  We present initial results on the use of Mixture Models for density
estimation in large astronomical databases. We provide herein both the
theoretical and experimental background for using a mixture model of Gaussians
based on the Expectation Maximization (EM) Algorithm. Applying these analyses
to simulated data sets we show that the EM algorithm - using the both the AIC &
BIC penalized likelihood to score the fit - can out-perform the best kernel
density estimate of the distribution while requiring no ``fine-tuning'' of the
input algorithm parameters. We find that EM can accurately recover the
underlying density distribution from point processes thus providing an
efficient adaptive smoothing method for astronomical source catalogs. To
demonstrate the general application of this statistic to astrophysical problems
we consider two cases of density estimation; the clustering of galaxies in
redshift space and the clustering of stars in color space. From these data we
show that EM provides an adaptive smoothing of the distribution of galaxies in
redshift space (describing accurately both the small and large-scale features
within the data) and a means of identifying outliers in multi-dimensional
color-color space (e.g. for the identification of high redshift QSOs).
Automated tools such as those based on the EM algorithm will be needed in the
analysis of the next generation of astronomical catalogs (2MASS, FIRST, PLANCK,
SDSS) and ultimately in the development of the National Virtual Observatory.

Astrophysics