Daniel Aloise
PhD thesis (2009)
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Published Version Terms of Use: All rights reserved. Download (1MB) |
Cite this document: | Aloise, D. (2009). Exact algorithms for minimum sum-of-squares clustering (PhD thesis, École Polytechnique de Montréal). Retrieved from https://publications.polymtl.ca/8451/ |
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Abstract
NP-Hardness of Euclidean sum-of-squares clustering -- Computational complexity -- An incorrect reduction from the K-section problem -- A new proof by reduction from the densest cut problem -- Evaluating a branch-and-bound RLT-based algorithm for minimum sum-of-squares clustering -- Reformulation-Linearization technique for the MSSC -- Branch-and-bound for the MSSC -- An attempt at reproducting computational results -- Breaking symmetry and convex hull inequalities -- A branch-and-cut SDP-based algorithm for minimum sum-of-squares clustering -- Equivalence of MSSC to 0-1 SDP -- A branch-and cut algorithm for the 0-1 SDP formulation -- Computational experiments -- An improved column generation algorithm for minimum sum-of-squares clustering -- Column generation algorithm revisited -- A geometric approach -- Generalization to the Euclidean space -- Computational results.
Uncontrolled Keywords
Optimisation mathématique; Classification automatique (Statistique) -- Mathématique; Moindres carrés
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Additional Information: | Le fichier PDF de ce document a été produit par Bibliothèque et Archives Canada selon les termes du programme Thèses Canada https://canada.on.worldcat.org/oclc/697933064 |
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Department: | Département de mathématiques et de génie industriel |
Academic/Research Directors: | Louis-Martin Rousseau and Pierre Hansen |
Date Deposited: | 04 Aug 2021 11:04 |
Last Modified: | 21 Sep 2021 10:51 |
PolyPublie URL: | https://publications.polymtl.ca/8451/ |
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