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The authors deal with the interesting problem of classifying sparse functional data. This task has been treated extensively in the literature from different points of view, most of them trying to extend ideas from the multivariate setting. Being Xi the trajectories and Yi the labels taking values on {−1, 1} (or on {0, 1} depending whether we are interested on discriminant functions or on probabilities of belonging to a certain group), the techniques are based on the two conditional distributions: Y |X orX |Y . The former is the most popular alternative based on estimating E [Y/X ] directly or using a transformation of the covariate. For instance, the use of a logistic regression after representing the trajectories in a fixed (Fourier, B-spline, wavelets) or data-driven (PC, PLS) basis is the approach employed by James (2002), Escabias et al. (2005, 2007), Cardot and Sarda (2005), Müller and Stadtmüller (2005), Leng and Müller (2006), Preda et al. (2007) or Müller and Yao (2008) among others. The works by Ferraty and Vieu (2003) or Febrero-Bande and González-Manteiga (2013) follow the ideas from the literature of the nonparametric regression framework allowing to extend the classification techniques to non-Hilbert spaces using norms and distances between trajectories. The third alternative is the transformation of the information of the functional covariateX using, for instance, notions of depth like in Cuevas et al. (2007) or Li et al. (2012). The first example in functional data of the use of the conditional distributionX |Y can be found in James and Hastie (2001) as the extension of classical linear

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