基于相关向量机的小世界神经元网络拓扑估计

Estimation of small-world neuronal network topology based on relevance vector machine

采用相关向量机从含噪时间序列中估计小世界神经元网络的节点动力学方程和拓扑结构。在具有多项式结构或能以幂级数展开的动力学系统中,将未知方程写成统一多项式形式,原动力学方程的项在统一多项式中是稀疏的,利用稀疏贝叶斯学习估计出稀疏项从而实现动力学方程和拓扑结构的估计。利用该方法对FHN小世界神经元网络进行节点动力学方程和拓扑估计,结果表明,该方法能快速准确地估计节点动力学方程结构和网络拓扑,对动力学方程系数和网络耦合强度有很高的估计精度,而且对噪声有强鲁棒性。

This paper applied relevance vector machine to estimate node dynamical equations and topology of small-world neuronal network from noisy time series.According to the fact that many dynamical equations or its power series expansion had polynomial structure,by constructing a unified polynomial and making the original dynamical equation sparse in the unified polynomial,obtained dynamical equations and network topology obtained while used sparse Bayesian learning to estimate the sparse nonzero terms.FHN small-world neuronal network as a paradigm demonstrated the estimation effect of the dynamical equations and network topology.The results show that the estimating strategy can identify equations structure and network topology accurately and quickly,the error is small in dynamical equations coefficients and couple strength estimation and is robust to noise.