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Clustering of points randomly distributed in n-dimensional space.

G Sadasiv1, Y Meng

  • 1Department of Electrical Engineering, University of Rhode Island, Kingston, Rhode Island 02881, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 20, 2001
PubMed
Summary

This study analyzes cluster sizes formed by randomly distributed points in n-dimensional space. It presents the size distribution for clusters connecting to nearest or nearest and next nearest neighbors.

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Area of Science:

  • * Computational geometry
  • * Statistical physics
  • * Spatial analysis

Background:

  • * Understanding spatial patterns is crucial in various scientific fields.
  • * Random point distributions are fundamental models in statistical physics and data analysis.
  • * Cluster formation in spatial data influences network properties and information diffusion.

Purpose of the Study:

  • * To derive and present the size distribution of clusters in n-dimensional space.
  • * To analyze cluster formation based on nearest and next nearest neighbor connections.
  • * To provide a mathematical framework for analyzing randomly distributed point sets.

Main Methods:

  • * Consideration of point distributions in n-dimensional Euclidean space.
  • * Definition of clusters based on connectivity to nearest and/or next nearest neighbors.

Related Experiment Videos

  • * Mathematical derivation and presentation of cluster size distributions.

    • Main Results:

    • * The study presents the size distribution of clusters formed under specified connectivity rules.
    • * Findings are applicable to n-dimensional spaces, offering generalized insights.
    • * The derived distributions characterize the typical sizes of emergent clusters.

    Conclusions:

    • * The size distribution of clusters in random spatial point sets is mathematically characterized.
    • * The findings offer a foundational understanding of percolation and connectivity in high-dimensional spaces.
    • * This work provides tools for analyzing clustered data in diverse scientific applications.