Abstract
We present a successive projection method for solving the unbalanced Procrustes problem: given matrix A ∈ R n × n and B ∈ R n × k, n > k, minimize the residual ‖AQ − B‖F with the orthonormal constraint Q T Q = I k on the variant Q ∈ R n × 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.
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Zhang, Z., Du, K. Successive projection method for solving the unbalanced Procrustes problem. SCI CHINA SER A 49, 971–986 (2006). https://doi.org/10.1007/s11425-006-0971-2
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DOI: https://doi.org/10.1007/s11425-006-0971-2