Z-Sequence: photometric redshift predictions for galaxy clusters with sequential random k-nearest neighbours

We introduce Z-Sequence, a novel empirical model that utilizes photometric measurements of observed galaxies within a specified search radius to estimate the photometric redshift of galaxy clusters. Z-Sequence itself is composed of a machine learning ensemble based on the k-nearest neighbours algorithm. We implement an automated feature selection strategy that iteratively determines appropriate combinations of filters and colours to minimize photometric redshift prediction error. We intend for Z-Sequence to be a standalone technique but it can be combined with cluster finders that do not intrinsically predict redshift, such as our own DEEP-CEE. In this proof-of-concept study, we train, fine-tune, and test Z-Sequence on publicly available cluster catalogues derived from the Sloan Digital Sky Survey. We determine the photometric redshift prediction error of Z-Sequence via the median value of vertical bar Delta z vertical bar/(1 + z) (across a photometric redshift range of 0.05 <= z <= 0.6) to be similar to 0.01 when applying a small search radius. The photometric redshift prediction error for test samples increases by 30-50 per cent when the search radius is enlarged, likely due to line-of-sight interloping galaxies. Eventually, we aim to apply 7-Sequence to upcoming imaging surveys such as the Legacy Survey of Space and Time to provide photometric redshift estimates for large samples of as yet undiscovered and distant clusters.

Automated summary

Z-Sequence is a novel empirical model that estimates the photometric redshift of galaxy clusters using photometric measurements of observed galaxies, relying on machine learning and automated feature selection to minimize prediction error. Testing shows that the photometric redshift prediction error of Z-Sequence is around 0.01 with a small search radius, but increases by 30-50% when the search radius is enlarged.