Article Dans Une Revue Journal of Global Optimization Année : 2021

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

Résumé

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.

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Dates et versions

hal-03395326 , version 1 (22-10-2021)

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Leo Liberti, Benedetto Manca. Side-constrained minimum sum-of-squares clustering: mathematical programming and random projections. Journal of Global Optimization, 2021, ⟨10.1007/s10898-021-01047-6⟩. ⟨hal-03395326⟩
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