The use of Kernel set and sample memberships in the identification of nonlinear time series

The problem of system modeling and identification has attracted considerable attention in the nonlinear time series analysis mostly because of a large number of applications in diverse fields like financial management, biomedical system, transportation, ecology, electric power systems, hydrology, and aeronautics. Many papers have been presented on the study of time series clustering and identification. Nonetheless, we would like to point out that in dealing with clustering time series, we should also take the vague case as they belong to two or more classes simultaneously into account. Because many patterns of grouping in time series really are ambiguous, those phenomena should not be assigned to certain specific classes inflexibly. In this paper, we propose a procedure that can effectively cluster nonlinear time series into several patterns based on kernel set. This algorithm also combines with the concept of a fuzzy set. The membership degree of each datum corresponding to the cluster centers is calculated and is used for performance index grouping. We also suggest a principle for extending the fuzzy set by kernel set and further interpret events in a sensible light through these sets. Finally, the procedure is demonstrated by set off RRI data and its performance is shown to compare favorably with other procedures published in the literature.We are grateful to the referees for their careful reading and helpful comments.