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We introduce Z-Sequence, a novel empirical model that utilises photometricmeasurements of observed galaxies within a specified search radius to estimatethe photometric redshift of galaxy clusters. Z-Sequence itself is composed of amachine learning ensemble based on the k-nearest neighbours algorithm. Weimplement an automated feature selection strategy that iteratively determinesappropriate combinations of filters and colours to minimise photometricredshift prediction error. We intend for Z-Sequence to be a standalonetechnique but it can be combined with cluster finders that do not intrinsicallypredict redshift, such as our own DEEP-CEE. In this proof-of-concept study wetrain, fine-tune and test Z-Sequence on publicly available cluster cataloguesderived from the Sloan Digital Sky Survey. We determine the photometricredshift prediction error of Z-Sequence via the median value of $|\Deltaz|/(1+z)$ (across a photometric redshift range of $0.05 \le \textit{z} \le0.6$) to be $\sim0.01$ when applying a small search radius. The photometricredshift prediction error for test samples increases by 30-50 per cent when thesearch radius is enlarged, likely due to line-of-sight interloping galaxies.Eventually, we aim to apply Z-Sequence to upcoming imaging surveys such as theLegacy Survey of Space and Time to provide photometric redshift estimates forlarge samples of as yet undiscovered and distant clusters.

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