Prog. Theor. Phys. Vol. 91 No. 2 (1994) pp. 397-402
Analysis of Learning Processes of Chaotic Time Series by Neural Networks
Research Institute of Electrical Communication, Tohoku University, Sendai 980
(Received November 2, 1993)
Study of the learning process of chaotic time series by neural networks with back-propagation algorithm showed the existence of a general learning process. The process was found to be efficiently characterized by newly defined normalized measures, the coherence and the direction-cosine for the motion of weight vectors.
DOI : 10.1143/PTP.91.397
- D. E. Rumelhart, J. L. McClelland and the PDP Research Group, Parallel Distributed Processing (MIT Press, 1986).
F. J. Pineda, Phys. Rev. Lett. 59 (1987), 2229[APS].
- K. Funahashi, Neural Networks 2 (1989), 183.
- K. Doya and S. Yoshizawa, Proceedings of the 3rd IJCNN 1 (1989), p. 27.
- M. Sato, Y. Murakami and K. Joe, Proc. Inter. Conf. on Fuzzy Logic and Neural Networks (1990), p. 601.
- J. Moody and C. Darken, Neural Comput. 1 (1989), 281.
- D. J. Amit, Modeling Brain Function (Cambridge Univ. Press, 1989).
T. M. Heskes, E. T. P. Slijpen and B. Kappen, Phys. Rev. A46 (1992), 5221[APS].
H. Suhwarze, M. Opper and W. Kinzel, Phys. Rev. A46 (1992), 6185[APS].
- H. Horner, Z. Phys. B87 (1992), 371.
M. Opper and D. Haussler, Phys. Rev. Lett. 66 (1991), 2677[APS].
H. S. Seung and H. Sompolinsky, Phys. Rev. A45 (1992), 6056[APS].
- J. A. McGeoch and A. L. Irion, The Psychology of Human Learning, 2nd ed. (Longmans, New York, 1952).
- The data will be described elsewhere.
- T. Hondou and Y. Sawada, Proceedings of IJCNN-Nagoya (1993), p. 2387.
- H. G. Schuster, Deterministic Chaos (Physik-Verlag, Germany, 1984).
- We used r = 1.99 for the simulation, since at r = 2 iteration of f can lead x = 0, which destroys the precision of our calculation.
- For example, S. Amari, IEEE Trans. EC-16(3) (1967), 299.
Citing Article(s) :
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Progress of Theoretical Physics Vol. 95 No. 4 (1996) pp. 817-822
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