Skip to main content
SpringerLink
Log in
Book cover

Classification as a Tool for Research pp 271–278Cite as

Methods for the Analysis of Skew-Symmetry in Asymmetric Multidimensional Scaling

  • Conference paper
  • First Online:

Abstract

The decomposition of any square matrix in symmetric and skew- symmetric components has inspired many methods in asymmetric multidimensional scaling (reviews are provided e.g. in Zielman and Heiser 1996; Bove and Rocci 1999; Borg and Groenen 2005; Saito and Yadohisa 2005). Separate analyzes of the two components seem preferable when symmetry is much more relevant in the data or when we want to represent separately skew-symmetric residuals of statistical models (e.g. symmetry or quasi-symmetry). In this paper two and three-way methods for the analysis of skew-symmetry are reviewed focalizing on multidimensional models with graphical capabilities.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Borg, I., & Groenen, P. J. F. (2005). Modern multidimensional scaling. Theory and applications (2nd ed.). New York: Springer.

    MATH  Google Scholar 

  • Bove, G. (1989). New methods of representation of proximity data. Doctoral thesis (in italian). Dipartimento di Statistica, Probabilita’ e Statistiche Applicate, Universita’ La Sapienza, Roma.

    Google Scholar 

  • Bove, G. (2006). Approaches to asymmetric multidimensional scaling with external information. In S. Zani, A. Cerioli, et al. (Eds.), Data analysis, classification and the forward search (pp. 69–76). Berlin: Springer.

    Chapter  Google Scholar 

  • Bove, G., & Rocci, R. (1999). Methods for asymmetric three-way scaling. In M. Vichi and O. Opitz (Eds.), Classification and data analysis. Theory and application (pp. 131–138). Berlin: Springer.

    Google Scholar 

  • Carroll, J. D. (1972). Individual differences and multidimensional scaling. In R. N. Shepard et al. (Eds.), Multidimensional scaling: Theory and applications in the behavioral sciences (Vol. 1, pp. 105–155). New York: Seminar Press.

    Google Scholar 

  • Critchley, F. (1988). On characterization of the inner-products of the space of square matrices of given order which render orthogonal the symmetric and the skew-symmetric subspaces. Warwick Statistics Research Report 171, University of Warwick, Coventry.

    Google Scholar 

  • Freeman, L. C. (1997). Uncovering organizational hierarchies. Computational and Mathematical Organization Theory, 3, 5–18.

    Article  MATH  Google Scholar 

  • Gower, J. C. (1977). The analysis of asymmetry and orthogonality. In J. R. Barra et al. (Eds.), Recent developments in statistics (pp. 109–123). Amsterdam: North Holland.

    Google Scholar 

  • Gower, J. C., & Zielman, B. (1992). Some remarks on orthogonality in the analysis of asymmetry. R.R.-92-08, Department of Data Theory, Leiden.

    Google Scholar 

  • Harshmann, R. A. (1978). Models for analysis of asymmetrical relationships among N objects or stimuli. Paper presented at the First Joint Meeting of the Psychometric Society and the Society for Mathematical Psychology, Hamilton, Ontario.

    Google Scholar 

  • Harshmann, R. A. (1981). DEDICOM Analysis of Skew-Symmetric Data. Part I:Theory. Unpublished technical memorandum, Bell Laboraries, Murray Hill.

    Google Scholar 

  • Kiers, H. A. L. (1993). An alternating least squares algorithm for PARAFAC2 and DEDICOM3. Computational Statistics and Data Analysis, 16, 103–118.

    Article  MATH  Google Scholar 

  • Kiers, H. A. L., & Takane, Y. (1993). Constrained DEDICOM. Psychometrika, 58, 339–355.

    Article  MATH  MathSciNet  Google Scholar 

  • Lundy, M. E., Harshmann, R. A., Paatero, P., & Swartzman, L. C. (2003). Application of the 3-way Dedicom model to skew-symmetric data for paired preference ratings of treatments for chronic back pain. Paper presented at the TRICAP 2003 Meeting, Lexington, Kentucky.

    Google Scholar 

  • Rocci, R., & Bove, G. (2002). Rotation techniques in asymmetric multidimensional scaling. Journal of Computational and Graphical Statistics, 11, 405–419.

    Article  MathSciNet  Google Scholar 

  • Saito, T., & Yadohisa, H. (2005). Data analysis of asymmetric structures. Advanced approaches in computational statistics. New York: Marcel Dekker.

    MATH  Google Scholar 

  • Zielman, B. (1991). Three-way scaling of asymmetric proximities. R.R.-91-01, Department of Data Theory, Leiden.

    Google Scholar 

  • Zielman, B. (1993). Two methods for multidimensional analysis of three-way skew-symmetric matrices. R.R.-93-01, Department of Data Theory, Leiden.

    Google Scholar 

  • Zielman, B., & Heiser, W. J. (1996). Models for asymmetric proximities. British Journal of Mathematical and Statistical Psychology, 49, 127–146.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Scienze dell’Educazione, Università degli Studi Roma Tre, Rome, Italy

    Giuseppe Bove

Authors
  1. Giuseppe Bove
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Giuseppe Bove .

Editor information

Editors and Affiliations

  1. LS für BWL, insb. Finanzwirtschaft und, Finanzdienstleistungen, TU Dresden, Helmholtzstr. 10, Dresden, 01062, Germany

    Hermann Locarek-Junge

  2. FG Computergestützte Statistik, Univ. Dortmund, Vogelpothsweg 87, Dortmund, 44227, Germany

    Claus Weihs

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bove, G. (2010). Methods for the Analysis of Skew-Symmetry in Asymmetric Multidimensional Scaling. In: Locarek-Junge, H., Weihs, C. (eds) Classification as a Tool for Research. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10745-0_29

Download citation

Publish with us

Policies and ethics

Search

Navigation