Commutative quaternion and multistate Hopfield neural networks
Commutative quaternion and multistate Hopfield neural networks
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DOI：
10.1109/ijcnn.2010.5596736
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发表时间：
2010-07
期刊：
影响因子：
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通讯作者：
T. Isokawa;H. Nishimura;N. Matsui
中科院分区：
文献类型：
--
作者：
T. Isokawa;H. Nishimura;N. Matsui
本文探讨了两种基于交换四元数的多态Hopfield神经网络，它们类似于Hamilton四元数，但具有交换乘法。在一种网络中，神经元的状态由两种相位和一个实数表示。另一类网络采用可交换四元数的分解形式，即神经元的状态由两个复值的组合组成。我们研究了这些网络的稳定性，即能量随网络状态的变化而单调减小。
This paper explores two types of multistate Hopfield neural networks, based on commutative quaternions that are similar to Hamilton's quaternions but with commutative multiplication. In one type of the networks, the state of a neuron is represented by two kinds of phases and one real number. The other type of the networks adopts the decomposed form of commutative quaternion, i.e., the state of a neuron consists of a combination of two complex values. We have investigated the stabilities of these networks, i.e., the energies monotonically decreases with respect to the changes of the network states.