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| 分形分析× | 循环量化分析 (RQA)× | |
|---|---|---|
| 领域 | 复杂系统 | 复杂系统 |
| 方法族 | Machine learning | Machine learning |
| 起源年份≠ | 1983 | 2007 |
| 提出者≠ | Benoit Mandelbrot | Marwan, Romano, Thiel & Kurths |
| 类型≠ | Geometric complexity quantification | Nonlinear time-series characterization |
| 开创性文献≠ | Mandelbrot, B. B. (1983). The Fractal Geometry of Nature. W. H. Freeman. ISBN: 978-0-7167-1186-5 | Marwan, N., Romano, M. C., Thiel, M., & Kurths, J. (2007). Recurrence plots for the analysis of complex systems. Physics Reports, 438(5–6), 237–329. DOI ↗ |
| 别名 | Box-Counting Analysis, Fractal Dimension Estimation, Multifractal Analysis, Fraktal Analiz | RQA, Recurrence Plot Analysis, Nonlinear Recurrence Analysis, Tekrarlama Kantifikasyon Analizi |
| 相关 | 2 | 2 |
| 摘要≠ | Fractal Analysis quantifies the self-similar, scale-invariant complexity of geometric objects and time series through the fractal dimension D and the Hurst exponent H. Introduced systematically by Benoit Mandelbrot in his 1983 landmark work, the framework extends classical Euclidean geometry to irregular shapes found in nature, finance, physiology, and materials science. It provides a single dimensionless index that captures how completely a pattern fills space across multiple scales. | Recurrence Quantification Analysis (RQA) is a nonlinear method for characterizing the dynamics of a time series by quantifying the small-scale structure of its recurrence plot. Introduced in its modern, comprehensive form by Marwan, Romano, Thiel, and Kurths in 2007, RQA extracts scalar measures — such as recurrence rate, determinism, laminarity, and Shannon entropy — that capture periodicity, chaos, stationarity, and transitions in complex dynamical systems. |
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