THE FRACTIONAL DISEN–FISHER PLANE: AN EFFECTIVE APPROACH TO DISTINGUISH COMPLEX TIME SERIES

Ang Li (), Du Shang and Pengjian Shang ()
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Ang Li: School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, P. R. China
Du Shang: ��State Key Laboratory of Advanced Rail Autonomous Operation, Beijing Jiaotong University, Beijing 100044, P. R. China
Pengjian Shang: School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, P. R. China

FRACTALS (fractals), 2024, vol. 32, issue 05, 1-33

Abstract: With the explosive growth of data quantity and rapid development of nonlinear dynamics as well as the growing demand for complex data classification in the field of artificial intelligence and machine learning, the research of complex time series, generated by complex systems, has attracted enormous interests. However, how to simultaneously distinguish different types of time series data and extract more accurate and detailed information from them in the light of localized and global scale perspectives remains significant and needs to be tackled. Thus, in this paper, we propose the fractional DisEn–Fisher plane, which is innovatively constructed by the fractional form of dispersion entropy and Fisher information measure. These are both effective tools to diagnose the essential properties of complex time series, to analyze the complexity of systems and to depict the contained statistical information with higher accuracy and effectiveness. Several classical entropy plane methods are selected as a comparison to design simulation experiments by simulated data and three real-world datasets. Comparative experimental results show that this method is a feasible and reliable improvement method, which will help to provide more additional information in time series recognition and dynamic characterization. It may not only provide new insights for further improvement of complex time series analysis, but also have important implications for developing complex data clustering methods.

Keywords: Feature Extraction; Fractional DisEn–Fisher Plane; Fractional Dispersion Entropy; Fractional Fisher Information Measure; Complex Time Series (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24500993

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