Kobayashi M. O(2) -Valued Hopfield Neural Networks.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2019;
30:3833-3838. [PMID:
30843853 DOI:
10.1109/tnnls.2019.2897994]
[Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
In complex-valued Hopfield neural networks (CHNNs), the neuron states are complex numbers whose amplitudes are: 1) they can also be described in special orthogonal matrices of order and 2) here, we propose a new Hopfield model, the O(2) -valued Hopfield neural network [ O(2) -HNN], whose neuron states are extended to orthogonal matrices. Its neuron states are embedded in 4-D space, while those of CHNNs are embedded in 2-D space. Computer simulations were conducted to compare the noise tolerance (NT) and storage capacity (SC) of CHNNs, O(2) -HNNs, and rotor Hopfield neural networks. In terms of SC, O(2) -HNNs outperformed the others, while in NT, they outdid CHNNs.
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