Dynamical systems for joint principal and minor component analysis

Most known principal or a minor subspace (or component) analyzers compute either the principal or the minor subspaces of a given data matrix but not both. This paper presents several methods for simultaneous computation of principal and minor subspaces of a symmetric matrix. Weighted versions of these methods for joint computation of principal and minor components are also given. The proposed methods are derived from the optimization of certain objective functions over orthogonal constraints. Several features such as penalty terms are added to obtain reliable algorithms