Class discrimination

The flow phenomena described by the Navier-Stokes equation fall into two classes discriminated by the nature of the compressibility effects to be taken into account. For compressible flow, the Navier-Stokes equation [Eq. (1)] has to be solved in com-... 

Up to this point the methods of classification operate in the same way. They differ considerably, however, in the way that rules for classification are derived. In this regard the various methods are of three types 1) class discrimination or hyperplane methods, 2) distance methods, and 3) class modeling methods. 

In the class discrimination methods or hyperplane techniques, of which linear discriminant analysis and the linear learning machine are examples, the equation of a plane or hyperplane is calculated that separates one class from another. These methods work well if prior knowledge allows the analyst to assume that the test objects must... 

This approach to feature selection leads to a set of descriptors that are optimal for class discrimination. These variables may or may not contain information that describes the classes. 

Figure 9.19 shows a plot of the two largest PLS components developed from the eight GC peaks and 109 training-set samples. The European honeybees are designated as 1, and the Africanized honeybees are 2. Separation of the honeybees by class is evident in the PLS plot of the data. The fact that class discrimination is only associated with the largest PLS component of the data is encouraging. 

Feature extraction. A small set of class-discriminating features is selected (extracted) from the descriptor space, which provide the basis for activity (class) predictions. Traditional feature-extraction methods are based on factor analysis and projection methods [58],... 

Himanen, J. P. et al. (2004). Repelling Class Discrimination Ephrin-A5 Binds to and Activates EphB2 Receptor Signaling. Nat. Neurosc. 7, 501-509. 

Rose, V.S., Wood, J. and MacFie, H.J.H. (1991). Single Class Discrimination Using Principal Component Analysis (Scd PCA). Quant.Struct.-Act.Relat., 10,359-368. 

Rose, V. S., Wood, J., MacFie, H. J. H. Single class discrimination using principal component analysis (SCD-PCA). Quant. Struct.-Act. Relat. 1991,10, 359-368. 

Discriminant analysis techniques (also called classification techniques) are concerned with classifying objects into one of two or more classes. Discriminant techniques are considered to be learning procedures. Given, a set of objects whose class identity is known, a model learns from the variables which have been measured for each of the objects, a procedure which can be used to assign a new object, whose class identity is unknown, into one of the predefined classes. Such a procedure is performed using a well-defined discriminatory rule. 

As a first step in this direction, a surface consisting of electric eel AChE and horse serum BChE was designed. Both of these enzymes are inhibited by TPPSi and the characteristic absorbance peaks for the porphyrin-enzyme complexes are different (421 vs. 446 nm). This allows for co-immobilization of the two enzymes from a simple mixture of equal concentrations onto the entire slide surface [25]. Exposure to those compounds inhibiting BChE competitively results in a loss in absorbance at 421 nm while compounds inhibiting AChE competitively result in a loss at 446 nm. Compounds inhibiting both enzymes result in a loss at both 421 nm and 446 nm. This combination of two enzymes allows for class discrimination of those compounds, which are inhibitors of BChE, inhibitors of AChE, inhibitors of both enzymes, and inhibitors of neither enzyme. Detection limits are approximately the same for the dual enzyme system as those observed for the single enzyme systems. 

Discriminant analysis (Figure 31) [41,487, 577 — 581] separates objects with different properties, e.g. active and inactive compounds, by deriving a linear combination of some other features e.g. of different physicochemical properties), which leads to the best separation of the individual classes. Discriminant analysis is also appropriate for semiquantitative data and for data sets, where activities are only characterized in qualitative terms. As in pattern recognition, training sets are used to derive a model and its stability and predictive ability is checked with the help of different test sets. 

Two fundamentally different statistical approaches to biomarker selection are possible. With the first, experimental data can be used to construct multivariate statistical models of increasing complexity and predictive power - well-known examples are Partial Least Square Discriminant Analysis (PLS-DA) (Barker Rayens, 2003 Kemsley, 1996 Szymanska et al., 2011) or Principal Component Linear Discriminant Analysis (PC-LDA) (Smit et al., 2007 Werf et al., 2006). Inspection of the model coefficients then should point to those variables that are important for class discrimination. As an alternative, univariate statistical tests can be... 

Wehrens, R. Franceschi, P. (2011). BioMark finding biomarkers in two-class discrimination problems. R package version 0.3.0. 

Within-class discrimination is an important factor in the forensic examination of materials, and Py-GC is an appropriate techniqne to distinguish closely related polymers. Vinyl acetate polymers, for example, may be plasticized internally or externally. Copolymers inclnde ethylhexyl acrylate, while phthalate plasticizers, such as dibutyl or di-isooctyl phthalate, may be used as external plasticizers in commercial products. 

Support vector machines were initially developed for class discrimination, and most of their applications have been for pattern classification. SVM classification is especially relevant for important cheminformatics problems, such as recognizing drug-like compounds, or discriminating between toxic and nontoxic compounds, and many such applications have been published. The QSAR applications of SVM regression, however, are rare, and this is unfortunate because it represents a viable alternative to multiple linear regression, PLS, or neural networks. In this section, we present several SVMR applications to QSAR datasets, and we compare the performance of several kernels. 

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