  We present a large catalog of optically selected galaxy clusters from the
application of a new Gaussian Mixture Brightest Cluster Galaxy (GMBCG)
algorithm to SDSS Data Release 7 data. The algorithm detects clusters by
identifying the red sequence plus Brightest Cluster Galaxy (BCG) feature, which
is unique for galaxy clusters and does not exist among field galaxies. Red
sequence clustering in color space is detected using an Error Corrected
Gaussian Mixture Model. We run GMBCG on 8240 square degrees of photometric data
from SDSS DR7 to assemble the largest ever optical galaxy cluster catalog,
consisting of over 55,000 rich clusters across the redshift range from 0.1 < z
< 0.55. We present Monte Carlo tests of completeness and purity and perform
cross-matching with X-ray clusters and with the maxBCG sample at low redshift.
These tests indicate high completeness and purity across the full redshift
range for clusters with 15 or more members.
