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Multidimensional Analysis of Near-Earth Asteroids

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Abstract

This paper proposes a quantitative approach to specify potentially hazardous asteroids using clustering tools to group a set of near-Earth asteroids (NEAs). The data pool adopted in the study contains a number of distinct indices characterizing\(\sim 25,000\) NEAs. The hierarchical clustering (HC) and multidimensional scaling (MDS) algorithmic techniques are adopted for generating two- and three-dimensional graphical representations reflecting the main features of the NEAs. These techniques provide useful computational visualization tools for extracting information embedded in data sets having multidimensional nature. The structure of the loci, given by the emerging clusters and patterns, leads to a deeper understanding of the problem. The HC and MDS rely on the selection of adequate metrics for comparing the objects in the data set. Therefore, a pool of prototype distances are tested and a number of numerical experiments reveal that the Clark distance characterizes more assertively the NEA data set. The overlapped clusters and the pattern of a curved polyhedron that emerge in the MDS charts reveal that some PHAs may be overlooked with standard classifications of NEAs based merely on some scalar index, such as the case of the perihelion distance\(q<1.3\) AU. Furthermore, it is observed that the MDS is superior in performance to the HC since it takes advantage of three-dimensional representations. In fact, three-dimensional plots require iterative operations of rotation, shifting and magnification for achieving an efficient visualization, but such procedures are straightforward with present day computational resources. This strategy allows the adoption of advanced scientific data processing and visualization techniques that lead to ‘maps’ close to our understanding of the NEA impact risk.

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Authors and Affiliations

  1. Department of Electrical Engineering, Institute of Engineering of Polytechnic of Porto, Porto, Portugal

    J. A. Tenreiro Machado

  2. Department of Physics, College of Basic Sciences, Lahijan Branch, Islamic Azad University, P. O. Box 1616, Lahijan, Iran

    S. Hamid Mehdipour

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  1. J. A. Tenreiro Machado

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  2. S. Hamid Mehdipour

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Correspondence toS. Hamid Mehdipour.

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