Optimizing Photometric Redshift Training Sets. I. Efficient Compression of the Galaxy Color–Redshift Relation with UMAP

Abstract Spectroscopic datasets are essential for training and calibrating photometric redshift (photo- z ) methods. However, spectroscopic redshifts (spec- z ’s) constitute a biased and sparse sampling of the photometric galaxy population, which creates difficulties for the common grid-based approach for mapping color to redshift using self-organizing maps (SOMs). Instead, we utilized the uniform manifold approximation and projection (UMAP) algorithm to compress a Rubin–Roman-like ugrizyJH color space into a thin and densely sampled manifold. Crucially, the manifold varies continuously and monotonically in redshift and specific star formation rate in roughly orthogonal directions. Using COSMOS2020 many-band photo- z ’s and compiled spec- z ’s as representative and nonrepresentative samples, respectively, we trained and tested redshift prediction from an SOM, from nearest neighbors in UMAP coordinates (UMAP- k NN- z ), and directly from nearest neighbors in the color space to assess how well location in each space maps to redshift. For the representative training set, UMAP- k NN- z exhibited smaller photo- z scatter and fraction of outliers than SOM-based methods. When training with the highly biased spec- z sample, UMAP- k NN- z maintained similar performance while SOM- and color-based methods predictions were significantly degraded, especially at z > 1.5 where training sets are the most sparse. The physically meaningful trends across the UMAP manifold allow for accurate redshift prediction even in such poorly sampled regions of color space. This suggests that representative, spectroscopically anchored training sets can be produced by interpolating between spectroscopic sources at the UMAP coordinates of photometric objects, maximizing the performance of photo- z algorithms.