Using evolution rule in complex time series comparison

Complex time series appear in numerous applications and are related to some essential physiological and natural systems. Their comparison faces big challenges: 1) with different complexity; 2) with significant phase shift in one series or shift\on the time axis. Existing methods work well for periodic time-series data, but fail to produce satisfactory results in complex time-series. In this paper, we introduce a novel distance function based on the evolution rule for complex time series comparison. Here, the evolution rule, as the innate generative mechanism of time series, is creatively used to characterize complicated dynamics from complex time series. The comparison includes different level comparisons: the coarse level is to compare the difference in complexity, and the fine level is to compare the difference in actual evolution behavior. The proposed method is inspired by the observation that similar sequences come from the same source, e.g. a person's heart, in the case of ECG, thus two similar series will have the same innate generative mechanism. The performance has been verified by the conducting experiments, and the experiment results show that the proposed method is superior to the previously existing methods in clustering and classification on some real data sets.