  In this paper a novel possibilistic c-means clustering algorithm, called
Adaptive Possibilistic c-means, is presented. Its main feature is that {\it
all} its parameters, after their initialization, are properly adapted during
its execution. Provided that the algorithm starts with a reasonable
overestimate of the number of physical clusters formed by the data, it is
capable, in principle, to unravel them (a long-standing issue in the clustering
literature). This is due to the fully adaptive nature of the proposed algorithm
that enables the removal of the clusters that gradually become obsolete. In
addition, the adaptation of all its parameters increases the flexibility of the
algorithm in following the variations in the formation of the clusters that
occur from iteration to iteration. Theoretical results that are indicative of
the convergence behavior of the algorithm are also provided. Finally, extensive
simulation results on both synthetic and real data highlight the effectiveness
of the proposed algorithm.
