Canonical variate models

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 More recently they have been superseded by the successful introduction of partial least squares analysis (PLS) in QSAR.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. 

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 methods of SIMCA, discriminant analysis and DPLS involve producing statistical models, such as principal components and canonical variates. Nearest neighbour methods are conceptually much simpler, and do not require elaborate statistical computations. 

The RBU model can be used to study the effect of exciting the vibrational modes treated within the model. For the reactions X (X=C1, 0 and H) + CH4 HX + CH3 we find that exciting a vibrational inode results in a lower threshold to reaction. It was also found that exciting the reactive C-H stretch enhances the reactivity more than exciting the CH4 umbrella mode. Vibrational enhancements for the umbrella and C-H stretch vibrations have also been found in other studies of the dynamics[75, 80] and in canonical variational transition state theory (C T) calculations [84]. Enhancement of the Cl + CH4 reaction due to vibrational excitation of the H-CH3 stretch has also been confirmed b experimental measurements by Zare and coworkers[85]. 

Canonical variates will be used in the formulation of subspace state-space models in Section 4.5. 

To include the information about process d3mamics in the models, the data matrix can be augmented with lagged values of data vectors, or model identification techniques such as subspace state-space modeling can be used (Section 4.5). Negiz and Cinar [209] have proposed the use of state variables developed with canonical variates based realization to implement SPM to multivariable continuous processes. Another approach is based on the use of Kalman filter residuals [326]. MSPM with dynamic process models is discussed in Section 5.3. The last section (Section 5.4) of the chapter gives a brief survey of other approaches proposed for MSPM. 

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

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. 

A Negiz and A Cinar. PLS, balanced and canonical variate realization techniques for identifying varma models in state space. Chemometrics Intell. Lah. Sys., 38 209-221, 1997. 

CVSS Canonical variate state space (models)... 

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.

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