最优加权随机汇池网络的自适应算法研究
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摘要
对最优加权随机汇池网络的自适应算法进行研究,以均方误差作为随机汇池网络输出性能评价指标,推导了最小均方(LMS)和Kalman-LMS算法的递归表达式,并应用到输入信号方差发生改变的非稳态情况中,结果表明两种自适应算法都能够迭代收敛到权的最优解。与LMS算法相比,Kalman-LMS算法不仅收敛速度快,而且权均方偏差每一步都是最优的,在网络节点的个数较少时,Kalman-LMS算法能够获得更小的均方误差,而随着网络节点的个数增加,两种自适应算法得到的均方误差趋于一致。
In this paper,the adaptive algorithm of optimally weighted stochastic pool network is studied.The mean square error is used as the output performance evaluation index of the stochastic pooling network.The recursive expressions of the least mean square(LMS)algorithm and the Kalman-LMS algorithm are derived.The related results show that,for the nonstationary case of varying variances of inputs,both adaptive algorithms can converge to the optimal solution of weight vectors.However,the Kalman-LMS algorithm not only has a fast convergence speed,but also the weight mean square deviation is optimal at each step.When the number of network nodes is small,Kalman-LMS can obtain a smaller mean square error.As the number of network nodes increases,the mean square error obtained by the two adaptive algorithms tends to be consistent.
In this paper,the adaptive algorithm of optimally weighted stochastic pool network is studied.The mean square error is used as the output performance evaluation index of the stochastic pooling network.The recursive expressions of the least mean square(LMS)algorithm and the Kalman-LMS algorithm are derived.The related results show that,for the nonstationary case of varying variances of inputs,both adaptive algorithms can converge to the optimal solution of weight vectors.However,the Kalman-LMS algorithm not only has a fast convergence speed,but also the weight mean square deviation is optimal at each step.When the number of network nodes is small,Kalman-LMS can obtain a smaller mean square error.As the number of network nodes increases,the mean square error obtained by the two adaptive algorithms tends to be consistent.
引文
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[20]Xu L,Duan F,Gao X,et al.Adaptive recursive algorithm for optimal weighted suprathreshold stochastic resonance[J].Royal Society Open Science.2017,4(9):1-12.
[21]景文腾,韩博,耿金花,等.最优加权随机汇池网络估计性能研究[J].复杂系统与复杂性科学,2018,15(3):89-93.Jing Wenteng,Han Bo,Gend Jinhua,et al.Study of estimation performance of optimally weighted stochastic pooling networks[J].Complex System and Complexity Science,2018,15(3):89-93.
[22]Widrow B,Stearns S D.Adaptive Signal Processing[M].王永德,龙宪惠,译.四川:四川大学出版社,1991.
[23]Xu L,Vladusich T,Duan F,et al.Decoding suprathreshold stochastic resonance with optimal weights[J].Physics Letters A.2015,379(38):2277-2283.
[2]Mcdonnell M D,Abbott D,Pearce C E M.An analysis of noise enhanced information transmission in an array of comparators[J].Microelectronics Journal,2002,33(12):1079-1089.
[3]Nguyen T.Robust data-optimized stochastic analog-to-digital converters[J].IEEE Transactions on Signal Processing,2007,55(6):2735-2740.
[4]Panzeri S,Petroni F,Petersen R S,et al.Decoding neuronal population activity in rat somatosensory cortex:role of columnar organization[J].Cerebral Cortex,2003,13(1):45-52.
[5]Hoch T,Wenning G,Obermayer K.Optimal noise-aided signal transmission through populations of neurons[J].Physical Review E,2003,68(1):011911.
[6]Nikitin A,Stocks N G,Morse R P.Enhanced information transmission with signal-dependent noise in an array of nonlinear elements[J].Physical Review E,2007,75(2Pt 1):021121.
[7]Zozor S,Amblard P O,Duchêne C.On pooling networks and fluctuation in suboptimal detection framework[J].Fluctuation&Noise Letters,2007,7(1):39-60.
[8]Martorell F,Rubio A.Cell architecture for nanoelectronic design[J].Microelectronics Journal,2008,39(8):1041-1050.
[9]Benzi R,Sutera A,Vulpiani A.The mechanism of stochastic resonance[J].Journal of Physical A,1981,14(11):453-458.
[10]Gammaitoni L,Hnggi P,Jung P,et al.Stochastic resonance[J].Reviews of Modern Physics,2008,70(1):45-105.
[11]Dykman M I,Mcclintock P V E.What can stochastic resonance do?[J].Nature,1998,391(6665):344.
[12]Kay S.Can detectability be improved by adding noise?[J].IEEE Signal Processing Letters,2000,7(1):8-10.
[13]Abbott D.Overview:unsolved problems of noise and fluctuations.[J].Chaos.2001,11(3):526-538.
[14]Oliaei O.Stochastic resonance in sigma-delta modulators[J].Electronics Letters,2003,39(2):173-174.
[15]Mcdonnell M D,Stocks N G,Pearce C E M,et al.Analog-to-digital conversion using suprathreshold stochastic resonance[J].Smart Structures,Devices,and Systems II,2005,5649(1/3):75-84.
[16]Widrow B,McCool J M,Larimore M G,et al.Stationary and nonstationary learning characteristics of the LMS adaptive filter[J].Proceedings of the IEEE,1976,64(8):1151-1162.
[17]Widrow B,Walach E.On the statistical efficiency of the LMS algorithm with nonstationary inputs[J].IEEE Transactions on Information Theory,1984,30(2):211-221.
[18]Kalman R.A new approach to linear filtering and prediction problems[J].Journal of Basic Engineering Transactions,1960,82(D):35-45.
[19]Mandic D P,Kanna S,Constantinides A G.On the Intrinsic relationship between the least mean square and Kalman filters[J].IEEE Signal Processing Magazine,2015,32(6):117-122.
[20]Xu L,Duan F,Gao X,et al.Adaptive recursive algorithm for optimal weighted suprathreshold stochastic resonance[J].Royal Society Open Science.2017,4(9):1-12.
[21]景文腾,韩博,耿金花,等.最优加权随机汇池网络估计性能研究[J].复杂系统与复杂性科学,2018,15(3):89-93.Jing Wenteng,Han Bo,Gend Jinhua,et al.Study of estimation performance of optimally weighted stochastic pooling networks[J].Complex System and Complexity Science,2018,15(3):89-93.
[22]Widrow B,Stearns S D.Adaptive Signal Processing[M].王永德,龙宪惠,译.四川:四川大学出版社,1991.
[23]Xu L,Vladusich T,Duan F,et al.Decoding suprathreshold stochastic resonance with optimal weights[J].Physics Letters A.2015,379(38):2277-2283.