Reliable Photometric Membership (RPM) of Galaxies in Clusters. I. A Machine Learning Method and its Performance in the Local Universe

Abstract: We introduce a new method to determine galaxy cluster membership based solely on photometric properties. We adopt a machine learning approach to recover a cluster membership probability from galaxy photometric parameters and finally derive a membership classification. After testing several machine learning techniques (such as Stochastic Gradient Boosting, Model Averaged Neural Network and k-Nearest Neighbors), we found the Support Vector Machine (SVM) algorithm to perform better when applied to our data. Our training and validation data are from the Sloan Digital Sky Survey (SDSS) main sample. Hence, to be complete to $M_r^* + 3$ we limit our work to 30 clusters with $z_{\text{phot-cl}} \le 0.045$. Masses ($M_{200}$) are larger than $\sim 0.6\times10^{14} M_{\odot}$ (most above $3\times10^{14} M_{\odot}$). Our results are derived taking in account all galaxies in the line of sight of each cluster, with no photometric redshift cuts or background corrections. Our method is non-parametric, making no assumptions on the number density or luminosity profiles of galaxies in clusters. Our approach delivers extremely accurate results (completeness, C $\sim 92\%$ and purity, P $\sim 87\%$) within R$_{200}$, so that we named our code {\bf RPM}. We discuss possible dependencies on magnitude, colour and cluster mass. Finally, we present some applications of our method, stressing its impact to galaxy evolution and cosmological studies based on future large scale surveys, such as eROSITA, EUCLID and LSST.