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Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Applications of lpnorms and their smooth approximations for gradient based learning vector quantization
 Verleysen, M. ; Katholieke Universiteit, Leuven: 22nd European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning, ESANN 2014. Proceedings : Bruges, Belgium, April 23  25, 2014 LouvainlaNeuve: Ciaco, 2014 ISBN: 9782874190957 pp.271276 
 European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN) <22, 2014, Bruges> 

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 Conference Paper 
 Fraunhofer IAIS () Fraunhofer ITEM () 
Abstract
Learning vector quantization applying nonstandard metrics became quite popular for classification performance improvement compared to standard approaches using the Euclidean distance. Kernel metrics and quadratic forms belong to the most promising approaches. In this paper we consider Minkowski distances (lpnorms). In particular, l1norms are known to be robust against noise in data, such that, if this structural knowledge is available in advance about the data, this norm should be utilized. However, application in gradient based learning algorithms based on distance evaluations need to calculate the respective derivatives. Because lpdistance formulas contain the absolute approximations thereof are required. We consider in this paper several approaches for smooth consistent approximations for numerical evaluations and demonstrate the applicability for exemplary real world applications.