A Bayesian approach to geometric subspace estimation

摘要: This paper presents a geometric approach to estimating subspaces as elements of the complex Grassmann-manifold, with each subspace represented by its unique, projection matrix. Variation between is modeled rotating their matrices via action unitary [elements group U(n)]. Subspace estimation or tracking then corresponds inferences on U(n). Taking Bayesian approach, posterior density derived U(n), and certain expectations under this are empirically generated. For choice Hilbert-Schmidt norm define errors, an optimal MMSE estimator derived. It shown that achieves lower bound expected squared errors associated all possible estimators. The computed using (Metropolis-adjusted) Langevin's-diffusion algorithm for sampling from posterior. use in tracking, prior model rotation, utilizes Newtonian dynamics, suggested.