Deriving Photometric Redshifts using Fuzzy Archetypes and Self-Organizing Maps. II. Comparing Sampling Techniques Using Mock Data

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.

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