Learning Entropy: On Shannon vs. Machine-Learning-Based Information in Time Series
The paper discusses the Learning-based information (L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{L}}$$\en...
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Published in | Database and Expert Systems Applications - DEXA 2022 Workshops pp. 402 - 415 |
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Main Authors | , |
Format | Book Chapter |
Language | English |
Published |
Cham
Springer International Publishing
|
Series | Communications in Computer and Information Science |
Subjects | |
Online Access | Get full text |
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Summary: | The paper discusses the Learning-based information (L\documentclass[12pt]{minimal}
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\begin{document}$${\varvec{L}}$$\end{document}) and Learning Entropy (LE\documentclass[12pt]{minimal}
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\begin{document}$${\varvec{L}}{\varvec{E}}$$\end{document}) in contrast to classical Shannon probabilistic Information (I\documentclass[12pt]{minimal}
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\begin{document}$${\varvec{I}}$$\end{document}) and probabilistic entropy (H\documentclass[12pt]{minimal}
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\begin{document}$${\varvec{H}}$$\end{document}). It is shown that L\documentclass[12pt]{minimal}
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\begin{document}$${\varvec{L}}$$\end{document} corresponds to the recently introduced Approximate Individual Sample-point Learning Entropy (AISLE\documentclass[12pt]{minimal}
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\begin{document}$${\varvec{A}}{\varvec{I}}{\varvec{S}}{\varvec{L}}{\varvec{E}}$$\end{document}). For data series, then, the LE should be defined as the mean value of L that is finally in proper accordance with Shannon's concept of entropy H\documentclass[12pt]{minimal}
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\begin{document}$${\varvec{H}}$$\end{document}. The distinction of L\documentclass[12pt]{minimal}
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\begin{document}$${\varvec{L}}$$\end{document} against I\documentclass[12pt]{minimal}
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\begin{document}$${\varvec{I}}$$\end{document} is explained by the real-time anomaly detection of individual time series data points (states). First, the principal distinction of the information concept of Ivs.L\documentclass[12pt]{minimal}
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\begin{document}$${\varvec{I}}\boldsymbol{ }{\varvec{v}}{\varvec{s}}.\boldsymbol{ }{\varvec{L}}$$\end{document} is demonstrated in respect to data governing law that L\documentclass[12pt]{minimal}
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\begin{document}$${\varvec{L}}$$\end{document} considers explicitly (while I\documentclass[12pt]{minimal}
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\begin{document}$${\varvec{I}}$$\end{document} does not). Second, it is shown that L\documentclass[12pt]{minimal}
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\begin{document}$${\varvec{L}}$$\end{document} has the potential to be applied on much shorter datasets than I\documentclass[12pt]{minimal}
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\begin{document}$${\varvec{I}}$$\end{document} because of the learning system being pre-trained and being able to generalize from a smaller dataset. Then, floating window trajectories of the covariance matrix norm, the trajectory of approximate variance fractal dimension, and especially the windowed Shannon Entropy trajectory are compared to LE\documentclass[12pt]{minimal}
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\begin{document}$${\varvec{L}}{\varvec{E}}$$\end{document} on multichannel EEG featuring epileptic seizure. The results on real time series show that L\documentclass[12pt]{minimal}
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\begin{document}$${\varvec{L}}$$\end{document}, i.e., AISLE\documentclass[12pt]{minimal}
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\begin{document}$${\varvec{A}}{\varvec{I}}{\varvec{S}}{\varvec{L}}{\varvec{E}}$$\end{document}, can be a useful counterpart to Shannon entropy allowing us also for more detailed search of anomaly onsets (change points). |
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ISBN: | 9783031143427 3031143426 |
ISSN: | 1865-0929 1865-0937 |
DOI: | 10.1007/978-3-031-14343-4_38 |