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Just Relax and Come Clustering!: A Convexification of k-Means Clustering
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
2011 (English)Report (Other academic)
Abstract [en]

k-means clustering is a popular approach to clustering. It is easy to implement and intuitive but has the disadvantage of being sensitive to initialization due to an underlying nonconvex optimization problem. In this paper, we derive an equivalent formulation of k-means clustering. The formulation takes the form of a L0-regularized least squares problem. We then propose a novel convex, relaxed, formulation of k-means clustering. The sum-of-norms regularized least squares formulation inherits many desired properties of k-means but has the advantage of being independent of initialization.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2011. , 12 p.
Series
LiTH-ISY-R, ISSN 1400-3902 ; 2992
Keyword [en]
Clustering ; K-means ; Sum-of-norms ; Group-lasso
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-97752ISRN: LiTH-ISY-R-2992OAI: oai:DiVA.org:liu-97752DiVA: diva2:650707
Available from: 2013-09-23 Created: 2013-09-23 Last updated: 2014-09-01Bibliographically approved

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Authority records BETA

Lindsten, FredrikOhlsson, HenrikLjung, Lennart

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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf