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Bicriterion seriation methods for skew-symmetric matrices.

Michael J Brusco1, Stephanie Stahl

  • 1Department of Marketing, College of Business, Florida State University, Tallahassee 32306-1110, USA. mbrusco@cob.fsu.edu

The British Journal of Mathematical and Statistical Psychology
|November 19, 2005
PubMed
Summary

We introduce a new bicriterion method for ordering skew-symmetric matrices, balancing sign and magnitude. This approach offers a better way to analyze data compared to direct ordering methods.

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Area of Science:

  • Combinatorial data analysis
  • Matrix decomposition
  • Data ordering techniques

Background:

  • Decomposition of asymmetric proximity matrices into symmetric and skew-symmetric components is standard.
  • Seriation of skew-symmetric matrices can highlight sign or magnitude information.
  • The choice of objective criterion significantly impacts the ordering results.

Purpose of the Study:

  • To propose a novel bicriterion approach for the seriation of skew-symmetric matrices.
  • To incorporate both sign and magnitude information into the seriation process.
  • To offer an effective alternative to direct seriation methods.

Main Methods:

  • Developing a bicriterion objective function for seriation.
  • Applying the bicriterion approach to skew-symmetric matrices.

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  • Conducting numerical demonstrations to evaluate the method.

    • Main Results:

    • The bicriterion procedure effectively seriate skew-symmetric matrices.
    • The method allows for favorable trade-offs between sign and magnitude information.
    • Demonstrated effectiveness as an alternative to direct seriation.

    Conclusions:

    • The proposed bicriterion approach is a valuable tool for analyzing skew-symmetric matrices.
    • This method enhances data analysis by balancing sign and magnitude.
    • Offers improved insights compared to traditional seriation techniques.