Canonical variate analysis

Cluster analysis is far from an automatic technique each stage of the process requires many decisions and therefore close supervision by the analyst. It is imperative that the procedure be as interactive as possible. Therefore, for this study, a menu-driven interactive statistical package was written for PDP-11 and VAX (VMS and UNIX) series computers, which includes adequate computer graphics capabilities. The graphical output includes a variety of histograms and scatter plots based on the raw data or on the results of principal-components analysis or canonical-variates analysis (14). Hierarchical cluster trees are also available. All of the methods mentioned in this study were included as an integral part of the package. 

Lipopolysaccharide extracts from different pathogenic and nonpatho-genic . coli strains were also analyzed by FT-IR with principle component analysis and canonical variate analysis (Kim et al, 2006b). The data showed that E. coli strains can be discriminated with >95% accuracy. Listeria species were also reliably classified by FT-IR coupled with an artificial neural network technology with a success rate of 96% (Rebuffo et al, 2006), while the identification rate for L. monocytogenes alone was 99.2%. 

The use of a direct combined (or polyphasic) approach can create highly specific soil fingerprints from normal constituents. This, in addition to the application of appropriate statistical analysis, would make soil analysis a more effective tool for routine forensic work, thus considerably extending its applicability. Indeed, combinations of different data each with its own discriminatory potential may result in probabilities of association or disassociation that even surpass those of techniques such as human DNA. Initial work using a canonical variate analysis has shown discrimination between soil types can be improved by including more analytical data. Figure 11.11 illustrates... 

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. 

The degree of methylation (DM) of pectin [60] can be estimated using a Py-MS technique. The application of principal component analysis and canonical variate analysis to the Py-MS data (see Section 5.5) showed a linear relationship between DM and the first canonical variate score of the data as shown in Figure 7.5.3. 

The chemometric methods discussed above have found widespread applications in chromatography, and many theoretical and practical chromatographers have become familiar with these techniques and have applied them successfully. However, other less well-known methods have also found applicability in the analysis of chromatographic retention data. Thus, canonical variate analysis has been applied in pyrolysis GC-MS, artificial neural network for the prediction of GLC retention indices, and factor analysis for the study of the retention behavior of A-benzylideneaniline derivatives. 

BC Juricek, DE Seborg, and WE Larimore. Fault detection using canonical variate analysis. Ind. Engg. Chem. Research, 43 458-474, 2004. 

WE Larimore. System identification, reduced-order filtering and modeling via canonical variate analysis. In Proc. of Automatic Control Conf, page 445, 1983. 

WE Larimore. Canonical variate analysis in identification, filtering, and adaptive control. In Proc. of IEEE Conf. on Decision and Control, page 596, 1990. 

WE Larimore. Identification and filtering of nonlinear systems using canonical variate analysis. In Nonlinear Modeling and Forecasting Proc of the Workshop on Nonlinear Modeling and Forecasting, Santa Fe, NM, Vol 12. Addison-Wesley, 1990. 

Rui Alves, M. and Oliveira, M.B. (2004) Predictive and interpolative biplots applied to canonical variate analysis in the discrimination of vegetable oils by dieir fatty add composition. J. Chemom., 18, 393-401. 

Discriminant function analysis. Discriminant function analysis (DFA) which is also referred to as canonical variates analysis is here the chosen cluster analysis method. DFA is usually used in a supervised mode, but can also be used in an unsupervised way. Here, the unsupervised mode is enabled by direct usage of the replicate information of object samples as classes. The effect of using DFA in this way is that it will reduce the within-replicate-group variance. DFA is in many ways similar to PCA. However, the... 

Canonical Correlation Analysis. Our method of canonical variate analysis uses factor scores as input. Since using the minimum number of data reduction factors (eigenvalue > 1.0, 1 in the PMR data) constrained the CV space to too low a dimensionality to take full advantage of all the data, the first 6 factors from each data set were used. It can be seen from the last colvimn of Table II that the PMR data input contained more factors than were significant, and that the MS data used somewhat too few factors (6 out of 9) based on the eigenvalue criterion. Table III shows the canonical variate... 

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. 

Principal components analysis is a well-established multivariate statistical technique that can be used to identify correlations within large data sets and to reduce the number of dimensions required to display the variation within the data. A new set of axes, principal components (PCs), are constructed, each of which accounts for the maximum variation not accounted for by previous principal components. Thus, a plot of the first two PCs displays the best two-dimensional representation of the total variance within the data. With pyrolysis mass spectra, principal components analysis is used essentially as a data reduction technique prior to performing canonical variates analysis, although information obtained from principal components plots can be used to identify atypical samples or outliers within the data and as a test for reproducibihty. 

However, the application of statistical techniques to urine head-space volatile profiles obtained from two cows over two complete cycles discriminated reproducibly between profiles obtained at different stages of the estrous cycle (Morgans, 1984). Data from 49 normalized peak areas from 83 chromatograms on canonical variates analysis (MacFie et al.,... 

Figure 2 Second principal component loadings versus wavelength plot of a set of 25 components used for canonical variates analysis of orange juice NIR reflectance spectra.

The technique chosen to perform the analysis was canonical variates analysis. Briefly, the method abstracts functions from combinations of PCs. It has been found with large sample sets ( 100 or more) that up to 25 PCs give optimal predictive ability. It is unwieldy to select the predictively important analytes from 25 PC dimensions. For this reason the PC-derived canonical varieties are computed wherein the dimensions available are one less than the munber of ascribed characteristics or groups. In the example noted above, therefore, the two CVs describe the 25 PC dimensions, since there are three groups in the analysis. In this example, a calibration discriminant analysis was calculated using 71 samples, and 23 prediction samples were used to test the calibration. Figure 6 illustrates the two-dimensional CVs calibration and prediction. 

Rgure 4 Canonical variates analysis of tea extract data. (Reprinted with permission from Vorhees KJ (ed.) (1994) Analytical Pyrolysis Techniques and Applications. London Butterworths Elsevier.)... 

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