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Structural information in two-dimensional patterns: entropy convergence and excess entropy.

David P Feldman1, James P Crutchfield

  • 1College of the Atlantic, Bar Harbor, Maine 04609, USA. dpf@santefe.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 6, 2003
PubMed
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We introduce novel information-theoretic methods to measure spatial patterns in multidimensional systems. The convergence rate of entropy density provides a new way to quantify global correlation and structure.

Area of Science:

  • Information theory
  • Spatial statistics
  • Complex systems analysis

Background:

  • Spatial structure and patterns are fundamental in many scientific fields.
  • Existing methods for quantifying spatial structure have limitations in higher dimensions.
  • Entropy density estimation in 2D is well-established using conditional entropies.

Purpose of the Study:

  • To develop new information-theoretic measures for spatial structure in any dimension.
  • To establish the convergence of entropy density as a metric for global correlation.
  • To compare this new method with existing techniques like mutual information and structure factors.

Main Methods:

  • Developing information-theoretic measures based on entropy density convergence.
  • Analyzing the rate of convergence of conditional entropies to their asymptotic values.

Related Experiment Videos

  • Comparing the proposed method with mutual-information and structure-factor analyses.

    • Main Results:

    • The convergence manner of conditional entropies quantifies global correlation and structure.
    • This approach is applicable to spatial systems in any dimension.
    • Entropy convergence offers a complementary perspective to mutual information and structure factors.

    Conclusions:

    • The rate of entropy convergence is a powerful new tool for analyzing multidimensional spatial systems.
    • This method enhances the understanding of global correlation and structure.
    • It provides a valuable alternative for spatial pattern quantification.