Abstract
Recently, two extensions of neural gas have been proposed: a fast batch version of neural gas for data given in advance, and extensions of neural gas to learn a (possibly fuzzy) supervised classification. Here we propose a batch version for supervised neural gas training which allows to efficiently learn a prototype-based classification, provided training data are given beforehand. The method relies on a simpler cost function than online supervised neural gas and leads to simpler update formulas. We prove convergence of the algorithm in a general framework, which also incorporates supervised k-means and supervised batch-SOM, and which opens the way towards metric adaptation as well as application to proximity data not embedded in a real-vector space.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Bottou, L., Bengio, Y.: Convergence properties of the k-means algorithm. In: Tesauro, G., Touretzky, D.S., Leen, T.K. (eds.) NIPS 1994, pp. 585–592. MIT, Cambridge (1994)
Conan-Guez, B., Rossi, F., El Golli, A.: A fast algorithm for the self-organizing map on dissimilarity data. In: Workshop on Self-Organizing Maps, pp. 561–568 (2005)
Cottrell, M., Hammer, B., Hasenfuss, A., Villmann, T.: Batch and median neural gas. Neural Networks (to appear, 2006)
Crammer, K., Gilad-Bachrach, R., Navot, A., Tishby, N.: Margin analysis of the LVQ algorithm. In: NIPS 2002 (2002)
Gath, I., Geva, A.B.: Unsupervised optimal fuzzy clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence 11(7), 773–781 (1989)
Hammer, B., Strickert, M., Villmann, T.: Supervised neural gas with general similarity measure. Neural Processing Letters 21(1), 21–44 (2005)
Hammer, B., Villmann, T.: Generalized relevance learning vector quantization. Neural Networks 15, 1059–1068 (2002)
Heskes, T.: Self-organizing maps, vector quantization, and mixture modeling. IEEE Transactions on Neural Networks 12, 1299–1305 (2001)
Kaski, S., Sinkkonen, J.: Principle of learning metrics for data analysis. Journal of VLSI Signal Processing, special issue on Machine Learning for Signal Processing 37: 177–188 (2004)
Kohonen, T.: Self-Organizing Maps. Springer, Heidelberg (1995)
Kohonen, T., Somervuo, P.: How to make large self-organizing maps for nonvectorial data. Neural Networks 15, 945–952 (2002)
Martinetz, T., Berkovich, S.G., Schulten, K.J.: Neural-gas network for vector quantization and its application to time-series prediction. IEEE Transactions on Neural Networks 4, 558–569 (1993)
Newman, D.J., Hettich, S., Blake, C.L., Merz, C.J.: UCI Repository of machine learning databases. University of California, Department of Information and Computer Science, Irvine, CA (1998), http://www.ics.uci.edu/~mlearn/MLRepository.html
Peltonen, J., Klami, A., Kaski, S.: Improved learning of Riemannian metrics for exploratory analysis. Neural Networks 17, 1087–1100 (2004)
Seo, S., Obermayer, K.: Self-organizing maps and clustering methods for matrix data. Neural Networks 17, 1211–1230 (2004)
Villmann, T., Hammer, B., Schleif, F., Geweniger, T., Herrmann, W.: Fuzzy classification by fuzzy labeled neural gas. Neural Networks (accepted, 2006)
Zhong, S., Ghosh, J.: A unified framework for model-based clustering. Journal of Machine Learning Research 4, 1001–1037 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hammer, B., Hasenfuss, A., Schleif, FM., Villmann, T. (2006). Supervised Batch Neural Gas. In: Schwenker, F., Marinai, S. (eds) Artificial Neural Networks in Pattern Recognition. ANNPR 2006. Lecture Notes in Computer Science(), vol 4087. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11829898_4
Download citation
DOI: https://doi.org/10.1007/11829898_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-37951-5
Online ISBN: 978-3-540-37952-2
eBook Packages: Computer ScienceComputer Science (R0)