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Fast global k-means clustering using cluster membership and inequality

Fast global k-means clustering using cluster membership and inequality. Presenter : Lin, Shu -Han Authors : Jim Z.C. Lai, Tsung -Jen Huang. Pattern Recognition (PR, 2010). Outline. Motivation Objective Methodology Experiments Conclusion Comments. Motivation. FGKM and MGKM

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Fast global k-means clustering using cluster membership and inequality

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  1. Fast global k-means clustering using cluster membership and inequality Presenter : Lin, Shu-Han • Authors : Jim Z.C. Lai, Tsung-Jen Huang Pattern Recognition(PR, 2010)

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

  3. Motivation • FGKM and • MGKM Have the same computational complexity MGKM Claims that it is moreeffectivethanFGKM (see 2008.PR.8.書漢.1027.Modified global k-means algorithm for minimum sum-of-squares clustering problems)

  4. Objectives , th=.9999 • Develop a set of inequalities to • Speed up FGKM and MGKM, called MFGKM • Using Karhunen-Loeve Transform (KLT) • closely related to the Principal Component Analysis (PCA)

  5. Methodology–MFGKM Red = proposed (or s Yj’ , called MCS)

  6. Methodology– cluster center selection algorithm (Speed up)

  7. Methodology– Candidate set construction algorithm

  8. Methodology– Candidate set construction algorithm (Cont.) 1. r10=2,r10=d(x10,c) |8.2-7.2|=1 1+|2.2-4.2|=3>r10,deletex10, x10cannotbethenearestneighborofx8 l+p m 1 2

  9. Methodology– Candidate set construction algorithm (Cont.) 2. rmax=2 m

  10. Methodology– Candidate set construction algorithm (Cont.) 3.

  11. Methodology– Candidate set construction algorithm (Cont.) 4. Diff(distortion) Diff=(r9-d(x8,x9))+(r10-d(x8,x10)) =2-1+2-1 m Return2andcenterofx9andx7

  12. Methodology– Candidate set construction algorithm (Cont.)

  13. Methodology– Candidate set construction algorithm (Cont.)

  14. Methodology– Candidate set construction algorithm (Cont.)

  15. Methodology– MCS

  16. Experiments–Computingtime 16

  17. Experiments–Distortion Leastdistortion Faster,butdistortion 17

  18. Conclusions • GKM • FGKM:faster,butlocal • MGKM:betterperformancethenFGKM,butneedsmorecomputationalcomplexity • MFGKM:faster,andbetterthenMGKM • MFGKM+MCS:fastestmethod,andperformanceiscomparabletoMGKM

  19. Comments • Advantage • Improvebothperformanceandspeed • Drawback • … • Application • …

  20. Methodology– k-Means sensitive to the choice of a starting point 20

  21. Methodology– The GKM algorithm Objectivefunction 21

  22. Methodology– Objectivefunction • Oldversion • Reformulatedversion 22

  23. Methodology– fast GKM algorithm • Oldversion • Proposedversion(auxiliaryclusterfunction) k-1 k-1 j y i i 23

  24. Methodology– modifiedGKM algorithm • Proposedversion S2 k-1 S2 S2 ci i S2 S2 24

  25. Methodology– modifiedGKM algorithm 25

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