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Adapted G-mode Clustering Method applied to Asteroid Taxonomy

Pedro Henrique Hasselmann
Observatorio Nacional, Rio de Janeiro, Brazil

Jorge Márcio Carvano
Observatorio Nacional, Rio de Janeiro, Brazil

Daniela Lazzaro
Observatorio Nacional, Rio de Janeiro, Brazil

Abstract

The original G-mode was a clustering method developed by A. I. Gavrishin in the late 60's for geochemical classification of rocks, but was also applied to asteroid photometry, cosmic rays, lunar sample and planetary science spectroscopy data. In this work, we used an adapted version to classify the asteroid photometry from SDSS Moving Objects Catalog. The method works by identifying normal distributions in a multidimensional space of variables. The identification starts by locating a set of points with smallest mutual distance in the sample, which is a problem when data is not planar. Here we present a modified version of the G-mode algorithm, which was previously written in FORTRAN 77, in Python 2.7 and using NumPy, SciPy and Matplotlib packages. The NumPy was used for array and matrix manipulation and Matplotlib for plot control. The Scipy had a import role in speeding up G-mode, Scipy.spatial.distance.mahalanobis was chosen as distance estimator and Numpy.histogramdd was applied to find the initial seeds from which clusters are going to evolve. Scipy was also used to quickly produce dendrograms showing the distances among clusters.

Finally, results for Asteroids Taxonomy and tests for different sample sizes and implementations are presented.

Keywords

clustering, taxonomy, asteroids, statistics, multivariate data, scipy, numpy

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