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Modified global k-means algorithm for minimum sum-of-squares clustering problems

Modified global k-means algorithm for minimum sum-of-squares clustering problems. Presenter : Lin, Shu -Han Authors : Adil M. Bagirov. Pattern Recognition (PR, 2008). Outline. Motivation Objective Methodology Experiments Conclusion Comments. Motivation. k- Means algorithm

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Modified global k-means algorithm for minimum sum-of-squares clustering problems

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  1. Modified global k-means algorithm forminimum sum-of-squares clustering problems Presenter : Lin, Shu-Han • Authors : Adil M. Bagirov Pattern Recognition (PR, 2008)

  2. Outline • Motivation • Objective • Methodology • Experiments • Conclusion • Comments

  3. Motivation • k-Meansalgorithm • sensitive to the choice of starting points • inefficient for solving clustering problems in large data sets • Global k-Means (GKM) algorithm • incremental algorithm (dynamically adds a cluster center at a time) • uses each data point as a candidate for the k-th cluster center

  4. Objectives Propose a new version of GKM

  5. Methodology– k-Means sensitive to the choice of a starting point 5

  6. Methodology– The GKM algorithm Objectivefunction 6

  7. Methodology– Objectivefunction • Oldversion • Reformulatedversion 7

  8. Methodology– fast GKM algorithm • Oldversion • Proposedversion(auxiliaryclusterfunction) 8

  9. Methodology– modifiedGKM algorithm • Proposedversion 9

  10. Methodology– modifiedGKM algorithm 10

  11. Experiments MSk-means:Multi-startk-means GKM:fastGlobalK-Means MGKM:ModifiedGlobalK-Means 11

  12. Experiments 12

  13. Experiments • Overall(14datasets,140results) • The MS k-meansalgorithm finds the best known (or near best known) solutions42 (33.3%) times • GKMalgorithm 76 (60.3%) times • MGKMalgorithm 102 (81.0%) times • Largekinlargedatasets(m) • The MS k-means algorithmfailedto find the best known (or near best known) solutions • GKM algorithmfinds such solutions 22 (45.8%) times • MGKM algorithm42(87.5%) times. 13

  14. Conclusions • AnewversionoftheGKM • Changethecomputationofstartingpoints • Byminimizetheauxiliaryclusterfunction • Giventolerance • IsmoreeffectivethanGKM • largedatasetespecially • Thechoiceofstartingpointsink-meansiscrucial

  15. Comments • Advantage • Theoreticallyanalysis • Drawback • Describewhytheythinktomodifyanythingtheytendtomodifyisimportant,orneedto. • Application • GKMoutperformsk-meansalgorithm

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