Two level minimization in multidimensional scaling

Authors:
Antanas Žilinskas;Julius Žilinskas
Affiliations:
Institute of Mathematics and Informatics, Vilnius, Lithuania 08663;Institute of Mathematics and Informatics, Vilnius, Lithuania 08663
Venue:
Journal of Global Optimization
Year:
2007

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Abstract

Multidimensional scaling with city block norm in embedding space is considered. Construction of the corresponding algorithm is reduced to minimization of a piecewise quadratic function. The two level algorithm is developed combining combinatorial minimization at upper level with local minimization at lower level. Results of experimental investigation of the efficiency of the proposed algorithm are presented as well as examples of its application to visualization of multidimensional data.