  We describe an automated method for detecting clusters of galaxies in imaging
and redshift galaxy surveys. The Adaptive Matched Filter (AMF) method utilizes
galaxy positions, magnitudes, and---when available---photometric or
spectroscopic redshifts to find clusters and determine their redshift and
richness. The AMF can be applied to most types of galaxy surveys: from
two-dimensional (2D) imaging surveys, to multi-band imaging surveys with
photometric redshifts of any accuracy (2.5D), to three-dimensional (3D)
redshift surveys. The AMF can also be utilized in the selection of clusters in
cosmological N-body simulations. The AMF identifies clusters by finding the
peaks in a cluster likelihood map generated by convolving a galaxy survey with
a filter based on a model of the cluster and field galaxy distributions. In
tests on simulated 2D and 2.5D data with a magnitude limit of r' ~ 23.5,
clusters are detected with an accuracy of Delta z ~ 0.02 in redshift and ~10%
in richness to z < 0.5. Detecting clusters at higher redshifts is possible with
deeper surveys. In this paper we present the theory behind the AMF and describe
test results on synthetic galaxy catalogs.
