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 110,000 COSMOS2020 many-band photo-z's and 15,000 spec-z's as representative and non-representative samples, respectively, we trained and tested redshift estimation from a SOM (SOM-z) and from nearest neighbors in UMAP space (UMAP-kNN-z). Compared to SOM-z, UMAP-kNN-z exhibited smaller photo-z scatter and fraction of outliers for the representative training set. When training with the highly biased spec-z sample, UMAP-kNN-z maintained similar performance, but the outlier fraction for SOM-z increased by nearly three times. The physically-meaningful trends across the UMAP manifold allow for accurate redshift regression even in regions of color space sparsely populated by spectroscopic objects, which comprise nearly 25% of the photometric sample. 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.
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