Geodesic
Autoassociative Hamming Neural Network
Russian journal of nonlinear dynamics, Tome 17 (2021) no. 2, pp. 175-193

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An autoassociative neural network is suggested which is based on the calculation of Hamming distances, while the principle of its operation is similar to that of the Hopfield neural network. Using standard patterns as an example, we compare the efficiency of pattern recognition for the autoassociative Hamming network and the Hopfield network. It is shown that the autoassociative Hamming network successfully recognizes standard patterns with a degree of distortion up to 40% and more than 60%, while the Hopfield network ceases to recognize the same patterns with a degree of distortion of more than 25% and less than 75%. A scheme of the autoassociative Hamming neural network based on McCulloch–Pitts formal neurons is proposed. It is shown that the autoassociative Hamming network can be considered as a dynamical system which has attractors that correspond to the reference patterns. The Lyapunov function of this dynamical system is found and the equations of its evolution are derived.
Keywords: autoassociative Hamming network, Hopfield network, iterative algorithm, pattern recognition, dynamical system, neurodynamics, attractors, stationary states. 
@article{ND_2021_17_2_a3,
     author = {E. S. Antipova and S. A. Rashkovskiy},
     title = {Autoassociative {Hamming} {Neural} {Network}},
     journal = {Russian journal of nonlinear dynamics},
     pages = {175--193},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ND_2021_17_2_a3/}
}
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E. S. Antipova; S. A. Rashkovskiy. Autoassociative Hamming Neural Network. Russian journal of nonlinear dynamics, Tome 17 (2021) no. 2, pp. 175-193. http://geodesic.mathdoc.fr/item/ND_2021_17_2_a3/