The Application of Manifold Learning to a Selection of Different Galaxy Populations and Scaling Relation Analysis

Abstract The growing volume of data produced by large astronomical surveys necessitates the development of efficient analysis techniques capable of effectively managing high-dimensional data sets. This study addresses this need by demonstrating some applications of manifold learning and dimensionality reduction techniques, specifically the self-organizing map (SOM), on the optical+near-infrared spectral energy distribution (SED) space of galaxies, with a focus on sample comparison, selection biases, and predictive power using a small subset. To this end, we utilize a large photometric sample from the five Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey fields and a subset with spectroscopic measurements from the KECK MOSDEF survey in two redshift bins at z ∼ 1.5 and z ∼ 2.2. We trained the SOM with the photometric data and mapped the spectroscopic data onto it as our study case. We found that MOSDEF targets do not cover all SED shapes existing in the SOM. Our findings reveal that active galactic nuclei within the MOSDEF sample are mapped onto the more massive regions of the SOM, confirming previous studies and known selection biases toward higher-mass, less dusty galaxies. Furthermore, SOMs were utilized to map measured spectroscopic features, examining the relationship between metallicity variations and galaxy mass. Our analysis confirmed that more massive galaxies exhibit lower [O iii ]/H β and [O iii ]/[O ii ] ratios and higher H α /H β ratios, consistent with the known mass–metallicity relation. These findings highlight the effectiveness of SOMs in analyzing and visualizing complex, multidimensional data sets, emphasizing their potential in data-driven astronomical studies.