Successive projection method for solving the unbalanced Procrustes problem

We present a successive projection method for solving the unbalanced Procrustes problem: given matrix A ∈ Rn × n and B ∈ Rn × k, n > k, minimize the residual ‖AQ − B‖F with the orthonormal constraint QTQ = Ik on the variant Q ∈ Rn × k. The presented algorithm consists of solving k least squares problems with quadratic constraints and an expanded balance problem at each sweep. We give a detailed convergence analysis. Numerical experiments reported in this paper show that our new algorithm is superior to other existing methods.