Journal of Combinatorial Optimization

, Volume 23, Issue 2, pp 224–251 | Cite as

Multi-way clustering and biclustering by the Ratio cut and Normalized cut in graphs

  • Neng Fan
  • Panos M. Pardalos


In this paper, we consider the multi-way clustering problem based on graph partitioning models by the Ratio cut and Normalized cut. We formulate the problem using new quadratic models. Spectral relaxations, new semidefinite programming relaxations and linearization techniques are used to solve these problems. It has been shown that our proposed methods can obtain improved solutions. We also adapt our proposed techniques to the bipartite graph partitioning problem for biclustering.


Ratio cut Normalized cut Clustering Biclustering Graph partitioning Spectral relaxation Semidefinite programming Quadratically constrained programming 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA

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