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| In this talk we discuss a quantity called conditional entropy of ordinal patterns (CEofOP).
It is similar to the celebrated permutation entropy: the latter characterizes the diversity of ordinal patterns themselves, whereas the CEofOP -- the average diversity of the ordinal patterns succeeding a given ordinal pattern.
We observe that in several relatively simple cases including systems with regular dynamics and Markov shifts over the binary alphabet, the CEofOP for a finite order $d$ coincides with the Kolmogorov-Sinai entropy, while the permutation entropy only asymptotically approaches it. Moreover, we demonstrate that under certain assumptions CEofOP provides a better estimation of the KS entropy than the permutation entropy.
Finally we discuss possible applications of the CEofOP to the segmentation of time series. |
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