We have recently proposed a new approach to the asteroid family classification by combining the classical HCM method with an automated procedure to add newly discovered members to existing families. This approach is specifically intended to cope with ever increasing asteroid data sets, and consists of several steps to segment the problem and handle the very large amount of data in an efficient and accurate manner. We briefly present all these steps and show the results from three subsequent updates making use of only the automated step of attributing the newly numbered asteroids to the known families. We describe the changes of the individual families membership, as well as the evolution of the classification due to the newly added intersections between the families, resolved candidate family mergers, and emergence of the new candidates for the mergers. We thus demonstrate how by the new approach the asteroid family classification becomes stable in general terms (converging towards a permanent list of confirmed families), and in the same time evolving in details (to account for the newly discovered asteroids) at each update.
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