Side-constrained minimum sum-of-squares clustering: mathematical programming and random projections

Leo Liberti () and Benedetto Manca ()
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Leo Liberti: CNRS LIX Ecole Polytechnique
Benedetto Manca: Università degli Studi di Cagliari

Journal of Global Optimization, 2022, vol. 83, issue 1, No 6, 83-118

Abstract: Abstract This paper investigates a mathematical programming based methodology for solving the minimum sum-of-squares clustering problem, also known as the “k-means problem”, in the presence of side constraints. We propose several exact and approximate mixed-integer linear and nonlinear formulations. The approximations are based on norm inequalities and random projections, the approximation guarantees of which are based on an additive version of the Johnson–Lindenstrauss lemma. We perform computational testing (with fixed CPU time) on a range of randomly generated and real data instances of medium size, but with high dimensionality. We show that when side constraints make k-means inapplicable, our proposed methodology—which is easy and fast to implement and deploy—can obtain good solutions in limited amounts of time.

Keywords: MINLP; k-means; Random projections; Side constraints (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10898-021-01047-6

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