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On Multidimensional Scaling with City-Block Distances

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Learning and Intelligent Optimization (LION 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8426))

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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.

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Acknowledgments

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

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Authors and Affiliations

  1. Vilnius University Institute of Mathematics and Informatics, Akademijos 4, 08663, Vilnius, Lithuania

    Nerijus Galiauskas & Julius Žilinskas

Authors
  1. Nerijus Galiauskas
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  2. Julius Žilinskas
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Corresponding author

Correspondence to Julius Žilinskas .

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Editors and Affiliations

  1. Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

  2. AT&T Labs Research, Middletown, New Jersey, USA

    Mauricio G.C. Resende

  3. University of Florida, Gainesville, Florida, USA

    Chrysafis Vogiatzis

  4. Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida, USA

    Jose L. Walteros

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Galiauskas, N., Žilinskas, J. (2014). On Multidimensional Scaling with City-Block Distances. In: Pardalos, P., Resende, M., Vogiatzis, C., Walteros, J. (eds) Learning and Intelligent Optimization. LION 2014. Lecture Notes in Computer Science(), vol 8426. Springer, Cham. https://doi.org/10.1007/978-3-319-09584-4_9

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  • DOI: https://doi.org/10.1007/978-3-319-09584-4_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09583-7

  • Online ISBN: 978-3-319-09584-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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