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On Multidimensional Scaling with City-Block Distances

  • Nerijus Galiauskas
  • Julius ŽilinskasEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8426)

Abstract

Multidimensional scaling is a technique for exploratory analysis of multidimensional data. The essential part of the technique is minimization of a function with unfavorable properties like multimodality, non-differentiability, and invariability with respect to some transformations. Recently various two-level optimization algorithms for multidimensional scaling with city-block distances have been proposed exploiting piecewise quadratic structure of the least squares objective function with such distances. A problem of combinatorial optimization is tackled at the upper level, and convex quadratic programming problems are tackled at the lower level. In this paper we discuss a new reformulation of the problem where lower level quadratic programming problems seem more suited for two-level optimization.

Keywords

Multidimensional scaling City-block distances Multilevel optimization Global optimization 

Notes

Acknowledgments

This research was funded by a grant (No. MIP-063/2012) from the Research Council of Lithuania.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Vilnius University Institute of Mathematics and InformaticsVilniusLithuania

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