Orthogonality of Decision Boundaries in Complex-Valued Neural Networks

Neural Computation

Volumn 16, Issue 1, 2004, Pages 73-97

  Nitta, Tohru ^a  

^a NATIONAL INSTITUTE OF ADVANCED INDUSTRIAL SCIENCE AND TECHNOLOGY AIST   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; ARTIFICIAL NEURAL NETWORK; DECISION SUPPORT SYSTEM;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; DECISION SUPPORT TECHNIQUES; NEURAL NETWORKS (COMPUTER);

EID: 0348156824     PISSN: 08997667     EISSN: None     Source Type: Journal    
DOI: 10.1162/08997660460734001     Document Type: Article

References (22)

1. Arena, P., Fortuna, L., Muscato, G., & Xibilia, M. G. (1998). Neural networks in multidimensional domains. Lecture Notes in Control and Information Science 234, Berlin: Springer-Verlag.
2. Arena, P., Fortuna, L., Re, R., & Xibilia, M. G. (1993). On the capability of neural networks with complex neurons in complex valued functions approximation. In Proc. IEEE Int. Conf. on Circuits and Systems (pp. 2168-2171). Washington, DC: IEEE.
3. Benvenuto, N., & Piazza, F. (1992). On the complex backpropagation algorithm. IEEE Trans. Signal Processing, 40(4), 967-969.
4. Georgiou, G. M., & Koutsougeras, C. (1992). Complex domain backpropagation. IEEE Trans. Circuits and Systems-II: Analog and Digital Signal Processing, 39(5), 330-334.
5. ICONIP. (2002). Complex-valued neural networks. In Proc. International Conference on Neural Information Processing (Vol. 3, pp. 1074-1103). Washington, DC: IEEE.
6. KES. (2001). Complex-valued neural networks and their applications. In N. Baba, L. C. Jain, & R. J. Howlett (Eds.), Knowledge-based intelligent information engineering systems and allied technologies (Part I, pp. 550-580). Tokyo: IOS Press.
7. KES. (2002). Complex-valued neural networks. In E. Damiani, R. J. Howlett, L. C. Jain, & N. Ichalkaranje (Eds.), Knowledge-based intelligent information engineering systems and allied technologies (Part I, pp. 623-647). Amsterdam: IOS Press.
8. Kim, M. S., & Guest, C. C. (1990). Modification of backpropagation networks for complex-valued signal processing in frequency domain. In Proc. Int. Joint Conf. on Neural Networks (Vol. 3, pp. 27-31). Washington, DC: IEEE.
9. Kim, T., & Adali, T. (2000). Fully complex backpropagation for constant envelope signal processing. In Proc. IEEE Workshop on Neural Networks for Signal Processing (pp. 231-240). Washington, DC: IEEE.
10. Kuroe, Y., Hashimoto, N., & Mori, T. (2002). On energy function for complex-valued neural networks and its applications. In Proc. Int. Conf. on Neural Information Processing (Vol. 3, pp. 1079-1083). Washington, DC: IEEE.
11. Lathi, B. P. (1998). Modern digital and analog communication systems (3rd ed.). New York: Oxford University Press.
12. Lippmann, R. P. (1987, April). An introduction to computing with neural nets. IEEE Acoustic, Speech and Signal Processing Magazine, 4-22.
13. Minsky, M. L., & Papert, S. A. (1969). Perceptions. Cambridge, MA: MIT Press.
14. Miyauchi, M., Seki, M., Watanabe, A., & Miyauchi, A. (1992). Interpretation of optical flow through neural network learning. In Proc. IAPR Workshop on Machine Vision Applications (pp. 523-528).
15. Miyauchi, M., Seki, M., Watanabe, A., & Miyauchi, A. (1993). Interpretation of optical flow through complex neural network. In Proc. Int. Workshop on Artificial Neural Networks: Lecture Notes in Computer Science 686, (pp. 645-650). Berlin: Springer-Verlag.
16. Nitta, T. (1993). A complex numbered version of the back-propagation algorithm. In Proc. World Congress on Neural Networks (Vol. 3, pp. 576-579). Mahwah, NJ: Erlbaum.
17. Nitta, T. (1997). An extension of the back-propagation algorithm to complex numbers. Neural Networks, 10(8), 1392-1415.
18. Nitta, T., & Furuya, T. (1991). A complex back-propagation learning. Transactions of Information Processing Society of Japan, 32(10), 1319-1329 (in Japanese).
19. Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1986a). Parallel distributed processing (Vol. 1). Cambridge, MA: MIT Press.
20. Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1986b). Learning representations by back-propagating errors. Nature, 323, 533-536.
21. Vapnik, V. N. (1998). Statistical learning theory. New York: Wiley.
22. Watanabe, A., Yazawa, N., Miyauchi, A., & Miyauchi, M. (1994). A method to interpret 3D motions using neural networks. IEICE Trans. Fundamentals of Electronics, Communications and Computer Sciences, E77-A(8), 1363-1370.