  In a companion paper, we proposed combining large numbers of "fuzzy
archetypes" with Self-Organizing Maps (SOMs) to derive photometric redshifts in
a data-driven way. In this paper, we investigate the performance of several
sampling approaches that build on this general idea using a mock catalog
designed to approximately simulate LSST ($ugrizY$) and Euclid ($YJH$) data from
$z=0-6$ at fixed LSST $Y=24$ mag. We test eight different approaches: two
brute-force methods, two Markov Chain Monte Carlo (MCMC)-based methods, two
hierarchical sampling methods, and two "quick-search" methods based on
quantities derived during the initial SOM training process. We find most
methods perform reasonably well with small catastrophic outlier fractions and
are able to robustly identify redshift probability distribution functions that
are multi-modal and/or poorly constrained. Once these insecure objects are
removed, the results are generally in good agreement with the strict accuracy
requirements necessary to meet Euclid weak lensing goals for most redshifts
above $z \sim 0.8$. These results demonstrate the utility of our data
clustering-based approach and highlight its effectiveness to derive quick and
accurate photo-z's using large numbers of templates.

Cosmology and Nongalactic Astrophysics