are Partial Least Square Discriminant Analysis (PLS-DA) (Barker Rayens, 2003 Kemsley, 1996 Szymanska et al., 2011) or Principal Component Linear Discriminant Analysis (PC-LDA) (Smit et al., 2007 Werf et al., 2006). Inspection of the model coefficients then should point to those variables that are important for class discrimination. As an alternative, univariate statistical tests can be... 

A total of 185 emission lines for both major and trace elements were attributed from each LIBS broadband spectrum. Then background-corrected, summed, and normalized intensities were calculated for 18 selected emission lines and 153 emission line ratios were generated. Finally, the summed intensities and ratios were used as input variables to multivariate statistical chemometric models. A total of 3100 spectra were used to generate Partial Least Squares Discriminant Analysis (PLS-DA) models and test sets. 

All data obtained by these novel techniques require a very deep and multifaceted analysis, in order to check the principal and fundamentals variables and to reject the others. In this scenario, chemometrics provide scientists with useful tools to interpret the large amounts of data generated by these complex analytical assays and allows for quality control, classification procedures, modelling studies. Discrimination between different molecules available as novel drugs and molecules having no interesting biological activities is easy by means of multivariate analysis. 

The rate constants, thermodynamic parameters of activation, equilibrium constant, and the isomerization enthalpy for conversion of cholest-5-en-3-one to cholest-4-en-3-one catalysed by EtONa in absolute ethanol were determined by classic and multivariate kinetic methodologies. The multivariate modelling kinetic treatment allowed the concentrations of the species involved to be calculated, revealed the 3,5-dienolate to be a highly reactive intermediate, and was able to discriminate among several applicable mechanisms, thereby supporting the one comprising two reversible steps.18... 

Gombar, V.K. and K. Enslein. 1991. A structure-biodegradability relationship model by discriminant analysis. In J. Devillers and W. Karcher, Eds., Applied Multivariate Analysis in SAR and Environmental Studies, pp. 377-414. Kluwer Academic Publ., Dordrecht, Holland. 

Supervised learning methods - multivariate analysis of variance and discriminant analysis (MVDA) - k nearest neighbors (kNN) - linear learning machine (LLM) - BAYES classification - soft independent modeling of class analogy (SIMCA) - UNEQ classification Quantitative demarcation of a priori classes, relationships between class properties and variables... 

Multivariate Analysis of Variance and Discriminant Analysis, and PLS Modeling... 

The principle of multivariate analysis of variance and discriminant analysis (MVDA) consists in testing the differences between a priori classes (MANOVA) and their maximum separation by modeling (MDA). The variance between the classes will be maximized and the variance within the classes will be minimized by simultaneous consideration of all observed features. The classification of new objects into the a priori classes, i.e. the reclassification of the learning data set of the objects, takes place according to the values of discriminant functions. These discriminant functions are linear combinations of the optimum set of the original features for class separation. The mathematical fundamentals of the MVDA are explained in Section 5.6. 

Fig. 3.2 Typical applications using chemical multivariate data (schematically shown for 2-dimensional data) cluster analysis (a) separation of categories (b), discrimination by a decision plane and classification of unknowns (c) modelling categories and principal component analysis (d), feature selection (X2 is not relevant for category separation) (eY relationship between a continuous property Y and the features Xi and X2 (f)...

There are a large number of mediods for supervised pattern recognition, mostly aimed at classification. Multivariate statisticians have developed many discriminant functions, some of direct relevance to chemists. A classical application is the detection of forgery of banknotes. Can physical measurements such as width and height of a series of banknotes be used to identify forgeries Often one measurement is not enough, so several parameters are required before an adequate mathematical model is available. 

By doing this it is possible to make a multivariate analysis of the results and obtain information on the discrimination power of the different HTS models. 

There are many other statistical models which can be used for the evaluation of DICE studies. Inclusion of not only a group factor, but also a time factor in the experiment methods of the analysis of variance (ANOVA) can be applied to find expression changes within the temporal course of the protein expression or to find interactions between the group and time factor. Several multivariate statistical methods are of use, too. Spots with similar expression profiles can be grouped by cluster analysis or, on the other hand, new spots can be assigned to existing groups by the methods of discriminant analysis. 

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