一类离散Hopfield网络吸引状态的特征分析
EIGENVECTOR ANALYSIS OF SZABLE STATES FOR A KIND OF DISCRETE HOPFIELD NETWORKS
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摘要: 该文首先讨论了超立方体图所对应的连接矩阵的特征向量,进而深入系统地分析了以n维超立方体为大规模局域连接模型的离散Hopfield网络的吸引特性之一,稳定吸引状态的位置、数量及其分布。研究结果表明,网络连接权矩阵的特征向量及其拼接向量均为网络的吸引子或吸引环,且其在网络状态空间中具有均匀对称的分布格局。Abstract: The eigenvector of n-cube graph is found and then a kind of Hopfield networks with n-cube as its structure and connection situation, called n-cube network, are analysed theoretically for the attractions states/cycles and their distribution in the state space of the network. The analysis shows that the eigenvectors of the connection matrix of the network and their linkages are, in general, either the attraction states or attraction cycles of the net, and the distribution of these states/cycles is symmetric and uniform in state space of the network.
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