Nonlinear Mean Shift for Clustering over Analytic Manifolds

The mean shift algorithm is widely applied for nonparametric clustering in Euclidean spaces. Recently, mean shift was generalized for clustering on matrix Lie groups. We further extend the algorithm to a more general class of nonlinear spaces, the set of analytic manifolds. As examples, two specific classes of frequently occurring parameter spaces, Grassmann manifolds and Lie groups, are considered. When the algorithm proposed here is restricted to matrix Lie groups the previously proposed method is obtained. The algorithm is applied to a variety of robust motion segmentation problems and multibody factorization. The motion segmentation method is robust to outliers, does not require any prior specification of the number of independent motions and simultaneously estimates all the motions present.