{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T20:57:21Z","timestamp":1781816241479,"version":"3.54.5"},"reference-count":54,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2016,1,8]],"date-time":"2016-01-08T00:00:00Z","timestamp":1452211200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.mdpi.com"],"crossmark-restriction":true},"short-container-title":["Entropy"],"abstract":"<jats:p>Entropy has been a common index to quantify the complexity of time series in a variety of fields. Here, we introduce an increment entropy to measure the complexity of time series in which each increment is mapped onto a word of two letters, one corresponding to the sign and the other corresponding to the magnitude. Increment entropy (IncrEn) is defined as the Shannon entropy of the words. Simulations on synthetic data and tests on epileptic electroencephalogram (EEG) signals demonstrate its ability of detecting abrupt changes, regardless of the energetic (e.g., spikes or bursts) or structural changes. The computation of IncrEn does not make any assumption on time series, and it can be applicable to arbitrary real-world data.<\/jats:p>","DOI":"10.3390\/e18010022","type":"journal-article","created":{"date-parts":[[2016,1,8]],"date-time":"2016-01-08T23:38:27Z","timestamp":1452296307000},"page":"22","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":64,"title":["Increment Entropy as a Measure of Complexity for Time Series"],"prefix":"10.3390","volume":"18","author":[{"given":"Xiaofeng","family":"Liu","sequence":"first","affiliation":[{"name":"College of IOT Engineering, Hohai University, Changzhou 213022, China"},{"name":"Changzhou Key Laboratory of Robotics and Intelligent Technology, Changzhou 213022, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Aimin","family":"Jiang","sequence":"additional","affiliation":[{"name":"College of IOT Engineering, Hohai University, Changzhou 213022, China"},{"name":"Changzhou Key Laboratory of Robotics and Intelligent Technology, Changzhou 213022, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ning","family":"Xu","sequence":"additional","affiliation":[{"name":"College of IOT Engineering, Hohai University, Changzhou 213022, China"},{"name":"Changzhou Key Laboratory of Robotics and Intelligent Technology, Changzhou 213022, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianru","family":"Xue","sequence":"additional","affiliation":[{"name":"Institute of Artificial Intelligence and Robotics, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2016,1,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1109\/TBME.2005.862547","article-title":"Variability, regularity, and complexity of time series generated by schizophrenic patients and control subjects","volume":"53","author":"Hornero","year":"2006","journal-title":"IEEE Trans. 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