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

我们对T.Kohonen探索的利用拓扑映射(TM)来检测长生物时间序列的非平稳性的方法进行了初步的考虑。1.将TM作为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TM的Lyapunov函数，定量地推导了输入信号的参考向量分布与概率分布之间的关系。TM的性质称为特征维度的自动选择，可以用来提取输入的内在结构。TM生成的参考向量的放置几乎不受输入空间坐标系选择的影响，TM的这一特性对于TM在信号分析中的应用是可行的。3.提出了一种利用TM生成的参考向量的放置及其构造的连续映射来检测长生物时间序列中非平稳的方法。4.将该方法应用于睡眠脑电信号的分析。经验证，所得结果与临床实际知识吻合较好。5.由于计算量较大，在实际应用中可能会出现问题，我们提出了减少计算量的设想。在上述研究结果的基础上，我们计划开发在连续映射中利用度量信息的方法，并将该方法应用于各种情况，收集更多的数据，以便与临床知识进行更紧密的比较，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.