Application of linear discriminant analysis

D. Coomans, M. Jonckheer, D.L. Massait, I. Broeckaert and P. Blockx, The application of linear discriminant analysis in the diagnosis of thyroid diseases. Anal. Chim. Acta, 103 (1978) 409-415. 

The application of linear discriminant analysis of the 16 amino acids foimd in Spanish honeys established both botanical and geographical differences (Perez Arquillue and Herrera Marteache, 1987). Gas chromatography (GC) analyses of free amino acids showed obvious differences when honey samples from the UK, Argentina, Australia, and Canada were compared (Gilbert et al., 1981). Pawlowska and Armstrong (1994)... 

Estevez Diaz-Flores JF, Estevez Diaz-Flores F, Calzadillo Hernandez C, Rodrigrez Rodrigrez EM, Romero Diaz C, Serra-Majem L. Application of linear discriminant analysis to the biochemical and haematological differentiation of opiate addicts from healthy subjects a case-controlled study. Eur J Clin Nutr 2004 58 449-55. 

Clarke, J.U. (1998). Evaluation of censored data methods to allow statistical comparisons among very small samples with below detection limits observations. Environmental Science Technology. Vol. 32, pp. 177-183. ISSN 1520-5851 Cole, R.A. Phelps, K. (1979). Use of canonical variate analysis in the differentiation of swede cultivars by gas-liquid chromatography of volatile hydrolysis products. Journal of the Science of Food and Agriculture. Vol. 30, pp. 669-676. ISSN 1097-0010 Coomans, D. Broeckaert, L Fonckheer, M Massart, D.L. Blocks, P. (1978). The application of linear discriminant analysis in the diagnosis of thyroid diseases. Analytica Chimica Acta. Vol. 103, pp. 409-415. ISSN 0003-2670 Coomans, D. Massart, D.L. Kaufman, L. (1979) Optimization by statistical linear discriminant analysis in analytical chemistry. Analytica Chimica Acta. Vol. 112, pp. 97-122. ISSN 0003-2670... 

Nevertheless, in most of the electronic tongue applications found in the literature, classification techniques like linear discriminant analysis (LDA) and partial least squares discriminant analysis (PLS-DA) have been used in place of more appropriate class-modeling methods. Moreover, in the few cases in which a class-modeling technique such as soft independent modeling of class analogy (SIMCA) is applied, attention is frequently focused only on its classification performance (e.g., correct classification rate). Use of such a restricted focus considerably underutilizes the significant characteristics of the class-modeling approach. 

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. 

They employed principal components analysis (PCA) and linear discriminant analysis (LDA) to distinguish the two types of polyps. The spectra (Fig. 2.9) have bands at similar wave numbers and their features are similar, making it difficult for the untrained eye to distinguish between them. The application illustrates the importance of multivariate analysis in clinical applications of Raman spectroscopy. It is often the case that there are only small differences between normal and diseased tissues. 

To establish a correlation between the concentrations of different kinds of nucleosides in a complex metabolic system and normal or abnormal states of human bodies, computer-aided pattern recognition methods are required (15, 16). Different kinds of pattern recognition methods based on multivariate data analysis such as principal component analysis (PCA) (8), partial least squares (16), stepwise discriminant analysis, and canonical discriminant analysis (10, 11) have been reported. Linear discriminant analysis (17, 18) and cluster analysis were also investigated (19,20). Artificial neural network (ANN) is a branch of chemometrics that resolves regression or classification problems. The applications of ANN in separation science and chemistry have been reported widely (21-23). For pattern recognition analysis in clinical study, ANN was also proven to be a promising method (8). 

For most applications in the "omics" fields, even the most simple multivariate techniques such as Linear Discriminant Analysis (LDA) cannot be applied directly. From Equation 2 it is clear that an inverse of the the covariance matrix 2 needs to be calculated, which is impossible in cases where the number of variables exceeds the number of samples. In practice, the number of samples is nowhere near the number of variables. For QDA, the situation is even worse to allow a stable matrix inversion, every single class should have at least as many samples as variables (and preferably quite a bit more). A common approach is to compress the information in the data into a low number of latent variables (LVs), either using PCA (leading... 

CE has also been successfully apphed to the study of muscle proteins, and some of these applications have been recently reviewed. - - Methods for the determination of muscle proteins were based on CZE, SDS-CE, or isoelectric focusing (CEIF). Meat species identification was carried out by analyzing sarcoplasmic or myofibrillar proteins by a replaceable polymer-filled SDS-CE method (Table 30.8). However, the analysis of sarcoplasmic protein profiles allowed better differentiation among beef, pork, and turkey meat (Figure 30.8). The importance of sample preparation in the established method was highlighted since sarcoplasmic proteins extracted by simply homogenizing meat with cold bidistilled water were most useful for meat species identification when protein profiles were examined by linear discriminant analysis. On the other hand, myofibrillar proteins extracted with 0.6 M NaCl/0.01 M phosphate buffer with 0.5% polyphosphates (pH 6.0) were not useful for raw meat species identification, although they may be of importance in the identification of heat-processed meats. ... 

Table 6.2 Diagnostic Pattern Recognition (DPR) in various applications (R-LDA, robust linear discriminant analysis LDA, linear discriminant analysis QDA, quadratic discriminant analysis RDA, regularised discriminant analysis ANN, artificial neural network PCA, principal component analysis SVM, support vector machine Nteach. number of teaching samples Npara, number of parameters used for classification (principal components etc)-, ratio, Nteach/Nparal Nvai, number of independent validation samples SE, sensitivity SP, specificity LOO, leave-one-out validation. AMI,... 

The first phase of data evaluation was to determine plasma concentration of sterols analyzed as described earlier. The standard addition method was used, calibration curves were constructed, and plasma sterol concentrations were determined. The second phase of data evaluation was to look for characteristic biomarkers and separate patient groups based on sterol concentrations. This was done by applying chemometrics (e.g., linear discriminant analysis) with sufficient validation. It was found that sterol concentration ratios are much more characteristic disease markers than the individual concentrations. Eor example, the concentration ratio of desmosterol to sitosterol was a much better marker of cholesterol-related disorders than the cholesterol concentration itself, and the concentration ratio of lathosterol to total plasma cholesterol was an excellent marker of statin treatment. Application of these analytical results by biochemists and medical doctors will hopefully result in better treatment of patients. 

Discriminant Analysis. Discriminant analysis is used to model a categorical response to a variable, for example, a flavor or treatment grouping, as a linear function of two or more predictors. Powers and Keith (27) published one of the earliest papers on the use of stepwise discriminant analysis (SDA) for gas chromatographic data. They were able to classify coffees using this technique. Other applications include work on wine classification (22) and sweet potato classification (25). 

Roth, V., Steinhage, V., Schroder, S. and Cremers, A. B. (1999b) Pattern recognition combining de-noising and linear discriminant analysis within a real world application. 8 International Conference on Computer Analysis of Images and Patterns, Ljubljana, pp. 251-266. 

Such definitive classification may be achieved with the aid of multivariate pattern recognition techniques such as hierarchical clustering, linear discriminant analysis (LDA) and artificial neural network analysis. Hierarchical clustering techniques compare sets of data (e.g. individually acquired spectra or spectra acquired by mapping of tissue) and group the data according to some measure of similarity. For mapping data, the application of cluster analysis... 

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