  During the last decades, many methods for the analysis of functional data
including classification methods have been developed. Nonetheless, there are
issues that have not been adressed satisfactorily by currently available
methods, as, for example, feature selection combined with variable selection
when using multiple functional covariates. In this paper, a functional ensemble
is combined with a penalized and constrained multinomial logit model. It is
shown that this synthesis yields a powerful classification tool for functional
data (possibly mixed with non-functional predictors), which also provides
automatic variable selection. The choice of an appropriate, sparsity-inducing
penalty allows to estimate most model coefficients to exactly zero, and permits
class-specific coefficients in multiclass problems, such that feature selection
is obtained. An additional constraint within the multinomial logit model
ensures that the model coefficients can be considered as weights. Thus, the
estimation results become interpretable with respect to the discriminative
importance of the selected features, which is rated by a feature importance
measure. In two application examples, data of a cell chip used for water
quality monitoring experiments and phoneme data used for speech recognition,
the interpretability as well as the selection results are examined. The
classification performance is compared to various other classification
approaches which are in common use.

Methodology;Applications