A generalized solution of the orthogonal procrustes problem

Psychometrika ◽  
1966 ◽  
Vol 31 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Peter H. Schönemann
Keyword(s):  
Generalized Solution ◽  
Orthogonal Procrustes Problem ◽  
Procrustes Problem

Uncertainty characterization of the orthogonal Procrustes problem with arbitrary covariance matrices

2017 ◽  
Vol 61 ◽  
pp. 210-220 ◽  
Author(s):  
Pedro Lourenço ◽  
Bruno J. Guerreiro ◽  
Pedro Batista ◽  
Paulo Oliveira ◽  
Carlos Silvestre
Keyword(s):  
Covariance Matrices ◽  
Uncertainty Characterization ◽  
Orthogonal Procrustes Problem ◽  
Procrustes Problem

scholarly journals Optimization for L1-Norm Error Fitting via Data Aggregation

2020 ◽  
Author(s):  
Young Woong Park
Keyword(s):  
Data Aggregation ◽  
State Of The Art ◽  
Subset Selection ◽  
Global Optimum ◽  
L1 Norm ◽  
Orthogonal Procrustes Problem ◽  
Monotonic Convergence ◽  
Procrustes Problem ◽  
Fitting Model ◽  
Norm Error

We propose a data aggregation-based algorithm with monotonic convergence to a global optimum for a generalized version of the L1-norm error fitting model with an assumption of the fitting function. The proposed algorithm generalizes the recent algorithm in the literature, aggregate and iterative disaggregate (AID), which selectively solves three specific L1-norm error fitting problems. With the proposed algorithm, any L1-norm error fitting model can be solved optimally if it follows the form of the L1-norm error fitting problem and if the fitting function satisfies the assumption. The proposed algorithm can also solve multidimensional fitting problems with arbitrary constraints on the fitting coefficients matrix. The generalized problem includes popular models, such as regression and the orthogonal Procrustes problem. The results of the computational experiment show that the proposed algorithms are faster than the state-of-the-art benchmarks for L1-norm regression subset selection and L1-norm regression over a sphere. Furthermore, the relative performance of the proposed algorithm improves as data size increases.

scholarly journals Orthogonal Procrustes and norm-dependent optimality

2020 ◽  
Vol 36 (36) ◽  
pp. 158-168
Author(s):  
Joshua Cape
Keyword(s):  
Matrix Perturbation ◽  
Numerical Examples ◽  
Recent Advances ◽  
Orthogonal Procrustes Problem ◽  
Procrustes Problem ◽  
Deterministic Bounds ◽  
Subspace Alignment

This note revisits the classical orthogonal Procrustes problem and investigates the norm-dependent geometric behavior underlying Procrustes alignment for subspaces. It presents generic, deterministic bounds quantifying the performance of a specified Procrustes-based choice of subspace alignment. Numerical examples illustrate the theoretical observations and offer additional, empirical findings which are discussed in detail. This note complements recent advances in statistics involving Procrustean matrix perturbation decompositions and eigenvector estimation.

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