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A polynomial algorithm for balanced clustering via graph partitioning

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  • Caraballo, Luis Evaristo
  • Díaz-Báñez, José-Miguel
  • Kroher, Nadine

Abstract

The objective of clustering is to discover natural groups in datasets and to identify geometrical structures which might reside there, without assuming any prior knowledge on the characteristics of the data. The problem can be seen as detecting the inherent separations between groups of a given point set in a metric space governed by a similarity function. The pairwise similarities between all data objects form a weighted graph whose adjacency matrix contains all necessary information for the clustering process. Consequently, the clustering task can be formulated as a graph partitioning problem. In this context, we propose a new cluster quality measure which uses the ratio of intra- and inter-cluster variance and allows us to compute the optimal clustering under the min-max principle in polynomial time. Our algorithm can be applied to both partitional and hierarchical clustering.

Suggested Citation

  • Caraballo, Luis Evaristo & Díaz-Báñez, José-Miguel & Kroher, Nadine, 2021. "A polynomial algorithm for balanced clustering via graph partitioning," European Journal of Operational Research, Elsevier, vol. 289(2), pages 456-469.
  • Handle: RePEc:eee:ejores:v:289:y:2021:i:2:p:456-469
    DOI: 10.1016/j.ejor.2020.07.031
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    References listed on IDEAS

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    3. Caraballo, L.E. & Díaz-Báñez, J.M. & Maza, I. & Ollero, A., 2017. "The block-information-sharing strategy for task allocation: A case study for structure assembly with aerial robots," European Journal of Operational Research, Elsevier, vol. 260(2), pages 725-738.
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    Cited by:

    1. Ah-Pine, Julien, 2022. "Learning doubly stochastic and nearly idempotent affinity matrix for graph-based clustering," European Journal of Operational Research, Elsevier, vol. 299(3), pages 1069-1078.
    2. Chen, Claire Y.T. & Sun, Edward W. & Miao, Wanyu & Lin, Yi-Bing, 2024. "Reconciling business analytics with graphically initialized subspace clustering for optimal nonlinear pricing," European Journal of Operational Research, Elsevier, vol. 312(3), pages 1086-1107.

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