Paper:

# Reduction Models in Competitive Learning Founded on Distortion Standards

## Michiharu Maeda^{*}, Noritaka Shigei^{**}, Hiromi Miyajima^{**},

and Kenichi Suzaki^{*}

^{*}Department of Computer Science and Engineering, Faculty of Information Engineering, Fukuoka Institute of Technology, 3-30-1 Wajiro-higashi, Higashi-ku, Fukuoka 811-0295, Japan

^{**}Department of Electrical and Electronic Engineering, Faculty of Engineering, Kagoshima University, 1-21-40 Korimoto, Kagoshima 890-0065, Japan

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.12 No.3, pp. 314-323, 2008.

- [1] S. Grossberg, “Adaptive pattern classification and universal recoding: I. Parallel development and coding of neural feature detectors,” Biol. Cybern. Vol.23, pp. 121-134, 1976.
- [2] D. J. Willshaw and C. von der Malsburg, “How patterned neural connections can be set up by self-organization,” Proc. R. Soc. Lond. B., Vol.194, pp. 431-445, 1976.
- [3] J. Hertz, A. Krogh, and R.G. Palmer, “Introduction to the theory of neural computation,” Addison-Wesley, 1991.
- [4] S. I. Gallant, “Neural network learning and expert systems,” The MIT Press, 1993.
- [5] T. Kohonen, “Self-organization and associative memory,” Springer-Verlag Berlin, 1989.
- [6] H.-U. Bauer and K. R. Pawelzik, “Quantifying the neighborhood preservation of self-organizing feature maps,” IEEE Trans. Neural Networks, Vol.3, No.4, pp. 570-579, 1992.
- [7] H. Ritter, T. Martinetz, and K. Schulten, “Neural computation and self-organizing maps: An introduction,” Addison-Wesley, 1992.
- [8] T. Martinetz and K. Schulten, “Topology representing networks,” Neural Networks, Vol.7, No.3, pp. 507-522, 1994.
- [9] T. Villmann, M. Herrmann, and T. M. Martinetz, “Topology preservation in self-organizing feature maps: Exact definition and measurement,” IEEE Trans. Neural Networks, Vol.8, No.2, pp. 256-266, 1997.
- [10] M. Maeda, H. Miyajima, and N. Shigei, “Parallel learning model and topological measurement for self-organizing maps,” Journal of Advanced Computational Intelligence and Intelligent Informatics, Vol.11, No.3, pp. 327-334, 2007.
- [11] E. Berglund and J. Sitte, “The parameterless self-organizing map algorithm,” IEEE Trans. Neural Networks, Vol.17, No.2, pp. 305-316, 2006.
- [12] Y. Linde, A. Buzo, and R. M. Gray, “An algorithm for vector quantizer design,” IEEE Trans. Commun., Vol.28, No.1, pp. 84-95, 1980.
- [13] H. Ritter and K. Schulten, “On the stationary state of Kohonen’s self-organizing sensory mapping,” Biol. Cybern., Vol.54, pp. 99-106, 1986.
- [14] H. Ritter and K. Schulten, “Convergence properties of Kohonen’s topology conserving maps, Fluctuations, stability, and dimension selection,” Biol. Cybern., Vol.60, pp. 59-71, 1988.
- [15] T. M. Martinetz, S. G. Berkovich, and K. J. Schulten, ““Neural-gas” network for vector quantization and its application to time-series prediction,” IEEE Trans. Neural Networks, Vol.4, No.4, pp. 558-569, 1993.
- [16] N. Shigei, H. Miyajima, and M. Maeda, “Competitive learning with fast neuron-insertion,” Journal of Advanced Computational Intelligence and Intelligent Informatics, Vol.9, No.6, pp. 590-598, 2005.
- [17] M. Maeda, N. Shigei, and H. Miyajima, “Construction of competitive learning by reduction with distortion standards,” Proc. Int. Conf. Intelligent Technologies, pp. 45-52, 2006.
- [18] B. Fritzke, “Growing cell structures –A self-organizing network for unsupervised and supervised learning,” Neural Networks, Vol.7, No.9, pp. 1441-1460, 1994.
- [19] D.-I. Choi and S.-H. Park, “Self-creating and organizing neural networks,” IEEE Trans. Neural Networks, Vol.5, No.4, pp. 561-575, 1994.
- [20] H. Xiong, M. N. S. Swamy, M. O. Ahmad, and I. King, “Branching competitive learning network: a novel self-creating model,” IEEE Trans. Neural Networks, Vol.15, No.2, pp. 417-429, 2004.
- [21] J. G. Rodriguez, A. Angelopoulou, and A. Psarrou, “Growing neural gas (GNG): a soft competitive learning method for 2D hand modeling,” IEICE Trans. Inf. & Syst., Vol.E89-D, No.7, pp. 2124-2131, 2006.
- [22] Y.-J. Zhang and Z.-Q. Liu, “Self-splitting competitive learning: a new on-line clustering paradigm,” IEEE Trans Neural Networks, Vol.13, No.2, pp. 369-380, 2002.
- [23] M. Maeda, H. Miyajima, and S. Murashima, “Construction of selforganizing algorithms for vector quantization,” EEJ Scripta Technica, John Wiley & Sons, Vol.127, No.1, pp. 47-55, 1999.
- [24] L. E. Reichl, “A modern course in statistical physics,” University of Texas Press, 1980.
- [25] H. Imai, “Information theory,” Shokodo, 1984.
- [26] A. Gersho and R. M. Gray, “Vector quantization and signal compression,” Kluwer Academic Publishers, 1992.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.