Associative Memory in quaternionic Hopfield Neural Network
Associative Memory in quaternionic Hopfield Neural Network
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DOI：
10.1142/s0129065708001440
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发表时间：
2008-04
影响因子：
8
通讯作者：
T. Isokawa;H. Nishimura;N. Kamiura;N. Matsui
中科院分区：
文献类型：
--
作者：
T. Isokawa;H. Nishimura;N. Kamiura;N. Matsui
研究了基于四元数Hopfield神经网络的联想记忆网络。这些网络由四元数神经元组成，输入，输出，阈值和连接权重都用四元数表示，这是一类超复数系统。介绍了网络的能量函数和嵌入模式的Hebbian规则。研究了三个神经元和四个神经元网络的稳定态及其稳定域。阐明了四元数网络中最多存在16个称为多重态分量的稳定态作为退化存储模式，并且每个稳定态在四元数网络中都有其盆区。
Associative memory networks based on quaternionic Hopfield neural network are investigated in this paper. These networks are composed of quaternionic neurons, and input, output, threshold, and connection weights are represented in quaternions, which is a class of hypercomplex number systems. The energy function of the network and the Hebbian rule for embedding patterns are introduced. The stable states and their basins are explored for the networks with three neurons and four neurons. It is clarified that there exist at most 16 stable states, called multiplet components, as the degenerated stored patterns, and each of these states has its basin in the quaternionic networks.