Abstract
Vector quantization and clustering are two different problems for which similar techniques are used. We analyze some approaches to the synthesis of a vector quantization codebook, and their similarities with corresponding clustering algorithms. We outline the role of fuzzy concepts in the performance of these algorithms, and propose an alternative way to use fuzzy concepts as a modeling tool for physical vector quantization systems, Neural Gas with a fuzzy rank function.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Jain, A.K., Dubes, R.C.: Algorithms for Clustering Data. Prentice Hall, Englewood Cliffs (1988)
Gersho, A.: On the structure of vector quantizers. IEEE Transactions on Information Theory 28(2), 157–166 (1982)
Gray, R.M.: Vector quantization. IEEE Acoustic, Speech and Signal Processing Magazine 1, 4–29 (1984)
Martinetz, T.M., 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(4), 558–569 (1993)
Bezdek, J.C.: Pattern recognition with fuzzy objective function algorithms. Plenum, New York (1981)
Baraldi, A., Blonda, P.: A survey of fuzzy clustering algorithms for pattern recognition. I. IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics) 29, 778–785 (1999)
Baraldi, A., Blonda, P.: A survey of fuzzy clustering algorithms for pattern recognition. II. IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics) 29, 786–801 (1999)
Aurenhammer, F.: Voronoi diagrams-a survey of a fundamental geometric data structure. ACM Computing Surveys 23(3), 345–405 (1991)
LLoyd, S.: Least squares quantization in pcm. IEEE Transactions on Information Theory 28, 129–137 (1982)
MacQueen, J.: Some methods for classification and analysis of multivariate observations. In: Le Cam, L., Neyman, J. (eds.) Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, University of California, January 1967, vol. I, pp. 281–297 (1967)
Linde, Y., Buzo, A., Gray, R.M.: An algorithm for vector quantizers design. IEEE Transactions on Communications COM-28, 84–95 (1980)
Geman, G., Geman, D.: Stochastic relaxation, gibbs distribution and bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence PAMI-6(6), 721–741 (1984)
Ritter, H.J., Martinetz, T.M., Schulten, K.J.: Neuronale Netze. Addison-Wesley, München (1991)
Rose, K.: Deterministic annealing for clustering, compression, classification, regression, and related optimization problems. Proceedings of IEEE 86(11), 2210–2239 (1998)
Hoffmann, T., Buhmann, J.M.: An annealed neural gas network for robust vector quantization. In: Vorbrüggen, J.C., von Seelen, W., Sendhoff, B. (eds.) ICANN 1996. LNCS, vol. 1112, pp. 151–156. Springer, Heidelberg (1996)
Rovetta, S., Zunino, R.: Efficient training of vector quantizers with analog circuit implementation. IEEE Transactions on Circuits and Systems, Part II 46(6), 688–698 (1999)
Bortolan, G., Degani, R.: A review of some methods for ranking fuzzy sets. Fuzzy sets and systems 15, 1–19 (1985)
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
Masulli, F., Rovetta, S. (2006). Fuzzy Concepts in Vector Quantization Training. In: Di Gesú, V., Masulli, F., Petrosino, A. (eds) Fuzzy Logic and Applications. WILF 2003. Lecture Notes in Computer Science(), vol 2955. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10983652_34
Download citation
DOI: https://doi.org/10.1007/10983652_34
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-31019-8
Online ISBN: 978-3-540-32683-0
eBook Packages: Computer ScienceComputer Science (R0)