Robust regression and outlier detection
Robust regression and outlier detection
SIAM Journal on Scientific Computing
The Linear l1 Estimator and the Huber M-Estimator
SIAM Journal on Optimization
On a differential equation approach to the weighted orthogonal Procrustes problem
Statistics and Computing
Future Generation Computer Systems - Selected papers on theoretical and computational aspects of structural dynamical systems in linear algebra and control
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In this paper, we reconsider the well-known oblique Procrustes problem where the usual least-squares objective function is replaced by a more robust discrepancy measure, based on the ℓ1 norm or smooth approximations of it.We propose two approaches to the solution of this problem. One approach is based on convex analysis and uses the structure of the problem to permit a solution to the ℓ1 norm problem. An alternative approach is to smooth the problem by working with smooth approximations to the ℓ1 norm, and this leads to a solution process based on the solution of ordinary differential equations on manifolds. The general weighted Procrustes problem (both orthogonal and oblique) can also be solved by the latter approach. Numerical examples to illustrate the algorithms which have been developed are reported and analyzed.