Feature selection with latent variable methods

3 Feature selection with latent variable methods 

There is no single and systematic approach for feature selection coupled with the full-spectra methods, for instance with PLS, but there are many diverse propositions. To mention at least some of them, we can start with Intermediate Least Squares (ILS) proposed by Frank [17], which calculates an 

Clark and Cramer III [25] carried out studies on chance correlation with PLS. For all the studied data dimensionality and different correlation 

In the approach, proposed by Centner et al. [26], the experimental variables can be eliminated that do not have more importance than artificial random. As this procedure motivated us to study feature selection in the wavelet domain, we present it in a more detailed way. 

The PLS model relating a variable y (m, 1) with a set of predictors X (m, n) can be presented in the following form  

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Additionally, Breiman et al. [23] developed a methodology known as classification and regression trees (CART), in which the data set is split repeatedly and a binary tree is grown. The way the tree is built, leads to the selection of boundaries parallel to certain variable axes. With highly correlated data, this is not necessarily the best solution and non-linear methods or methods based on latent variables have been proposed to perform the splitting. A combination between PLS (as a feature reduction method — see Sections 33.2.8 and 33.3) and CART was described by... 

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