Hyperbolic Hopfield neural networks with directional multistate activation function

被引:40
作者
Kobayashi, Masaki [1 ]
机构
[1] Univ Yamanashi, Ctr Math Sci, Takeda 4-3-11, Kofu, Yamanashi 4008511, Japan
关键词
Complex-valued neural networks; Hopfield neural networks; Hyperbolic number; Projection rule; ASSOCIATIVE MEMORY; RULE;
D O I
10.1016/j.neucom.2017.10.053
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
Complex-valued Hopfield neural networks (CHNNs) have been applied to various fields, although they tend to suffer from low noise tolerance. Rotational invariance, which is an inherent property of CHNNs, reduces noise tolerance. CHNNs have been used in attempts to extend by Clifford algebra, such as hyperbolic and quaternion algebra. In this work, the directional multistate activation function is introduced to hyperbolic Hopfield neural networks (HHNNs), and the stability condition is also given. The proposed models do not have rotational invariance, and have fewer pseudomemories than CHNNs. The projection rule is also introduced to the HHNNs. In general, the diagonal elements should be eliminated from the obtained matrix for noise tolerance, although they cannot be eliminated in HHNNs. We investigate the relation between the diagonal elements and noise tolerance by computer simulations. (c) 2017 Elsevier B.V. All rights reserved.
引用
收藏
页码:2217 / 2226
页数:10
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