The problem of selecting the most discriminatory variables in the input space is indeed challenging in kernel-based classification, since at the end, the classifier uses new (transformed, combined, possibly infinite, etc.) features in the kernel-induced space. Given that the kernel trick allows the classifier to use similarity measures without explicity computing such feature space, one way to select variables is to weight the contribution of each variable while measuring the similarity, in other words, while evaluating kernel computations. Variables obtaining higher weights can be selected as relevant for the classification task whereas those having low weights can be discarded. The problem then is to adjust those weights, specially in high dimensional input spaces such as gene expression or proteomic spectra data. Several approaches have been proposed: in our paper [1] we combine a Gaussian weighted-kernel classifier with an iterative stochastic probability estimation algorithm to discover the relevance distribution over the set of variables; other authors have considered gradient-descent, genetic algorithms, evolutionary strategies, bayesian estimation (see references within) in an attempt to solve this problem.

[1] Rojas-Galeano S, Hsieh E, Agranoff D, Krishna S, Fernandez-Reyes D (2008) Estimation of Relevant Variables on High-Dimensional Biological Patterns Using Iterated Weighted Kernel Functions. PLoS ONE 3(3): e1806. doi:10.1371/journal.pone.0001806