  We present a new geometrical method aimed at determining the members of open
clusters. The methodology estimates, in an N-dimensional space, the membership
probabilities by means of the distances between every star and the cluster
central overdensity. It can handle different sets of variables, which have to
satisfy the simple condition of being more densely distributed for the cluster
members than for the field stars (as positions, proper motions, radial
velocities and/or parallaxes are). Unlike other existing techniques, this fact
makes the method more flexible and so can be easily applied to different
datasets. To quantify how the method identifies the clus- ter members, we
design series of realistic simulations recreating sky regions in both position
and proper motion subspaces populated by clusters and field stars. The re-
sults, using different simulated datasets (N = 1, 2 and 4 variables), show that
the method properly recovers a very high fraction of simulated cluster members,
with a low number of misclassified stars. To compare the goodness of our
methodology, we also run other existing algorithms on the same simulated data.
The results show that our method has a similar or even better performance than
the other techniques. We study the robustness of the new methodology from
different subsamplings of the ini- tial sample, showing a progressive
deterioration of the capability of our method as the fraction of missing
objects increases. Finally, we apply all the methodologies to the real cluster
NGC 2682, indicating that our methodology is again in good agreement with
preceding studies.
