  The directional mean shift (DMS) algorithm is a nonparametric method for
pursuing local modes of densities defined by kernel density estimators on the
unit hypersphere. In this paper, we show that any DMS iteration can be viewed
as a generalized Expectation-Maximization (EM) algorithm; in particular, when
the von Mises kernel is applied, it becomes an exact EM algorithm. Under the
(generalized) EM framework, we provide a new proof for the ascending property
of density estimates and demonstrate the global convergence of directional mean
shift sequences. Finally, we give a new insight into the linear convergence of
the DMS algorithm.
