Multidimensional scaling with city-block distances based on combinatorial optimization and systems of linear equations. (English) Zbl 1178.90280

Žilinskas, J.

Math. Model. Anal. 14, No. 2, 259-270 (2009).

Summary: Multidimensional scaling is a technique for exploratory analysis of multidimensional data. The essential part of the technique is minimization of a multimodal function with unfavorable properties like invariants and non-differentiability. In this paper a two-level optimization based on combinatorial optimization and systems of linear equations is proposed exploiting piecewise quadratic structure of the objective function with city-block distances. The approach is tested experimentally and improvement directions are identified.

MSC:

90C27

Combinatorial optimization

Keywords:

multilevel optimization