to henceforth by the vector $C$) to redshift is ultimately an empirical question. In @Masters15 (hereafter M15) we demonstrated a method, based on the *self-organizing map* (SOM; [@Kohonen90]) algorithm, to constrain the empirical multidimensional color distribution of galaxies present in a survey. This technique allowed us to project the multicolor distribution of galaxies in a topologically ordered way onto a two-dimensional grid. By applying this technique to a well-studied deep field with uniform *ugrizYJH* photometry, we were able to demonstrate that spectroscopic surveys to date do not sample the full color-space of galaxies in a *Euclid*-like survey, and thus the color-redshift relation is not fully constrained with existing spectroscopy. This issue is of particular concern for machine learning-based photo-z estimation, which requires color-complete training samples, but also affects the calibration of template-based techniques.

The analysis in M15 motivated a survey designed to systematically map the color-redshift relation over the currently undersampled regions of galaxy color space relevant to *Euclid*. M15 estimated that $\sim$5000 new redshifts, carefully distributed in color space, would be sufficient to meet the stringent requirements for weak lensing cosmology. This “direct" approach to photo-z calibration is complementary to approaches based on spatial cross-correlation of photometric samples with 