Functional relevance learning in learning vector quantization for hyperspectral data

Classification accuracy of hyperspectral data frequently depends on only a few spectral windows distinguishing different classes or materials. Hence, classifier systems should not only achieve a good performance but also figure out what is essential for this decision. Learning vector quantization is a robust prototype-based classification method which, together with the relevance learning strategy, assesses the relative contribution of spectral bands for efficient classification. Original relevance learning is based on the scaled Euclidean distance, weighting each band independently. This yields a vectorial relevance profile indicating those spectral bands which distinguish the classes best. We propose the use of the functional Sobolev distance instead of the Euclidean, together with a relevance function as profile taking into account the functional properties of spectra. The relevance function is a superposition of a small set of simple basis functions like Gaussians or Lorentzians. In this way the number of parameters to be optimized in relevance learning is drastically decreased such that an inherent stabilization is obtained while the classification accuracy level is retained. We demonstrate the ability of the functional approach for ground cover classification of an AVIRIS hyperspectral data set (Lunar Crater Volcanic Field).