Accurate spectroscopic redshift estimation using nonnegative matrix factorization: Application to MUSE spectra

¹ Université Lyon 1, ENS de Lyon, CNRS, CRAL, UMR 5574, Saint-Genis-Laval, France
² Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, 14482 Potsdam, Germany
³ Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Rua das Estrelas, 4150-762 Porto, Portugal
⁴ Departamento de Física e Astronomia, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal
⁵ Institut für Physik und Astronomie, Universität Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Golm, Germany
⁶ National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 26 November 2025
Accepted: 4 March 2026

Abstract

Accurate and automated galaxy redshift determinations are 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 nonnegative 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 applied 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 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.