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| 复形态联想记忆及其性能分析 |
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陈松灿1,2, 刘伟龙1
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1.南京航空航天大学,计算机科学与工程系,江苏,南京,210016;2.南京大学,计算机软件新技术国家重点实验室,江苏,南京,210093
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| 摘要: |
| 在Ritter的实域形态联想记忆(real morphological associative memory,简称RMAM)模型的基础上,通过在复数域中序关系的引入构成复数格和环,导出了在复数域上与RMAM相一致的联想规则,构建了一类复域MAM(complex MAM,简称CMAM),从而将RMAM从实域推广至复域,使其可直接处理复信号(如经FFT(fast Fourier Transformation)变换所得数据).证明了该模型的收敛性,分析了其纠错能力和存储能力,并获得了与RMAM相一致的一系列定理和性质.此外,还比较了复形态网络和其他网络(如Hopfield神经网络)的异同.计算机仿真结果表明了CMAM的可行性. |
| 关键词: 联想记忆 神经网络 形态学 格 复域 |
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| 基金项目:国家自然科学基金资助项目(69701004);国家教育部青年骨干教师资助项目;南京大学计算机软件新技术国家重点实验室基金资助项目 |
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| Complex Morphological Associative Memories and Their Performance Analysis |
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CHEN Song-can,LIU Wei-long
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| Abstract: |
| On the basis of Ritter real morphological associative memory (RMAM), complex lattices and complex rings are defined respectively through introducing two ordinal relationships between complex numbers, consequently the same recall rules are obtained as RMAM in complex domain and construct a class of complex MAM (CMAM), called extended RMAM. The CMAM can directly process complex signals such as FFT-ed complex data. In this paper, the convergence of the proposed model is proved, its error-correction capability and storage capacity are analyzed,and at the same time the corresponding theorems and properties similar to the RMAM are obtained.Further the difference between the CMAM andother neural networks such as Hopfield network is stressed.The carried-out computer simulations show its feasibility. |
| Key words: associative memory neural networks morphology lattice complex lattice |
