1. Fractional-order state space reconstruction: a new frontier in multivariate complex time series
- Author
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Jieren Xie, Guanghua Xu, Xiaobi Chen, Xun Zhang, Ruiquan Chen, Zengyao Yang, Churui Fang, Peiyuan Tian, Qingqiang Wu, and Sicong Zhang
- Subjects
Nonlinear time series analysis ,Multi-span transition networks ,Multivariate statistical complexity ,Fractional order state space ,Medicine ,Science - Abstract
Abstract This paper presents a novel approach to the phase space reconstruction technique, fractional-order phase space reconstruction (FOSS), which generalizes the traditional integer-order derivative-based method. By leveraging fractional derivatives, FOSS offers a novel perspective for understanding complex time series, revealing unique properties not captured by conventional methods. We further develop the multi-span transition entropy component method (MTECM-FOSS), an advanced complexity measurement technique that builds upon FOSS. MTECM-FOSS decomposes complexity into intra-sample and inter-sample components, providing a more comprehensive understanding of the dynamics in multivariate data. In simulated data, we observe that lower fractional orders can effectively filter out random noise. Time series with diverse long- and short-term memory patterns exhibit distinct extremities at different fractional orders. In practical applications, MTECM-FOSS exhibits competitive or superior classification performance compared to state-of-the-art algorithms when using fewer features, indicating its potential for engineering tasks.
- Published
- 2024
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