Feature selection in functional data classification with recursive maxima hunting

Dimensionality reduction is one of the key issues in the design of effective machine learning methods for automatic induction. In this work, we introduce recursive maxima hunting (RMH) for variable selection in classification problems with functional data. In this context, variable selection techniques are especially attractive because they reduce the dimensionality, facilitate the interpretation and can improve the accuracy of the predictive models. The method, which is a recursive extension of maxima hunting (MH), performs variable selection by identifying the maxima of a relevance function, which measures the strength of the correlation of the predictor functional variable with the class label. At each stage, the information associated with the selected variable is removed by subtracting the conditional expectation of the process. The results of an extensive empirical evaluation are used to illustrate that, in the problems investigated, RMH has comparable or higher predictive accuracy than the standard dimensionality reduction techniques, such as PCA and PLS, and state-of-the-art feature selection methods for functional data, such as maxima hunting.

The mRMR variable selection method: a comparative study for functional data

The use of variable selection methods is particularly appealing in statistical problems with functional data. The obvious general criterion for variable selection is to choose the `most representative' or `most relevant' variables. However, it is also clear that a purely relevance-oriented criterion could lead to select many redundant variables. The mRMR (minimum Redundance Maximum Relevance) procedure, proposed by Ding and Peng (2005) and Peng et al. (2005) is an algorithm to systematically perform variable selection, achieving a reasonable trade-off between relevance and redundancy. In its original form, this procedure is based on the use of the so-called mutual information criterion to assess relevance and redundancy. Keeping the focus on functional data problems, we propose here a modified version of the mRMR method, obtained by replacing the mutual information by the new association measure (called distance correlation) suggested by Sz\'ekely et al. (2007). We have also performed an extensive simulation study, including 1600 functional experiments (100 functional models $\times$ 4 sample sizes $\times$ 4 classifiers) and three real-data examples aimed at comparing the different versions of the mRMR methodology. The results are quite conclusive in favor of the new proposed alternative.