  We combine photometric information of the WISE and 2MASS all-sky infrared
databases, and demonstrate how to produce clean and complete galaxy catalogs
for future analyses. Adding 2MASS colors to WISE photometry improves
star-galaxy separation efficiency substantially at the expense of loosing a
small fraction of the galaxies. We find that 93% of the WISE objects within
W1<15.2 mag have a 2MASS match, and that a class of supervised machine learning
algorithms, Support Vector Machines (SVM), are efficient classifiers of objects
in our multicolor data set. We constructed a training set from the SDSS
PhotoObj table with known star-galaxy separation, and determined redshift
distribution of our sample from the GAMA spectroscopic survey. Varying the
combination of photometric parameters input into our algorithm we show that W1
- J is a simple and effective star-galaxy separator, capable of producing
results comparable to the multi-dimensional SVM classification. We present a
detailed description of our star-galaxy separation methods, and characterize
the robustness of our tools in terms of contamination, completeness, and
accuracy. We explore systematics of the full sky WISE-2MASS galaxy map, such as
contamination from Moon glow. We show that the homogeneity of the full sky
galaxy map is improved by an additional J<16.5 mag flux limit. The all-sky
galaxy catalog we present in this paper covers 21,200 sq. degrees with dusty
regions masked out, and has an estimated stellar contamination of 1.2% and
completeness of 70.1% among 2.4 million galaxies with $z_{med}= 0.14$.
WISE-2MASS galaxy maps with well controlled stellar contamination will be
useful for spatial statistical analyses, including cross correlations with
other cosmological random fields, such as the Cosmic Microwave Background. The
same techniques also yield a statistically controlled sample of stars as well.
