Peter Benner, Jens Fankhänel: Computational solutions of a family of generalized Procrustes problems

Author(s):

Peter Benner
Jens Fankhänel

Title:

Peter Benner, Jens Fankhänel: Computational solutions of a family of generalized Procrustes problems

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 06, 2014

Mathematics Subject Classification:

    []

Abstract:

We consider a family of generalized Procrustes problems. In this class of problems, one aims at aligning a set of vectors to a given second set of vectors. The distance between both sets is measured in the q norm, and for the alignment, isometries with # respect to the p norm are allowed. In contrast to the classical Procrustes problem with p = q = 2, we allow p and q to differ. We will see that it makes a difference whether the problem is real or cast over the complex field. Therefore, we discuss the solutions for p = 2 separately for these cases. We show that all the real cases can be solved efficiently. Most of the complex cases can up to now only be solved approximately in polynomial time, but we show the existence of polynomial time algorithms for q ∈ {2, 4, ∞}. Computational experiments illustrate the suggested algorithms.

Keywords:

Banach spaces, optimization, generalized Procrustes problems

Language:

English

Publication time:

06/2014