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An algorithm for extracting maximum cardinality subsets with perfect dominance or anti-Robinson structures.

Michael J Brusco1, Stephanie Stahl

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

The British Journal of Mathematical and Statistical Psychology
|November 1, 2007
PubMed
Summary

This study introduces an algorithm to find the largest subset of objects that allows for perfect matrix seriation. This method optimizes both dominance and anti-Robinson structures for improved data ordering.

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Area of Science:

  • Data analysis
  • Matrix ordering
  • Computational mathematics

Background:

  • Seriation of asymmetric matrices commonly uses the dominance index.
  • Seriation of symmetric matrices often employs the anti-Robinson gradient index.
  • Perfect matrix structures are rarely achieved with empirical data.

Purpose of the Study:

  • To develop an algorithm for identifying maximum cardinality subsets for perfect matrix seriation.
  • To address the challenge of achieving perfect dominance and anti-Robinson structures in real-world datasets.

Main Methods:

  • An algorithm is presented to find the largest subset of objects yielding a perfect seriation structure.
  • The algorithm is demonstrated for dominance, anti-Robinson, and strongly anti-Robinson structures.
  • MATLAB implementations are provided for the developed algorithm.

Main Results:

  • The algorithm successfully identifies maximum cardinality subsets for perfect matrix seriation.
  • Demonstrated effectiveness for various seriation criteria including dominance and anti-Robinson structures.
  • Availability of MATLAB code facilitates practical application of the method.

Conclusions:

  • The developed algorithm enables the identification of subsets with perfect matrix structures.
  • This approach enhances the ability to perform accurate seriation on empirical data.
  • The provided MATLAB implementations support the practical use of these methods in data analysis.