Linear discriminant analysis canonical variate

Fig. 33.1. Canonical variate plot for three classes with different thyroid status. The boundaries are obtained by linear discriminant analysis [2].

While principal components models are used mostly in an unsupervised or exploratory mode, models based on canonical variates are often applied in a supervisory way for the prediction of biological activities from chemical, physicochemical or other biological parameters. In this section we discuss briefly the methods of linear discriminant analysis (LDA) and canonical correlation analysis (CCA). Although there has been an early awareness of these methods in QSAR [7,50], they have not been widely accepted. More recently they have been superseded by the successful introduction of partial least squares analysis (PLS) in QSAR. Nevertheless, the early pattern recognition techniques have prepared the minds for the introduction of modem chemometric approaches. 

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... 

Fourier transform mid-infrared (FTIR), near-infrared (FTNIR), and Raman (FT-Raman) spectroscopy were used for discrimination among 10 different edible oils and fats, and for comparing the performance of these spectroscopic methods in edible oil/fat studies. The FTIR apparatus was equipped with a deuterated triglycine sulfate (DTGS) detector, while the same spectrometer was also used for FT-NIR and FT-Raman measurements with additional accessories and detectors. The spectral features of edible oils and fats were studied and the unsaturation bond (C=C) in IR and Raman spectra was identified and used for the discriminant analysis. Linear discriminant analysis (LDA) and canonical variate analysis (CVA) were used for the disaimination and classification of different edible oils and fats based on spectral data. FTIR spectroscopy measurements in conjunction with CVA yielded about 98% classification accuracy of oils and fats followed by FT-Raman (94%) and FTNIR (93%) methods however, the number of factors was much higher for the FT-Raman and FT-NIR methods. 

The most frequently used supervised pattern recognition method is the linear discriminant analysis (LDA), not to be confused with its twin brother canonical correlation analysis (CCA) or canonical variate analysis (CVA). Recently, classification and regression trees (CART) produced surprisingly good results. Artificial neural networks (ANNs) can be applied for both prediction and pattern recognition (supervised and unsupervised). 

Fig. 1. Pattern recognition methods. ANN, artificial neural networks BP ANN, back-propagation ANN CA, cluster analysis CART, classification and regression trees (recursive partitioning) CCA, canonical correlation analysis CVA, canonical variate analysis kNN, -nearest neighbor methods LDA, linear discriminant analysis PCA, principal component analysis PLS DA, partial least squares regression discriminant analysis SIMCA, soft independent modeling of class analogy SOM, self-organizing maps.

Most traditional approaches to classification in science are called discriminant analysis and are often also called forms of hard modelling . The majority of statistically based software packages such as SAS, BMDP and SPSS contain substantial numbers of procedures, referred to by various names such as linear (or Fisher) discriminant analysis and canonical variates analysis. There is a substantial statistical literature in this area. 

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