A new network representation for time series analysis from the perspective of combinatorial property of ordinal patterns

Revealing system behavior from observed time series is a fundamental problem worthy of in-depth study and exploration, and has attracted extensive attention in a wide range of fields due to its wide application values. In this paper, we propose a novel network construction method for time series analysis, which is different from the existing ordinal network method concerning the transition probability of ordinal patterns in transition networks. The proposed network representation is based on the combinatorial property concerning the inversion number of ordinal patterns from the ordinal partitions of time series. For the proposed network construction method, the network nodes are represented by each ordinal partition of time series and the edge weight between network nodes is determined by a novel proximity relationship of ordinal patterns which is a newly defined metric based on the inversion number of ordinal patterns. Using random signals and chaotic signals as examples, we demonstrate the potential of the proposed network construction method for the network representation of time series. We also employ the proposed network construction method in quantitative EEG for the identification of three different physiological and pathological brain states. According to the results of AUC values, one can observe that the discriminating power of the AND of the proposed network construction method is slightly stronger than that of the available ordinal network. The experimental results illustrate that our proposed network construction method opens up a new pathway for network representation of time series, which is capable of quantifying time series for feature extraction and pattern learning for time series analysis.