Fuzzy Supervised Self-Organizing Map for Semi-supervised Vector Quantization

In this paper we propose a new approach to combine unsupervised and supervised vector quantization for clustering and fuzzy classification using the framework of neural vector quantizers like self-organizing maps or neural gas. For this purpose the original cost functions are modified in such a way that both aspects, unsupervised vector quantization and supervised classification, are incorporated. The theoretical justification of the convergence of the new algorithm is given by an adequate redefinition of the underlying dissimilarity measure now interpreted as a dissimilarity in the data space combined with the class label space. This allows a gradient descent learning as known for the original algorithms. Thus a semi-supervised learning scheme is achieved. We apply this method for a spectra image cube of remote sensing data for landtype classification. The obtained fuzzy class visualizations allow a better understanding and interpretation of the spectra.

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