Anomaly Detection in Fractal Time Series with LSTM Autoencoders

Lyudmyla Kirichenko, Yulia Koval, Sergiy Yakovlev and Dmytro Chumachenko ()
Additional contact information
Lyudmyla Kirichenko: Department of Artificial Intelligence, Kharkiv National University of Radio Electronics, 61166 Kharkiv, Ukraine
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
Dmytro Chumachenko: Mathematical Modelling and Artificial Intelligence Department, Kharkiv Aviation Institute, National Aerospace University, 61072 Kharkiv, Ukraine

Mathematics, 2024, vol. 12, issue 19, 1-14

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.

Keywords: anomaly detection; Hurst exponent; fractal Brownian motion; machine learning; LSTM autoencoder (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/19/3079/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/19/3079/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:19:p:3079-:d:1490397

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().