Fundamental Study on Non-stationary Detection Method of Long Biological Time Series Using Topological Mappings

我们利用拓扑映射（TM）的方法，探索T.Kohonen，以检测非平稳的长生物时间序列的基本考虑。主要研究结果如下：1.将TM看作一种自适应矢量量化算法，从理论上分析了TM的特性。通过构造特征向量的李雅普诺夫函数，定量地导出了参考向量分布与输入信号概率分布之间的关系。2.特征向量的特征维数自动选择特性可以用来提取输入信号的内在结构。3.提出了一种利用TM产生的参考向量的位置和由其构造的连续映射来检测长生物时间序列中非平稳信号的方法。睡眠脑电图的分析。结果表明，该方法计算量大，在实际应用中存在一定的困难，提出了减少计算量的方法。基于上述结果，我们计划开发在连续映射中利用度量信息的方法，并将此方法应用于各种情况，收集更大数量的数据，以便与临床知识进行更密切的比较，提高检测的可靠性。

We made fundamental consideration on the method of utilizing topological mappings(TM),explored by T.Kohonen,in order to detect non-stationary in long biological time series. We obtained results below.1.We analyzed properties of TM theoretically by treating TM as a kind of adaptive vector quantization algorithm. We derived quantitatively the relationship between the reference vector distribution and the probability distribution of input signal,by constructing Lyapunov function for TM.2.Property of TM,called as automatic selection of characteristic dimension,can be used to extract intrinsic structure of input. Placement of reference vectors generated by TM is little affected by choice of coordinate system in input space,and this property of TM is plausible for the application of TM to signal analysis.3.We proposed the method of detecting non-stationary in long biological time series,which makes use of the placement of reference vectors generated by TM and continuated mappings constructed by it.4.The proposed method was applied,as an example,to the analysis of sleep EEG. It was confirmed that obtained results was in good agreement with knowledge in clinical fields.5.As the amount of calculation is so large that it may cause problem in applying this method,we made an idea for reducing the amount of calculation. This idea can actually reduce the amount of calculation to large extent.On the basis of results above,we plan to develop methods in which we utilize metric information in continuated mappings,and to apply this method to various cases and to gather larger amount of data, in order to make closer comparison with clinical knowledge and to improve reliability of the detection.