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Fast reconstruction of an original continuous series from a recurrence plot
Yoshito Hirata1, Yuki Kitanishi2, Hiroki Sugishita3
1Faculty of Engineering, Information and Systems, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan.
Chaos (Woodbury, N.Y.)
|January 1, 2022
Summary
We developed a new algorithm to improve time series reconstruction using recurrence plots. This method refines data by calculating local distances and weighted averages, enhancing time series analysis.
Area of Science:
- Data Science
- Time Series Analysis
- Signal Processing
Background:
- Recurrence plots (RPs) are powerful tools for visualizing nonlinear dynamical systems.
- Reconstructing original time series from RPs can be challenging due to information loss.
- Existing methods may not fully capture the local dynamics for accurate reconstruction.
Purpose of the Study:
- To propose a novel algorithm for refining time series reconstruction from recurrence plots.
- To enhance the accuracy of time series reconstruction by leveraging local neighborhood information.
- To provide a method for improving the fidelity of reconstructed time series data.
Main Methods:
- Developed an algorithm that refines time series reconstruction based on recurrence plots (contact maps).
- Calculated local distances using Jaccard coefficients between a point and its neighbors in the previous resolution.
- Applied a weighted averaging scheme based on these local distances for refinement.
Main Results:
- The proposed algorithm successfully refines the reconstruction of original time series.
- Demonstrated the utility of the method through two distinct examples.
- The refinement process effectively utilizes local neighborhood information for improved accuracy.
Conclusions:
- The algorithm offers a significant improvement in time series reconstruction from recurrence plots.
- This method provides a valuable tool for analyzing and reconstructing complex time series data.
- The approach is effective in enhancing the quality of reconstructed time series for various applications.
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