Abstract
We present the review of our works related to the theory of vector neural networks. The interconnection matrix always is constructed according to the generalized Hebb’s rule, which is well-known in the Machine Learning. We accentuate the main principles and ideas. Analytical calculations are based on the probability approach. The obtained theoretical results are verified with the aid of computer simulations.
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.
Similar content being viewed by others
References
Hertz, J., Krogh, A., Palmer, R.: Introduction to the Theory of Neural Computation. Addison-Wesley, NY (1991)
Noest, J.: Discrete-state phasor neural networks. Phys. Rev. A 38, 2196–2199 (1988)
Kanter, I.: Potts-glass models of neural networks. Phys. Rev. A 37, 2739–2742 (1988)
Cook, J.: The mean-field theory of a Q-state neural network model. J. Phys. A 22, 2000–2012 (1989)
Vogt, H., Zippelius, A.: Invariant Recognition in Potts Glass Neural Networks. J. Phys. A 25, 2209–2226 (1992)
Kryzhanovsky, B., Mikaelian, A.: On the Recognition Ability of a Neural Network on Neurons with Parametric Transformation of Frequencies. Doklady Mathematics 65(2), 286–288 (2002)
Fonarev, A., Kryzhanovsky, B., et al.: Parametric dynamic neural network recognition power. Optical Memory & Neural Networks 10(4), 31–48 (2001)
Bloembergen, N.: Nonlinear optics, Benjamin, NY (1965)
Nakamura, Y., Torii, K., Munaka, T.: Neural-network model composed of multidimensional spin neurons. Phys. Rev. B 51, 1538–1546 (1995)
Kryzhanovsky, B., Litinskii, L.: Vector models of associative memory. In: Lectures on Neuroinformatics on V Russian Conference Neuroinformatics – 2003, vol. 1, pp. 72–85. Moscow Engineering Physical Institute Press, Moscow (2003) (in Russian)
Kryzhanovsky, B., Litinskii, L., Fonarev, A.: Parametrical Neural Network Based on the Four-Wave Mixing Process. Nuclear Instruments and Methods in Physics Research Section A 502, 517–519 (2003)
Kryzhanovsky, B., Litinskii, L.: Vector models of associative memory. Automaton and Remote Control 64(11), 1782–1793 (2003)
Kryzhanovsky, B., Litinskii, L., Mikaelian, A.: Parametrical Neural Network. Optical Memory & Neural Networks 12(3), 138–156 (2003)
Kryzhanovsky, B., Litinskii, L., Mikaelian, A.: Vector neuron representation of q-valued neural networks. In: Prokhorov, D. (ed.) Proceedings of IEEE International Joint Conference on Neural Networks – 2004, vol. 1, pp. 909–915. IEEE Press, Budapest (2004)
Kryzhanovsky, B., Litinskii, L., Mikaelian, A.: Vector Neurons Model of Associative Memory. Information technologies and computer systems 1, 68–81 (2004) (in Russian)
Kryzhanovsky, B., Mikaelian, A.: An associative memory capable of recognizing strongly correlated patterns. Doklady Mathematics 67(3), 455–459 (2003)
Kryzhanovsky, B., Litinskii, L., Fonarev, A.: An effective associative memory for pattern recognition. In: Berthold, M.R., Lenz, H.-J., Bradley, E., Kruse, R., Borgelt, C. (eds.) IDA 2003. LNCS, vol. 2810, pp. 179–186. Springer, Heidelberg (2003)
Kryzhanovsky, B., Kryzhanovsky, V., Fonarev, A.: Decorrelating parametrical neural network. In: Proceedings of IEEE International Joint Conference on Neural Networks–2005, vol. 1, pp. 153–157. IEEE Press, Montreal (2005)
Kryzhanovsky, B., Mikaelian, A., Fonarev, A.: Vector Neural Net Identifying Many Strongly Distorted and Correlated Patterns. In: International Conference on Information Optics and Photonics Technology, Photonics Asia-2004, vol. 5642, pp. 124–133. SPIE Press, Beijing (2004)
Litinskii, L.: Parametrical Neural Networks and Some Other Similar Architectures. Optical Memory & Neural Networks 15(1), 11–19 (2006)
Kryzhanovsky, B., Kryzhanovsky, V., Magomedov, B., et al.: Vector Perceptron as Fast Search Algorithm. Optical Memory & Neural Networks 13(2), 103–108 (2004)
Kryzhanovsky, B.V., Kryzhanovsky, V.M.: Distinguishing Features of a Small Hopfield Model with Clipping of Synapses. Optical Memory & Neural Networks 17(3), 193–200 (2008)
Alieva, D., Kryzhanovsky, B., Kryzhanovsky, V., et al.: Q-valued neural network as a system of fast identification and pattern recognition. Pattern Recognition and Image Analysis 15(1), 30–33 (2005)
Kryzhanovsky, B.V., Mikaelian, A.L., Koshelev, V.N., et al.: On recognition error bound for associative Hopfield memory. Optical Memory & Neural Networks 9(4), 267–276 (2000)
Kryzhanovsky, V.M., Simkina, D.I.: Properties of clipped phase-vector of associative memory. Bulletin of Computer and Information Technologies 11, 20–25 (2007) (in Russian)
Kryzhanovsky, V.M.: Modified q-state Potts Model with Binarized Synaptic Coefficients. In: Kůrková, V., Neruda, R., Koutník, J. (eds.) ICANN 2008,, Part II. LNCS, vol. 5164, pp. 72–80. Springer, Heidelberg (2008)
Kryzhanovsky, V.M., Kryzhanovsky, B., Fonarev, A.: Application of Potts-model Perceptron for Binary Patterns Identification. In: Kůrková, V., Neruda, R., Koutník, J. (eds.) ICANN 2008, Part I. LNCS, vol. 5163, pp. 553–561. Springer, Heidelberg (2008)
Kryzhanovsky, V.M., Kryzhanovsky, B.V.: In: Lectures on Neuroinformatics on XI Russian Conference, Neuroinformatics – 2009. Moscow Engineering Physical Institute Press, Moscow (in press, 2009) (in Russian)
Perez-Vicente, C.J., Amit, D.J.: Optimized network for sparsely coded patterns. J. Phys. A 22, 559–569 (1989)
Palm, G., Sommer, F.T.: Information capacity in recurrent McCulloch-Pitts networks with sparsely coded memory states. Network 3, 1–10 (1992)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Kryzhanovsky, B., Kryzhanovsky, V., Litinskii, L. (2010). Machine Learning in Vector Models of Neural Networks. In: Koronacki, J., Raś, Z.W., Wierzchoń, S.T., Kacprzyk, J. (eds) Advances in Machine Learning II. Studies in Computational Intelligence, vol 263. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05179-1_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-05179-1_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05178-4
Online ISBN: 978-3-642-05179-1
eBook Packages: EngineeringEngineering (R0)