Discriminant Classification Methods

Alternatives to Multiple Linear Regression Discriminant Analysis, Neural Networks and Classification Methods... 

One of the powerful classification methods is multivariate variance and discriminant analysis (MVDA) (Dillon and Goldstein [1984] Ahrens and Lauter [1974] Danzer et al. [1984]). 

There are many classification methods apart from linear discriminant analysis (Derde et al. [1987] Frank and Friedman [1989] Huberty [1994]). Particularly worth mentioning are the SIMCA method (Soft independent modelling of class analogies) (Wold [1976] Frank [1989]), ALLOC (Coomans et al. [1981]), UNEQ (Derde and Massart [1986]), PRIMA (Juricskay and Veress [1985] Derde and Massart [1988]), DASCO (Frank [1988]), etc. 

Li-Xian Sim, Danzer K, Thiel G (1997) Classification of wine samples by means of artificial neural networks and discrimination analytical methods. Fresenius J Anal Chem 359 143... 

Two groups of objects can be separated by a decision surface (defined by a discriminant variable). Methods using a decision plane and thus a linear discriminant variable (corresponding to a linear latent variable as described in Section 2.6) are LDA, PLS, and LR (Section 5.2.3). Only if linear classification methods have an insufficient prediction performance, nonlinear methods should be applied, such as classification trees (CART, Section 5.4), SVMs (Section 5.6), or ANNs (Section 5.5). 

The main classification methods for drug development are discriminant analysis (DA), possibly based on principal components (PLS-DA) and soft independent models for class analogy (SIMCA). SIMCA is based only on PCA analysis one PCA model is created for each class, and distances between objects and the projection space of PCA models are evaluated. PLS-DA is for example applied for the prediction of adverse effects by nonsteroidal anti-... 

A number of PLS variants have been deployed, for instance, for developing nonlinear models and for predicting together several response variables (PLS-2). Furthermore, when category indices are taken as response variables, PLS may work as a classification method which is usually called PLS discriminant analysis (PLS-DA). 

So, the chemical direction discriminates Barolo from the other wines, the physical direction discriminates between Barbera and Grignolino. The classification ability of the selected variables is very good and probably some variables can be cancelled without noticeable loss of separation of the categories. Therefore, a small figure shows the relevant information given by a data matrix of 178 rows and 8 columns. Anyway, classification methods and feature selection methods will not modify the quality of these conclusions. 

These efforts to improve the classification ability by correction of the original LDA model with the use of graphical means that search for a better discriminant line are the prelude to the use of classification methods with separate class models the bayesian analysis. 

In the same way as linear discriminant analysis is the most-used classification method, stepwise selection by LDA (SLDA) is the selection method that shows the greatest number of applications in food chemistry. 

Discriminant analysis (DA) performs samples classification with an a priori hypothesis. This hypothesis is based on a previously determined TCA or other CA protocols. DA is also called "discriminant function analysis" and its natural extension is called MDA (multiple discriminant analysis), which sometimes is named "discriminant factor analysis" or CD A (canonical discriminant analysis). Among these type of analyses, linear discriminant analysis (LDA) has been largely used to enforce differences among samples classes. Another classification method is known as QDA (quadratic discriminant analysis) (Frank and Friedman, 1989) an extension of LDA and RDA (regularized discriminant analysis), which works better with various class distribution and in the case of high-dimensional data, being a compromise between LDA and QDA (Friedman, 1989). 

Questions of type (2.1) may be answered by analysis of variance or by discriminant analysis. All these methods may be found under the name supervised learning or supervised pattern recognition methods. In the sense of question (2.1.3) one may speak of supervised classification or even better of re-classification methods. In situations of type (2.2) methods from the large family of regression methods are appropriate. 

This supervised classification method, which is the most used, accepts a normal multivariate distribution for the variables in each population ((Ai,..., A ) Xi) ), and calculates the classification functions minimising the possibility of incorrect classification of the observations of the training group (Bayesian type rule). If multivariate normality is accepted and equality of the k covariance matrices ((Ai,..., Xp) NCfti, X)), Linear Discriminant Analysis (LDA) calculates... 

The most popular classification methods are Linear Discriminant Analysis (LDA), Quadratic Discriminant Analysis (QDA), Regularized Discriminant Analysis (RDA), K th Nearest Neighbours (KNN), classification tree methods (such as CART), Soft-Independent Modeling of Class Analogy (SIMCA), potential function classifiers (PFC), Nearest Mean Classifier (NMC) and Weighted Nearest Mean Classifier (WNMC). Moreover, several classification methods can be found among the artificial neural networks. 

Linear discriminant analysis (LDA) is a classification method that uses the distance between the incoming sample and the class centroid to classify the sample. For LDA using Mahalanobis distances, the classification metric uses the pooled variance-covariance matrix to weight the Mahalanobis distance ) between the incoming... 

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