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