Discriminant feature reduction

Several statistics for multivariate tests are known from the literature [AHRENS and LAUTER, 1981 FAHRMEIR and HAMERLE, 1984] the user of statistical packages may find several of them implemented and will rely on their performing correctly. Other, different, tests for separation of groups are used to determine the most discriminating results in discriminant analysis with feature reduction. 

Context-dependent situations often lead to a large-scale input dimension. Because the required number of training examples increases with the number of measured variables or features, reducing the input dimensionality may improve system performance. In addition, decision discriminants will be less complex (because of fewer dimensions in the data) and more easily determined. The reduction in dimensionality can be most readily achieved by eliminating redundancy in the data so that only the most relevant features are used for mapping to a given set of labels. 

Chiral recognition of A-[Co(phen)3]3+ has been observed in a modified /3-cyclodextrin.772 Chiral discrimination has also been seen in photoinduced energy transfer from luminescent chiral lanthanoid complexes773 to [Co(phen)3]3+ and between photoexcited [Ru(bpy)3]2+ and [Co(phen)3]3+ co-adsorbed on smectite clays.774 The [Co(bpy)3]3+ ion has been incorporated into clays to generate ordered assemblies and also functional catalysts. When adsorbed onto hectorite, [Co(bpy)3]3+ catalyzes the reduction of nitrobenzene to aniline.775 The ability of [Co(phen)3]3+ to bind to DNA has been intensively studied, and discussion of this feature is deferred until Section 6.1.3.1.4. 

At this stage, however, discriminant analysis as well as factor analysis, do not provide a real reduction in dimensions from the practical (experimental) point of view because in the linear combinations used in both methods we still need all the original features. 

A real reduction in dimension is possible in discriminant analysis on a statistical basis because we can delete features bearing redundant information, i.e. which are highly correlated to others, in an eliminating process which finds an optimum feature set with a statistically sufficient discriminating power and a risk of error which is still acceptable. Hence, only with DA can we offer real economical advantages. 

The number of features combined in a vector-type representation is indicative of the dimensionality of the problem space. Low-dimensional representations, on the one hand, allow easy visualization but are most often not very discriminative. Highdimensional representations, on the other hand, such as those encoded in Daylight fingerprints [23], MACCS keys [24], or UNITY fingerprints [25], provide more detailed accounts on structural or chemical variations. However, this is achieved at the cost of visualization. Part of these high-dimensional representations describe specific local features of molecules, and because not all molecules in the data contain these features, gaps or zeros are introduced in the data representation. For certain data mining methods, this could be problematic. In many cases, dimensionality reduction procedures are applied to reduce the complexity of the representation. The reduction of the dimensionality is accomplished by means of 1) variable selection procedures, 2)... 

Derivative filters The main advantage of derivative spectroscopy lies in the enhancement of the spectral fine structures combined with a reduction of broad baseline effects. Unfortunately, derivative spectroscopy requires a high SNR, which is sometimes hard to achieve, particularly if the IR microspectra are acquired with high spatial resolution. The example of Figure 6.8, panels C and D, demonstrates that the application of a first derivative Savitzky-Golay filter with nine smoothing points to the raw spectral data in combination with vector normalisation dramatically enhances the number of discriminative spectral features. We consider this combination to be the most effective and robust combination of pre-processing routines for classification analysis. ... 

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