  Calibrating the photometric redshifts of >10^9 galaxies for upcoming weak
lensing cosmology experiments is a major challenge for the astrophysics
community. The path to obtaining the required spectroscopic redshifts for
training and calibration is daunting, given the anticipated depths of the
surveys and the difficulty in obtaining secure redshifts for some faint galaxy
populations. Here we present an analysis of the problem based on the
self-organizing map, a method of mapping the distribution of data in a
high-dimensional space and projecting it onto a lower-dimensional
representation. We apply this method to existing photometric data from the
COSMOS survey selected to approximate the anticipated Euclid weak lensing
sample, enabling us to robustly map the empirical distribution of galaxies in
the multidimensional color space defined by the expected Euclid filters.
Mapping this multicolor distribution lets us determine where - in galaxy color
space - redshifts from current spectroscopic surveys exist and where they are
systematically missing. Crucially, the method lets us determine whether a
spectroscopic training sample is representative of the full photometric space
occupied by the galaxies in a survey. We explore optimal sampling techniques
and estimate the additional spectroscopy needed to map out the color-redshift
relation, finding that sampling the galaxy distribution in color space in a
systematic way can efficiently meet the calibration requirements. While the
analysis presented here focuses on the Euclid survey, similar analysis can be
applied to other surveys facing the same calibration challenge, such as DES,
LSST, and WFIRST.
