We present a successive projection method for solving the unbalanced Procrustes problem: given matrix A ∈ Rn×n and B ∈ Rn×κ, n ＞κ, minimize the residual ‖AQ - B‖F with the orthonormal constraint QTQ ...We present a successive projection method for solving the unbalanced Procrustes problem: given matrix A ∈ Rn×n and B ∈ Rn×κ, n ＞κ, minimize the residual ‖AQ - B‖F with the orthonormal constraint QTQ = Iκ on the variant Q ∈ Rn×κ. 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.展开更多
基金The work was supported in part by the National Natural Science Foundation of China (Grant No. 60372033).
文摘We present a successive projection method for solving the unbalanced Procrustes problem: given matrix A ∈ Rn×n and B ∈ Rn×κ, n ＞κ, minimize the residual ‖AQ - B‖F with the orthonormal constraint QTQ = Iκ on the variant Q ∈ Rn×κ. 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.
