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

Modified global k-means algorithm forminimum sum-of-squares clustering problems

Presenter : Lin, Shu-Han

  • Authors : Adil M. Bagirov

Pattern Recognition (PR, 2008)


Outline

Outline

  • Motivation

  • Objective

  • Methodology

  • Experiments

  • Conclusion

  • Comments


Motivation

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


Objectives

Objectives

Propose a new version of GKM


Methodology k means

Methodology– k-Means

sensitive to the choice of a starting point

5


Methodology the gkm algorithm

Methodology– The GKM algorithm

Objectivefunction

6


Methodology objective function

Methodology– Objectivefunction

  • Oldversion

  • Reformulatedversion

7


Methodology fast gkm algorithm

Methodology– fast GKM algorithm

  • Oldversion

  • Proposedversion(auxiliaryclusterfunction)

8


Methodology modified gkm algorithm

Methodology– modifiedGKM algorithm

  • Proposedversion

9


Methodology modified gkm algorithm1

Methodology– modifiedGKM algorithm

10


Experiments

Experiments

MSk-means:Multi-startk-means

GKM:fastGlobalK-Means

MGKM:ModifiedGlobalK-Means

11


Experiments1

Experiments

12


Experiments2

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


Conclusions

Conclusions

  • AnewversionoftheGKM

    • Changethecomputationofstartingpoints

    • Byminimizetheauxiliaryclusterfunction

    • Giventolerance

    • IsmoreeffectivethanGKM

      • largedatasetespecially

  • Thechoiceofstartingpointsink-meansiscrucial


Comments

Comments

  • Advantage

    • Theoreticallyanalysis

  • Drawback

    • Describewhytheythinktomodifyanythingtheytendtomodifyisimportant,orneedto.

  • Application

    • GKMoutperformsk-meansalgorithm


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