An exact algorithm for semi-supervised minimum sum-of-squares clustering

The minimum sum-of-squares clustering (MSSC), or k-means type clustering, is traditionally considered an unsupervised learning task. In recent years, the use of background knowledge to improve the cluster quality and promote interpretability of the clustering process has become a hot research topic...

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Veröffentlicht in:Computers & operations research Jg. 147; S. 105958
Hauptverfasser: Piccialli, Veronica, Russo Russo, Anna, Sudoso, Antonio M.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Ltd 01.11.2022
Schlagworte:
Branch and cut
Constrained clustering
Global optimization
Semidefinite programming
Semidefinite programming
Global optimization
Branch and cut
Constrained clustering
ISSN:0305-0548, 1873-765X
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Zusammenfassung:The minimum sum-of-squares clustering (MSSC), or k-means type clustering, is traditionally considered an unsupervised learning task. In recent years, the use of background knowledge to improve the cluster quality and promote interpretability of the clustering process has become a hot research topic at the intersection of mathematical optimization and machine learning research. The problem of taking advantage of background information in data clustering is called semi-supervised or constrained clustering. In this paper, we present branch-and-cut algorithm for semi-supervised MSSC, where background knowledge is incorporated as pairwise must-link and cannot-link constraints. For the lower bound procedure, we solve the semidefinite programming relaxation of the MSSC discrete optimization model, and we use a cutting-plane procedure for strengthening the bound. For the upper bound, instead, by using integer programming tools, we use an adaptation of the k-means algorithm to the constrained case. For the first time, the proposed global optimization algorithm efficiently manages to solve real-world instances up to 800 data points with different combinations of must-link and cannot-link constraints and with a generic number of features. This problem size is about four times larger than the one of the instances solved by state-of-the-art exact algorithms. •An SDP-based branch-and-cut algorithm for MSSC with must-link and cannot-link constraints.•An SDP-based heuristic providing a bound on the optimality gap of the produced clustering.•Our exact algorithm can solve instances 4 times larger than those solved by state-of-the-art exact algorithms.•Cluster evaluation metrics confirm the advantage of finding a globally optimal clustering.
ISSN:0305-0548
1873-765X
DOI:10.1016/j.cor.2022.105958