Binary associative memories with complemented operations

Gamino-Carranza, Arturo

International Journal of Applied Mathematics and Computer Science, Tome 33 (2023) no. 2, pp. 249-265.

Résumé

Associative memories based on lattice algebra are of great interest in pattern recognition applications due to their excellent storage and recall properties. In this paper, a class of binary associative memory derived from lattice memories is presented, which is based on the definition of new complemented binary operations and threshold unary operations. The new learning method generates memories M and W; the former is robust to additive noise and the latter is robust to subtractive noise. In the recall step, the memories converge in a single step and use the same operation as the learning method. The storage capacity is unlimited, and in autoassociative mode there is perfect recall for the training set. Simulation results suggest that the proposed memories have better performance compared to other models.

Détail

Keywords: associative memory, neural network, morphological associative memory, perfect recall
Mots-clés : pamięć asocjacyjna, sieć neuronowa, pamięć asocjacyjna morfologiczna

Bibliographie

[1] [1] Barkalov, A., Titarenko, L. and Mazurkiewicz, M. (2022). Improving the LUT count for Mealy FSMs with transformation of output collections, International Journal of Applied Mathematics and Computer Science 32(3): 479-494, DOI: 10.34768/amcs-2022-0035.

[2] [2] Chung, F.-L. and Lee, T. (1994). Towards a high capacity fuzzy associative memory model, Proceedings of the 1994 IEEE International Conference on Neural Networks (ICNN’94), Florida, USA, Vol. 3, pp. 1595-1599, DOI: 10.1109/ICNN.1994.374394.

[3] [3] Feng, N., Cao, X., Li, S., Ao, L. and Wang, S. (2009). A new method of morphological associative memories, Emerging Intelligent Computing Technology and Applications, with Aspects of Artificial Intelligence, ICIC 2009, Ulsan, South Korea, pp. 407-416, DOI: 10.1007/978-3-642-04020-7 43.

[4] [4] Feng, N.-Q., Tian, Y., Wang, X.-F., Song, L.-M., Fan, H.-J. and Shuang-Xi, W. (2015). Logarithmic and exponential morphological associative memories, Journal of Software 26(7): 1662-1674, DOI: 10.13328/j.cnki.jos.004620.

[5] [5] Feng, N. and Yao, Y. (2016). No rounding reverse fuzzy morphological associative memories, Neural Network World 26(6): 571-587, DOI: 10.14311/NNW.2016.26.033.

[6] [6] Gamino-Carranza, A. (2022). Binary associative memories, https://github.com/arturogam/Binary-Associative-Memories, (programming code).

[7] [7] Hassoun, M.H. (1993). Associative Neural Memories: Theory and Implementation, Oxford University Press, Inc., New York.

[8] [8] Hattori, M., Fukui, A. and Ito, H. (2002). A fast method of constructing kernel patterns for morphological associative memory, 9th International Conference on Neural Information Processing, ICONI 02, Singapore, pp. 1058-1063, DOI: 10.1109/ICONIP.2002.1198222.

[9] [9] Hopfield, J.J. (1982). Neural networks and physical systems with emergent collective computational abilities, Proceedings of the National Academy of Sciences of the United States of America 79(8): 2554-2558, DOI: 10.1073/pnas.79.8.2554.

[10] [10] Ishi, S., Fukumizu, K. and Watanabe, S. (1996). A network of chaotic elements for information processing, Neural Networks 9(1): 25-40, DOI: 10.1016/0893-6080(95)00100-X.

[11] [11] Kosko, B. (1991). Fuzzy associative memories, Proceedings of the 2nd Joint Technology Workshop on Neural Networks and Fuzzy Logic, Houston, USA, pp. 3-58.

[12] [12] Lee, G. and Farhat, N.H. (2001). Parametrically coupled sine map networks, International Journal of Bifurcation and Chaos 11(07): 1815-1834, DOI: 10.1142/S0218127401003048.

[13] [13] Liu, P. (1999). The fuzzy associative memory of max-min fuzzy neural network with threshold, Fuzzy Sets and Systems 107(2): 147-157, DOI: 10.1016/S0165-0114(97)00352-7.

[14] [14] McEliece, R., Posner, E., Rodemich, E. and Venkatesh, S. (1987). The capacity of the Hopfield associative memory, IEEE Transactions on Information Theory 33(4): 461-482, DOI: 10.1109/TIT.1987.1057328.

[15] [15] Mustafa, A.A. (2018). Probabilistic binary similarity distance for quick binary image matching, IET Image Processing 12(10): 1844-1856, DOI: 10.1049/iet-ipr.2017.1333.

[16] [16] Rani, S.S., Rao, N. and Vatsal, S. (2018). Review on neural networks associative memory models, International Journal of Pure and Applied Mathematics 120(6): 3143-3154.

[17] [17] Ritter, G.X., Sussner, P. and Díaz de León, J.L. (1998). Morphological associative memories, IEEE Transactions on Neural Networks 2(9): 281-293, DOI: 10.1109/72.661123.

[18] [18] Ritter, G.X. and Urcid, G. (2021). Introduction to Lattice Algebra. With Applications in AI, Pattern Recognition, Image Analysis, and Biomimetic Neural Networks, Chapman and Hall/CRC, Boca Raton.

[19] [19] Salgado-Ramírez, J.C., Vianney Kinani, J.M., Cendejas-Castro, E.A., Rosales-Silva, A.J., Ramos-Díaz, E. and Díaz-de Léon-Santiago, J.L. (2022). New model of heteroasociative min memory robust to acquisition noise, Mathematics 10(148): 2-35, DOI: 10.3390/math10010148.

[20] [20] Sussner, P. (2000). Observations on morphological associative memories and the kernel method, Neurocomputing 31(1-4): 167-183, DOI: 10.1016/S0925-2312(99)00176-9.

[21] [21] Sussner, P. and Valle, M.E. (2006). Implicative fuzzy associative memories, IEEE Transactions on Fuzzy Systems 14(6): 793-807, DOI: 10.1109/TFUZZ.2006.879968.

[22] [22] Tikhonenko, O., Ziółkowski, M. and Kempa, W.M. (2021). Queueing systems with random volume customers and a sectorized unlimited memory buffer, International Journal of Applied Mathematics and Computer Science 31(3): 471-486, DOI: 10.34768/amcs-2021-0032.

[23] [23] Urcid, G. and Ritter, G.X. (2007). Noise masking for pattern recall using a single lattice matrix associative memory, in V.G. Kaburlasos and G.X. Ritter (Eds), Computational Intelligence Based on Lattice Theory, Springer, Berlin/Heidelberg, pp. 81-100, DOI: 10.1007/978-3-540-72687-6_5.

[24] [24] Wang, S. and Lu, H. (2004). On new fuzzy morphological associative memories, IEEE Transactions on Fuzzy Systems 12(3): 316-323, DOI: 10.1109/TFUZZ.2004.825977.

[25] [25] Wang, T. and Jia, N. (2017). A GCM neural network using cubic logistic map for information processing, Neural Computing and Applications 28(7): 1891-1903, DOI: 10.1007/s00521-016-2407-4.

[26] [26] Wang, T., Jia, N. and Wang, K. (2012). A novel GCM chaotic neural network for information processing, Communications in Nonlinear Science and Numerical Simulation 17(12): 4846-4855, DOI: 10.1016/j.cnsns.2012.05.011.

[27] [27] Xia, G., Tang, Z. and Li, Y. (2004). Hopfield neural network with hysteresis for maximum cut problem, Neural Information Processing-Letters and Reviews 4(2): 19-26.

[28] [28] Xiao, P., Yang, F. and Yu, Y. (1997). Max-min encoding learning algorithm for fuzzy max-multiplication associative memory networks, 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation, Orlando, USA, pp. 3674-3679, DOI: 10.1109/ICSMC.1997.633240.

[29] [29] Zhang, S., Lin, S. and Chen, C. (1993). Improved model of optical fuzzy associative memory, Optics Letters 18(21): 1837–1839, DOI: 10.1364/OL.18.001837.

[30] [30] Zheng, L. and Tang, X. (2005). A new parameter control method for S-GCM, Pattern Recognition Letters 26(7): 939-942, DOI: 10.1016/j.patrec.2004.09.041.