Generalized entropy plane based on permutation entropy and distribution entropy analysis for complex time series

Entropy is an accessible way to work as a measure of the irregularity and the uncertainty between the predicting knowledge and the given time series. Statistical complexity measure (SCM) combining Shannon entropy and the extensive Jensen–Shannon divergence provides important additional information regarding the peculiarities of the underlying probability distribution, not already detected by the entropy. In this paper, we extend the traditional complexity-entropy causality plane, which applies the diagram of SCM versus normalized Shannon entropy, to two generalized complexity-entropy plane based on Permutation entropy (PE) and Permuted distribution entropy (PEDisEn). Moreover, as the important extension of the Shannon entropy, the Tsallis entropy and Rényi entropy are used to construct the plane. We discuss the parameter selection for the PE plane and PEDisEn plane respectively. Outlier detection is recently a heated point focusing on discovering patterns that occur infrequently in the time series in data mining. However, there exists few entropy plane based methods in outlier detection. We apply the proposed procedure to the real world data for outlier detection. It turns out that the generalized entropy plane is robust to the type of original series and is efficient for detecting outliers.