Estimating good discrete partitions from observed data: symbolic false nearest neighbors

Area of Science:

• Dynamical systems theory
• Nonlinear dynamics
• Time series analysis

Background:

• Symbolic analysis of time series requires discrete state space partitions.
• Finding 'generating' partitions that preserve dynamical information is challenging, especially in higher dimensions.
• Existing methods often require deep knowledge of the system's dynamics.

Purpose of the Study:

• To develop a novel statistic and algorithm for refining empirical partitions in symbolic state reconstruction.
• To optimize partitions for preserving deterministic dynamical information.
• To provide a method applicable to observed time series, robust to noise.

Main Methods:

• Introduced a statistic to refine empirical partitions.
• Developed an algorithm minimizing 'symbolic false nearest neighbors'.
• Focused on optimizing a key property of generating partitions to avoid topological degeneracies.

Main Results:

• The algorithm refines partitions for symbolic state reconstruction.
• Minimizing symbolic false nearest neighbors enhances the quality of symbolic representation.
• The method is data-driven, requiring only the observed time series.

Conclusions:

• The proposed method offers a practical approach to symbolic analysis of complex dynamics.
• It enhances state reconstruction from time series data, outperforming existing methods in certain aspects.
• The technique is valuable for analyzing noisy or incompletely understood dynamical systems.