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Séminaire du GERAD

Global Optimization for Cardinality-Constrained Minimum Sum-of-Squares Clustering via Semidefinite Programming

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14 déc. 2022   10h30 — 11h30

Veronica Piccialli Sapienza Università di Roma, Italie

Veronica Piccialli

Séminaire en format hybride au local 4488 du GERAD ou Zoom.

The minimum sum-of-squares clustering (MSSC), or \(k\)-means type clustering, traditionally belongs to the unsupervised learning domain. However, using background knowledge to improve the cluster quality and promote the interpretability of the clustering process has attracted the attention of both the mathematical optimization and the machine learning community. Including background information leads to the so-called semi-supervised or constrained clustering. In this talk, we focus on exact algorithms for different variants of the MSSC problem: vanilla or unconstrained MSSC, MSSC with pairwise constraints (must-link and cannot-link constraints) and strict cardinality constraints. In all cases, the main ingredient is the use of semidefinite programming (SDP) tools for solving large-scale clustering problems to global optimality. The numerical results show that this class of approaches significantly increases the size of instances that can be solved to global optimality and represents state of the art for this class of problems.

This is a joint work with Anna Russo Russo, Antonio Maria Sudoso, and Angelika WIegele.

Daniel Aloise responsable

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Séminaire hybride au GERAD
Zoom et salle 4488
Pavillon André-Aisenstadt
Campus de l'Université de Montréal
2920, chemin de la Tour

Montréal Québec H3T 1J4
Canada

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