Support vector machine for functional data classification

In many applications, input data are sampled functions taking their values in infinite-dimensional spaces rather than standard vectors. This fact has complex consequences on data analysis algorithms that motivate their modifications. In fact most of the traditional data analysis tools for regression, classification and clustering have been adapted to functional inputs under the general name of functional data analysis (FDA). In this paper, we investigate the use of support vector machines (SVMs) for FDA and we focus on the problem of curve discrimination. SVMs are large margin classifier tools based on implicit nonlinear mappings of the considered data into high-dimensional spaces thanks to kernels. We show how to define simple kernels that take into account the functional nature of the data and lead to consistent classification. Experiments conducted on real world data emphasize the benefit of taking into account some functional aspects of the problems.