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An enhanced branch-and-bound algorithm for a partitioning problem.

Michael J Brusco1

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

The British Journal of Mathematical and Statistical Psychology
|June 14, 2003
PubMed
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This study introduces an efficient branch-and-bound algorithm for partitioning objects using dissimilarity matrices. It minimizes within-subset dissimilarities, offering improved bounds for optimal object clustering.

Area of Science:

  • Data Science
  • Operations Research
  • Computer Science

Background:

  • Object partitioning relies on analyzing symmetric, non-negative dissimilarity matrices.
  • Minimizing within-subset dissimilarities is a key objective in data clustering.

Purpose of the Study:

  • To develop an efficient algorithm for partitioning objects based on dissimilarity matrices.
  • To improve upon existing mathematical programming methods for clustering problems.

Main Methods:

  • An improved branch-and-bound algorithm is proposed.
  • Enhanced upper bounds are achieved via a fast exchange algorithm.
  • Sharper lower bounds are obtained through sequential submatrix solutions.

Main Results:

Related Experiment Videos

  • The improved branch-and-bound algorithm demonstrates high efficiency.
  • Computational results confirm the effectiveness for synthetic and empirical data.
  • A modified algorithm for minimizing partition diameter is also presented.

Conclusions:

  • The branch-and-bound methodology is highly effective for object partitioning.
  • The proposed improvements lead to more efficient and accurate clustering.
  • This approach offers a robust solution for problems involving dissimilarity matrices.