A quadratically converging algorithm of multidimensional scaling

Article type: Research Article

Authors: Žilinskas, Antanas

Affiliations: Institute of Mathematics and Informatics, 2600 Vilnius, Akademijos St. 4, Vytautas Magnus University, 3600 Kaunas, Vileikos St. 8, Lithuania

Abstract: Multidimensional scaling (MDS) is well known technique for analysis of multidimensional data. The most important part of implementation of MDS is minimization of STRESS function. The convergence rate of known local minimization algorithms of STRESS function is no better than superlinear. The regularization of the minimization problem is proposed which enables the minimization of STRESS by means of the conjugate gradient algorithm with quadratic rate of convergence.

Keywords: local minimization, conjugate gradients, quadratic convergence rate

DOI: 10.3233/INF-1996-7207

Journal: Informatica, vol. 7, no. 2, pp. 268-274, 1996