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Anomaly Detection in Fractal Time Series with LSTM Autoencoders

Author

Listed:
  • Lyudmyla Kirichenko

    (Department of Artificial Intelligence, Kharkiv National University of Radio Electronics, 61166 Kharkiv, Ukraine
    Institute of Mathematics, Lodz University of Technology, 90-924 Lodz, Poland)

  • Yulia Koval

    (Department of Artificial Intelligence, Kharkiv National University of Radio Electronics, 61166 Kharkiv, Ukraine)

  • Sergiy Yakovlev

    (Institute of Mathematics, Lodz University of Technology, 90-924 Lodz, Poland
    Institute of Computer Sciences and Artificial Intelligence, V.N. Karazin Kharkiv National University, 61022 Kharkiv, Ukraine)

  • Dmytro Chumachenko

    (Mathematical Modelling and Artificial Intelligence Department, Kharkiv Aviation Institute, National Aerospace University, 61072 Kharkiv, Ukraine
    Computer Science and Artificial Intelligence Lab, Massachusetts Institute of Technology, Cambridge, MA 02139, USA)

Abstract

This study explores the application of neural networks for anomaly detection in time series data exhibiting fractal properties, with a particular focus on changes in the Hurst exponent. The objective is to investigate whether changes in fractal properties can be identified by transitioning from the analysis of the original time series to the analysis of the sequence of Hurst exponent estimates. To this end, we employ an LSTM autoencoder neural network, demonstrating its effectiveness in detecting anomalies within synthetic fractal time series and real EEG signals by identifying deviations in the sequence of estimates. Whittle’s method was utilized for the precise estimation of the Hurst exponent, thereby enhancing the model’s ability to differentiate between normal and anomalous data. The findings underscore the potential of machine learning techniques for robust anomaly detection in complex datasets.

Suggested Citation

  • Lyudmyla Kirichenko & Yulia Koval & Sergiy Yakovlev & Dmytro Chumachenko, 2024. "Anomaly Detection in Fractal Time Series with LSTM Autoencoders," Mathematics, MDPI, vol. 12(19), pages 1-14, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:19:p:3079-:d:1490397
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