Constrained Clustering: General Pairwise and Cardinality Constraints

Adel Bibi, Ali Alqahtani, Bernard Ghanem

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


In this work, we study constrained clustering, where constraints are utilized to guide the clustering process. In existing works, two categories of constraints have been widely explored, namely pairwise and cardinality constraints. Pairwise constraints enforce the cluster labels of two instances to be the same (must-link constraints) or different (cannot-link constraints). Cardinality constraints encourage cluster sizes to satisfy a user-specified distribution. However, most existing constrained clustering models can only utilize one category of constraints at a time. In this paper, we enforce the above two categories into a unified clustering model starting with the integer program formulation of the standard K-means. As these two categories provide useful information at different levels, utilizing both of them is expected to allow for better clustering performance. However, the optimization is difficult due to the binary and quadratic constraints in the proposed unified formulation. To alleviate this difficulty, we utilize two techniques: equivalently replacing the binary constraints by the intersection of two continuous constraints; the other is transforming the quadratic constraints into bi-linear constraints by introducing extra variables. Then we derive an equivalent continuous reformulation with simple constraints, which can be efficiently solved by Alternating Direction Method of Multipliers (ADMM) algorithm. Extensive experiments on both synthetic and real data demonstrate: (1) when utilizing a single category of constraint, the proposed model is superior to or competitive with state-of-the-art constrained clustering models, and (2) when utilizing both categories of constraints jointly, the proposed model shows better performance than the case of the single category. The experimental results show that the proposed method exploits the constraints to achieve perfect clustering performance with improved clustering to 2-5% in classical clustering metrics, e.g. ...
Original languageEnglish (US)
Pages (from-to)1-1
Number of pages1
JournalIEEE Access
StatePublished - Jan 12 2023

Bibliographical note

KAUST Repository Item: Exported on 2023-01-17
Acknowledgements: The work was done when Adel Bibi was at KAUST. This work was supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research and the Deanship of Scientific Research, King Khalid University of Kingdom of Saudi Arabia under research grant number (RGP1/357/43).

ASJC Scopus subject areas

  • General Engineering
  • General Computer Science
  • General Materials Science


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