Generalized functional relevance learning vector quantization

Generalized learning vector quantization (GRLVQ) is a prototype based classification algorithm with metric adaptation weighting each data dimensions according to their relevance for the classification task. We present in this paper an extension for functional data, which are usually very high dimensional. This approach supposes the data vectors have to be functional representations. Taking into account, these information the so-called relevance profile are modeled by superposition of simple basis functions depending on only a few parameters. As a consequence, the resulting functional GRLVQ has drastically reduced number of parameters to be adapted for relevance learning. We demonstrate the ability of the new algorithms for standard functional data sets using different basis functions, namely Gaussians and Lorentzians.