Trajectory analysis through entropy characterization over coded representation

TL;DR

This paper introduces a novel method for characterizing trajectories using entropy derived from coded representations, providing a new perspective on pattern analysis in diverse data such as physiological and astronomical trajectories.

Contribution

It develops an entropic framework based on chain coding for trajectory analysis, extending traditional geometric and fractional dimensionality methods.

Findings

Robust entropic characterization across diverse trajectory data

Effective differentiation of pattern formation and creativity

Applicable to physiological and astronomical data

Abstract

Any continuous curve in a higher dimensional space can be considered a trajectory that can be parameterized by a single variable, usually taken as time. It is well known that a continuous curve can have a fractional dimensionality, which can be estimated using already standard algorithms. However, characterizing a trajectory from an entropic perspective is far less developed. The search for such characterization leads us to use chain coding to discretize the description of a curve. Calculating the entropy density and entropy-related magnitudes from the resulting finite alphabet code becomes straightforward. In such a way, the entropy of a trajectory can be defined and used as an effective tool to assert creativity and pattern formation from a Shannon perspective. Applying the procedure to actual experimental physiological data and modelled trajectories of astronomical dynamics proved the robustness of the entropic characterization in a wealth of trajectories of different origins and the insight that can be gained from its use.