Linear discriminant analysis recognition techniques

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 More recently they have been superseded by the successful introduction of partial least squares analysis (PLS) in QSAR.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

Current methods for supervised pattern recognition are numerous. Typical linear methods are linear discriminant analysis (LDA) based on distance calculation, soft independent modeling of class analogy (SIMCA), which emphasizes similarities within a class, and PLS discriminant analysis (PLS-DA), which performs regression between spectra and class memberships. More advanced methods are based on nonlinear techniques, such as neural networks. Parametric versus nonparametric computations is a further distinction. In parametric techniques such as LDA, statistical parameters of normal sample distribution are used in the decision rules. Such restrictions do not influence nonparametric methods such as SIMCA, which perform more efficiently on NIR data collections. 

Na and K) employing different pattern recognition techniques [PCA, linear discriminant analysis (LDA) and ANNs], ANNs were trained by an error back-propagation algorithm and they were found to be very efficient for classifying and discriminating food products. 

The data processing of the multivariate output data generated by the gas sensor array signals represents another essential part of the electronic nose concept. The statistical techniques used are based on commercial or specially designed software using pattern recognition routines like principal component analysis (PCA), cluster analysis (CA), partial least squares (PLSs) and linear discriminant analysis (LDA). 

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... 

Linear discriminant analysis (LDA), originally proposed by Fisher in 1936 [8], is the oldest and most studied supervised pattern recognition method. As the name suggests, it is a linear technique, that is the decision boundaries separating the classes in the multidimensional space of the variables are linear surfaces (hyperplanes). From a probabilistic standpoint, it is a parametric method, as its underlying hypothesis is that, for each category, the data follow a multivariate normal distribution. This means that the likelihood in Equation (2), for each class, is defined as... 

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