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We introduce a new method to determine galaxy cluster membership based solelyon photometric properties. We adopt a machine learning approach to recover acluster membership probability from galaxy photometric parameters and finallyderive a membership classification. After testing several machine learningtechniques (such as Stochastic Gradient Boosting, Model Averaged Neural Networkand k-Nearest Neighbors), we found the Support Vector Machine (SVM) algorithmto perform better when applied to our data. Our training and validation dataare from the Sloan Digital Sky Survey (SDSS) main sample. Hence, to be completeto $M_r^* + 3$ we limit our work to 30 clusters with $z_{\text{phot-cl}} \le0.045$. 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 inaccount all galaxies in the line of sight of each cluster, with no photometricredshift cuts or background corrections. Our method is non-parametric, makingno assumptions on the number density or luminosity profiles of galaxies inclusters. Our approach delivers extremely accurate results (completeness, C$\sim 92\%$ and purity, P $\sim 87\%$) within R$_{200}$, so that we named ourcode {\bf RPM}. We discuss possible dependencies on magnitude, colour andcluster mass. Finally, we present some applications of our method, stressingits impact to galaxy evolution and cosmological studies based on future largescale surveys, such as eROSITA, EUCLID and LSST.

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