Paper:
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 standard dimensionality reduction techniques, such as PCA and PLS, and state-of-the-art feature selection methods for functional data, such as maxima hunting.

Review:
This paper presents an approach, called Recursive Maxima Hunting (RMH), for selecting features for functional data classification. The proposed method is shown to yield good results on simulated and real data. Although it is an adaptation of an existing method, this work remains very interesting.
This paper presents an approach, called Recursive Maxima Hunting (RMH), for selecting features for functional data classification. RMH is an adaptation of the Maxima Hunting (MH) approach, which selects features having a relevance score that is locally maximum (the distance correlation being used as relevance score). One drawback of the MH approach is that it misses the features that are not individually relevant (and are thus not local maxima) but that become relevant when combined with other relevant features. To address this problem, RMH selects the features in a recursive way, and at each stage the data are corrected by removing the information brought by the last selected feature. In practice, the method assumes that the underlying process is a Brownian motion and corrects the data by subtracting the conditional expectation of the process given the value of the last selected feature. The proposed approach was applied on 4 simulated datasets and 4 real datasets, and yields good results.  Although it is an adaptation of an existing method, this is a very interesting work. Overall, the paper is well structured and clearly written.   Some comments: - I am not sure to understand why one needs to exclude redundant points around a selected maximum (lines 15 and 20 of Algorithm 1). Isn’t the redundancy problem addressed by doing the data correction? For example, in Figure 2, one can see that the points in the close vicinity of t=5/8 have a very low distance correlation. It thus seems that one can hardly find redundant points after the correction. If it is not always the case, the authors should show an example that would help to understand why removing neighbouring points is needed. - The conditional expectation of the Brownian motion is t/t0 * X(t0) while Equation (7) says it is min(t,t0)/t0 * X(t0). If it is not a typo, the authors should discuss why they chose that correction. - It would be interesting to know the sample sizes of the real datasets.   Typos / others - Line 30: consistis —> consists - Line 72: searching from the next one —> searching for - Equation (2): two different notations are used for the distance variance. - Line 91: indepentence —> independence - Line 181: reasoble —> reasonable - Line 182: RMH algorithms —> RMH algorithm - Lines 15 and 20 of Algorithm 1: what is theta? - Lines 208-209: this sentence is not clear, since in RMH the number of selected features actually depends on some stopping criterion (i.e. the values of r and s). - Figure 4: on most x-axis labels, 50 is written instead of 1000 (for the sample size).