Abstract
The convergence of Oja+’s MCA learning algorithm was proven in past by using a deterministic continuous-time dynamical system with restrictive condition that the learning rate must converge to zero. This paper gives a new proof for the convergence of the Oja+’s MCA algorithm via a corresponding deterministic discrete-time (DDT) dynamical system. This approach allows the learning rate to be some constant. In this paper, the fixed points of the DDT system are determined and an invariant set is obtained. Based on the invariant set, the convergence is proven.
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References
Oja, E.: Principal Components, Minor Components, and Linear Neural Network. IEEE Trans. Neural Networks 5, 927–935 (1992)
Cirrincione, G., Cirrincione, M., Hérault, J., Huffel, S.V.: The MCA EXIN Neuron for the Minor Component Analysis. IEEE Trans. Neural Networks 13(1), 160–187 (2002)
Xu, L., Oja, E., Suen, C.: Modified Hebbian Learning for Curve and Surface Fitting. Neural Networks 13, 441–459 (1992)
Feng, D.Z., Bao, Z., Jiao, L.C.: Total Least Mean Squares Algorithm. IEEE Trans. Signal Processing 46, 2122–2130 (1998)
Luo, F., Unbehauen, R., Cichocki, A.: A Minor Component Analysis Algorithm. Neural Networks 19(2), 291–197 (1997)
Zhang, Q.F.: On the Discrete-Time Dynamics of a PCA Learning Algorithm. Neurocomputing 55, 761–769 (2003)
Zuffiria, P.J.: On the Discrete-Time Dynamics of the Basic Hebbian Neural-Network Node. Neural Computation 11(2), 529–533 (2000)
Fiori, S., Piazza, F.: Neural MCA for Robust Beamforming. In: Proc. of International Symposium on Circuits and Systems (ISCAS 2000), vol. III, pp. 614–617 (2000)
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© 2004 Springer-Verlag Berlin Heidelberg
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Lv, J., Ye, M., Yi, Z. (2004). Convergence Analysis for Oja+ MCA Learning Algorithm. In: Yin, FL., Wang, J., Guo, C. (eds) Advances in Neural Networks – ISNN 2004. ISNN 2004. Lecture Notes in Computer Science, vol 3173. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28647-9_133
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DOI: https://doi.org/10.1007/978-3-540-28647-9_133
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22841-7
Online ISBN: 978-3-540-28647-9
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