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

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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.