一類離散Hopfield網(wǎng)絡(luò)吸引狀態(tài)的特征分析
EIGENVECTOR ANALYSIS OF SZABLE STATES FOR A KIND OF DISCRETE HOPFIELD NETWORKS
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摘要: 該文首先討論了超立方體圖所對應(yīng)的連接矩陣的特征向量,進而深入系統(tǒng)地分析了以n維超立方體為大規(guī)模局域連接模型的離散Hopfield網(wǎng)絡(luò)的吸引特性之一,穩(wěn)定吸引狀態(tài)的位置、數(shù)量及其分布。研究結(jié)果表明,網(wǎng)絡(luò)連接權(quán)矩陣的特征向量及其拼接向量均為網(wǎng)絡(luò)的吸引子或吸引環(huán),且其在網(wǎng)絡(luò)狀態(tài)空間中具有均勻?qū)ΨQ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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許進,保錚,超立方體的譜,工程數(shù)學(xué)學(xué)報,1999,(4),1-5.[2]汪云九,神經(jīng)信息的編碼,97中國神經(jīng)計算大會論文集(CCNS97),武漢,1997,Vol 132-37.[3]F. Luccio, L. Pagli, On a new Boolean function with applications, IEEE Trans. on Computers.1999, 48(3), 296-310.[4]R.J. Lechner, Harmonic Analysis of Switching Functions, Recent Development in SwitchingTheory, Washinton: Academic Press, 1971, 122-229.[5]北京大學(xué)數(shù)學(xué)系,高等代數(shù),北京,高等教育出版社,1988年第二版,第五章[6]閻平凡,黃端旭,人工神經(jīng)網(wǎng)絡(luò)-模型,分析與應(yīng)用,合肥,安徽教育出版社,1991年,第三章.[7]J..J. Hopfield, Neural networks and physical system with emergent collective computer abilities.Proc. Natl. Acad. USA, 1982, 79(3), 2554-2558.[8]Li Yujian, Wang Xiangdong, Chen Chuan, The maximum number of orthogonal memory patterns,Proc. of 1998 International Conference on Neural Networks and Brain(ICNN B98), Beijing,1998, 79-81.[9]張軍英,許進,保錚,一類離散Hopfield網(wǎng)絡(luò)的吸引特性研究,電子與信息學(xué)報,2001,23(9),872-882. -
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