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