Funtional vector quantization by neural maps

We propose the utilization of Sobolev-norms in unsupervised and supervised vector quantization for clustering and classification of functional data. Sobolev-norms differ from the usual Minkowski-norm by the incorporation of derivatives such that the functional shape is taken into account. This leads to a more appropriate modelling of functional data. As we figure out, the Sobolev-norm can easily plugged into prototype based adaptive vector quantization algorithms to process functional data adequately. We show for an example application in remote sensing data analysis that this methodology may lead to improved performance of the algorithms.