The EM Perspective of Directional Mean Shift Algorithm
This work offers theoretical insights for researchers in nonparametric density estimation on spheres, but it is incremental as it refines existing methods without major practical breakthroughs.
The paper shows that the directional mean shift algorithm can be viewed as a generalized EM algorithm, providing a new proof for its ascending property and demonstrating global convergence, with specific results for the von Mises kernel case.
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.