Trajectory classification through Freeman's curve encoding and entropic analysis

Area of Science:

• Dynamical Systems and Complexity Science
• Information Theory
• Computational Physics

Background:

• Trajectory analysis is crucial in understanding complex systems.
• Traditional methods may struggle with high-dimensional or noisy data.
• Characterizing motion patterns requires robust quantitative measures.

Purpose of the Study:

• To develop a novel method for classifying two-dimensional trajectories.
• To apply entropic analysis to coded trajectory representations.
• To demonstrate the method's versatility with diverse examples.

Main Methods:

• Discretizing trajectories into an 8-symbol code using the Freeman procedure.
• Applying entropic analysis, including Kolmogorov-Sinai entropy.
• Utilizing effective complexity and informational distance measures.
• Developing classification schemes based on entropy variables.

Main Results:

• The entropic analysis of coded trajectories provides a robust classification framework.
• The Hénon-Heiles model was successfully classified, validating the method's complexity analysis capabilities.
• Human posture data was analyzed, showing the method's applicability to real-world experimental data.

Conclusions:

• The proposed entropic analysis of coded trajectories offers a powerful tool for trajectory classification.
• This method is adaptable to various complex systems, from theoretical models to experimental data.
• The approach facilitates the differentiation and understanding of distinct motion dynamics.