Divergence based vector quantization of spectral data

Unsupervised and supervised vector quantization models for clustering and classification are usually designed for processing of Euclidean vectorial data. Yet, in this scenario the physical context might be not adequately reflected. For example, spectra can be seen as positive functions (positive measures). Yet, this context information is not used in Euclidean vector quantization. - In this contribution we propose a methodology for extending gradient based vector quantization approaches utilizing divergences as dissimilarity measure instead of the Euclidean distance for positive measures. Divergences are specifically designed to judge the dissimilarities between positive measures and have frequently an underlying physical meaning. We present in the paper the mathematical foundation for plugging divergences into vector quantization schemes and their adaptation rules. Thereafter, we demonstrate the ability of this methodology for the self-organizing map as widely ranged vector quantizer, applying it for topographic data clustering of a hyperspectral AVIRIS image cube taken from a lunar crater volcanic field.