Canonical Discriminate Analysis

In addition, a canonical discriminant analysis (CDA) was performed on the groups defined by the cluster analysis. This statistical procedure was performed to evaluate group differences as defined by the cluster analysis. CDA analysis assumes that the groups are different and calculates the largest difference between the groups (48). 

Figure 7. Canonical discriminant analysis plot (CD2 vs CD1) Samples are plotted by groups as determined by a cluster analysis.

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). 

Petrakis, P. N., Agiomyrgianaki, A., Christophoridou, S., Spyros, A., and Dais, P. (2008). Geographical characterization of Greek virgin olive oil (Cv. Koroneiki) using 1H and 31P NMR fingerprinting with canonical discriminant analysis and classification binary trees. J. Agric. Food Chem. 56, 3200-3207. 

Because of the difficulties associated with the Delphinium classification, the diterpene alkaloid content was assessed as an aid to determining the chemical taxonomic diversity of the toxic larkspur species [59]. Plant samples were collected from 18 different locations in five western states in the US. The crude methanolic extracts were analyzed for diterpene alkaloids using FI-ESI-MS. The data from the individual ESI mass spectra were statistically analyzed using canonical discriminant analysis and analysis of variance. In brief, the sample (100 mg) was extracted by mechanical shaking at room temperature with methanol (5mL) for 16h. Reserpine (500 p.g) was added as an internal reference standard and the sample mixed for 5 min and then centrifuged. An aliquot (30 jxL) of the supernatant was then diluted with of 1 1 methanol/1 % acetic acid (1.0 mL) and an aliquot (20 jjlL)... 

Figure 8.9 Plot of the canonic discriminant analysis carried out for mute and concentrated musts used for balsamic vinegar production from three Italian regions...

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). 

The artificial intelligence systems to which sensor arrays are coupled supply the closest likeness to the human olfactory system. Some of the recent theories on olfaction require that the human nose has only relatively few types of receptor, each with low specificity. The activation of differing patterns of these receptors supplies the brain with sufficient information for an odour to be described, if not recognized. As a consequence of this belief, the volatile chemical-sensing systems commercially available only contain from 6 to 32 sensors, each having relatively low specificity. Statistical methods such as principal component analysis, canonical discriminant analysis and Euclidian distances are used for mapping or linked to artificial neural nets as an aid to classification of the odour fingerprints . 

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. 

Murota A. (1993) Canonical discriminant analysis applied to the headspace GC profiles of coffee cultivars. Biosci. Biotech. Biochem. 57, 1043-8. 

FIGURE 17.39 Stepwise canonical discriminant analysis of biotic indicators measured along phosphorus gradient in WCA-2A. (From Corstanje et al., 2007.)... 

Multivariate data analysis (MDA) Principal component analysis (PCA), canonical discriminate analysis (CDA), featured within (FW) and cluster analysis (CA). 

D. Bertrand, P. Courcoux, J. -C. Autran, R. Meritan. Stepwise canonical discriminant analysis of continuous digitalized signals application to chromatograms of wheat proteins. J Chemometrics 4 413-428, 1990. 

Zhao G, Maclean AL (2000) A comparison of canonical discriminant analysis and principal component analysis for spectral transformation. Photogramm Eng Remote Sens 66 841-847 Hopfer H, Buffon PA, Ebeler SE, Heymann H (2013) The combined effects of storage temperature and packaging on the sensory, chemical, and physical properties of a cabernet sauvi-gnon wine. J Agric Food Chem 61 3320-3334... 

Friendly M, Fox J (2010) candisc generalized canonical discriminant analysis. R package Lemon J (2006) Plotrix a package in the red light district of R. R-News 6 8-12 Mevik B-H, Wehrens R (2007) The PLS package principal component and partial least squares regression. R. J Stat Softw 18 1-24... 

Plant respiratory properties are stable genetic traits that differ among species and to a lesser extent within species. Measurements of properties such as metabolic heat rates, COi rates, and energy efficiencies produce particular combinations of respiratory properties sufficiently unique to separate Eucalyptus species by canonical analysis of the respiratory variables [68-70]. Canonical discriminant analysis using the measured respiratory properties 0, Rqoi. 0IRcoi. and and... 

Figure 7. First and second canonical variables, CANl and CAN2, for respiration traits from 15 Eucalyptus species examined by canonical discriminant analysis. CANl is dominated by d> and while CAN2 is influenced more by / co2 and O/Rcoi- Each species has a distinct combination of respiratory parameters that gives rise to the separations shown. The dashed vertical line emphasizes the general separation of species in the two major Eucalyptus subgenera on the basis of the respiratory traits. Capital letters in this plot refer to Symphomyrtus species small letters refer to Monocalyptus species.

M. Kramer, P. J. Weldon, and J. F. Carroll, Composite scores for concurrent behaviours constructed using canonical discriminant analysis, J. Animal Behav., 11 763-768, 2009. 

---