Masten Bourahma, Nicolas F. Bouché, Roland Bacon, Johan Richard, Tanya Urrutia, Afonso Vale, Martin Wendt, T. T. Thai

Accurate and automated galaxy redshift determination is essential for maximizing the scientific return of spectroscopic surveys. In this paper, we propose a data-driven method to address this challenge. The method first learns a rest-frame representation of galaxy spectra using Non-negative Matrix Factorization (NMF). The method then reconstructs new spectra using this representation at different trial redshifts, and identifies the correct redshift by selecting the one that minimizes the reconstruction error. We apply our method to galaxy spectra from the Multi Unit Spectroscopic Explorer (MUSE), covering redshifts from 0 to 6.7. Our method achieves an overall success rate of 93.7%. We further demonstrate two applications: (i) the separation between true and false sources, and (ii) the detection of blended sources from one-dimensional spectra. Our results demonstrate that NMF-based representations provide a powerful and physically motivated framework for redshift estimation in current and future large spectroscopic surveys.