基于功率谱及有限穿越可视图的癫痫脑电信号分析算法

针对可视图（VG）算法存在噪声鲁棒性差的问题，提出一种改进的有限穿越可视图（LPVG）建网方法。该算法基于可视图（VG）算法的可视性准则，并设定有限穿越视距，将时间序列中满足条件的点连接起来，从而将时间序列映射为网络。首先，对LPVG算法进行性能分析；然后，将LPVG算法结合功率谱密度（PSD）算法应用到癫痫发作前、中、后脑电信号的识别上；最后，提取三种状态下癫痫脑电信号的LPVG网络特征参数，研究癫痫对网络拓扑结构的影响。仿真结果表明，与VG和水平穿越可视图（HVG）相比，虽然LPVG算法的时间复杂度较高，但是LPVG对信号中的噪声具有较强的鲁棒性：分别对周期、随机、分形和混沌四种时间序列进行LPVG建网，发现随着噪声强度增大，LPVG网络聚类系数的波动率均为最低，分别为6.73%、0.05%、0.99%和3.20%。接下来对脑电信号的PSD和LPVG建网分析结果表明，癫痫发作中，PSD值在delta频带下显著增强，而在theta频带下显著降低；LPVG网络拓扑结构有所改变，网络中各模块的独立性有所提高，网络的平均路径长度增大，复杂度降低。所提的功率谱密度和有限穿越可视图算法能够有效表征癫痫前、中、后三种状态下的脑电信号能量分布和单通道信号可视化后的网络拓扑结构的异常，为癫痫的病理研究和临床诊断提供帮助。

Analysis algorithm of electroencephalogram signals for epilepsy diagnosis based on power spectral density and limited penetrable visibility graph

Focused on poor robustness to noise of the Visibility Graph (VG) algorithm, an improved Limited Penetrable Visibility Graph (LPVG) algorithm was proposed. LPVG algorithm could map time series into networks by connecting the points of time series which satisfy the certain conditions based on the visibility criterion and the limited penetrable distance. Firstly, the performance of LPVG algorithm was analyzed. Secondly, LPVG algorithm was combined with Power Spectrum Density (PSD) to apply to the automatic identification of epileptic ElectroEncephaloGram (EEG) before, during and after the seizure. Finally, the characteristic parameters of the LPVG network in the three states were extracted to study the influence of epilepsy seizures on the network topology. The simulation results show that compared with VG and Horizontal Visibility Graph (HVG), although LPVG had a high time complexity, it had strong robustness to noise in the signal:when mapping the typical periodic, random, fractal and chaos time series into networks by LPVG, it was found that as the noise intensity increased, the fluctuation rates of clustering coefficient by LPVG network were always the lowest, respectively 6.73%, 0.05%, 0.99% and 3.20%. By the PSD and LPVG analysis, it was found that epilepsy seizure had great influence on the brain energy. PSD was obviously enhanced in the delta frequency band, and significantly reduced in the theta frequency band; the topological structure of the LPVG network changed during the seizure, characterized by the independent enhanced network module, increased average path length and decreased graph index complexity. The PSD and LPVG applied in this paper could be taken as an effective measure to characterize the abnormality of the energy distribution and topological structure of single EEG signal channel, which would provide help for the pathological study and clinical diagnosis of epilepsy.