Variable selection in classification for multivariate functional data

Abstract When classification methods are applied to high-dimensional data, selecting a subset of the predictors may lead to an improvement in the predictive ability of the estimated model, in addition to reducing the model complexity. In Functional Data Analysis (FDA), i.e., when data are functions, selecting a subset of predictors corresponds to selecting a subset of individual time instants in the time interval in which the functional data are measured. In this paper, we address the problem of selecting the most informative time instants in multivariate functional data, a case much less studied than its single-variate counterpart. Our proposal allows one to use in a very simple way high-order information of the data, e.g. monotonicity or convexity by means of the functional data derivatives. The aforementioned problem is addressed with tools of Global Optimization in continuous variables: the time instants are selected to maximize the correlation between the class label and the Support Vector Machine score used for classification. The effectiveness of the proposal is shown in univariate and multivariate datasets.