Kernel Computation in Morphological Bidirectional Associative Memories
Conference paper
Abstract
Morphological associative memories (MAMs) use a lattice algebra approach to store and recall pattern associations. The lattice matrix operations endow MAMs with properties that are completely different than those of traditional associative memory models. In the present paper, we focus our attention to morphological bidirectional associative memories (MBAMs) capable of storing and recalling non-boolean patterns degraded by random noise. The notions of morphological strong independence (MSI), minimal representations, and kernels are extended to provide the foundation of bidirectional recall when dealing with noisy inputs. For arbitrary pattern associations, we present a practical solution to compute kernels in MBAMs by induced MSI.
Keywords
Associative Memory Kernel Computation Minimal Representation Pattern Association Memory Scheme
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Download
to read the full conference paper text
References
- 1.Chen, H., et al.: Higher order correlation model for associative memories. In: Denker, J.S. (ed.) Neural Networks for Computing, AIP Proc., vol. 151 (1986)Google Scholar
- 2.Cuninghame-Green, R.: Minimax algebra. Lectures Notes in Economics and Mathematical Systems, vol. 166. Springer, New York (1979)MATHGoogle Scholar
- 3.Hopfield, J.J.: Neurons with graded response have collective computational properties like those of two state neurons. In: Proc. of the National Academy of Sciences, U.S.A., vol. 81, pp. 3088–3092 (1984)Google Scholar
- 4.Kohonen, T.: Correlation matrix memory. IEEE Trans. Computers C-21, 353–359 (1972)CrossRefGoogle Scholar
- 5.Kosko, B.: Bidirectional associative memories. IEEE Trans. Systems, Man, and Cybernetics 18(1), 49–60 (1988)CrossRefMathSciNetGoogle Scholar
- 6.McEliece, R., et al.: The capacity of the Hopfield associative memory. Trans. Information Theory 1, 33–45 (1987)Google Scholar
- 7.Okajima, K., Tanaka, S., Fujiwara, S.: A heteroassociative memory with feedback connection. In: Proc. IEEE 1st Inter. Conf. Neural Networks, vol. 2, pp. 711–718 (1987)Google Scholar
- 8.Ritter, G.X.: Image Algebra. University of Florida, Gainesville, FL (1994) (Unpublished manuscript), Available at ftp://ftp.cise.ufl.edu/pub/scr/ia/documents
- 9.Ritter, G.X., Sussner, P., Diaz de Leon, J.L.: Morphological associative memories. IEEE Trans. Neural Networks 9(2), 281–293 (1998)CrossRefGoogle Scholar
- 10.Ritter, G.X., Diaz de Leon, J.L., Sussner, P.: Morphological bidirectional associative memories. Neural Networks 12(6), 851–867 (1999)CrossRefGoogle Scholar
- 11.Ritter, G.X., Urcid, G.: Minimal representations and morphological associative memories for pattern recall. In: Proc. 7th Iberoamerican Congress on Pattern Recogniton (2002)Google Scholar
- 12.Ritter, G.X., Urcid, G., Iancu, L.: Reconstruction of noisy patterns using morphological associative memories. J. of Math. Imaging and Vision 19(5), 95–111 (2003)MATHCrossRefMathSciNetGoogle Scholar
- 13.Sussner, P.: Observations on morphological associative memories and the kernel method. Neurocomputing 31, 167–183 (2000)CrossRefGoogle Scholar
- 14.Sussner, P.: Binary autoassociative morphological memories based on the kernel and dual kernel methods. In: Int. Joint Conf. on Neural Networks (2003)Google Scholar
- 15.Wu, Y., Pados, D.A.: A feedforward bidirectional associative memory. IEEE Trans. Neural Networks 11(4), 859–866 (2000)CrossRefGoogle Scholar
Copyright information
© Springer-Verlag Berlin Heidelberg 2003