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Presenter : Lin, Shu -Han Authors : Jeen-Shing Wang, Jen- Chieh Chiang

A cluster validity measure with a hybrid parameter search method for the support vector clustering algorithm. Presenter : Lin, Shu -Han Authors : Jeen-Shing Wang, Jen- Chieh Chiang. PR (2008 ). Outline. Introduction of SVC Motivation Objective Methodology Experiments

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Presenter : Lin, Shu -Han Authors : Jeen-Shing Wang, Jen- Chieh Chiang

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  1. A cluster validity measurewith a hybrid parameter search method for the support vector clustering algorithm Presenter : Lin, Shu-Han Authors : Jeen-Shing Wang, Jen-Chieh Chiang PR (2008)

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

  3. SVC • SVC is from SVMs • SVMs is supervised clustering technique • Fast convergence • Good generalization performance • Robustness for noise • SVC is unsupervised approach • Data points map to HD feature space using a Gaussian kernel. • Look for smallest sphere enclose data. • Map sphere back to data space to form set of contours. • Contours are treated as the cluster boundaries. 3

  4. SVC - Sphere Analysis a To find the minimal enclose sphere with soft margin: To solve this problem, the Lagrangian function: 4

  5. SVC - Sphere Analysis 5

  6. SVC - Sphere Analysis Karush-Kuhn-Tucker complementarity: 6

  7. SVC -Sphere Analysis Wolfe dual optimization problem a • Bound SV; Outlier To find the minimal enclose sphere with soft margin: C : existence of outliersallowed 7

  8. SVC -Sphere Analysis Mercer kernel Kernel: Gaussian a Gaussian function: The distance (similarity) between x and a: q :|clusters|&thesmoothness/tightnessoftheclusterboundaries. 8

  9. Motivation • DrawbacksofClustervalidation • Compactness • Differentdensitiesorsize • Asthe#ofclustersincreases,itwillmonotonicdecrease • Separation • Irregularclusterstructures 9

  10. Motivation • Theirpreviousstudy • Canhandle • Differentsizes • Differentdensities • Arbitraryshape • But… 10

  11. Objectives–AclustervaliditymethodandaparametersearchalgorithmforSVCObjectives–AclustervaliditymethodandaparametersearchalgorithmforSVC • Autodeterminethetwoparameter: • Increasingqleadtoincreasing#ofclusters • Cregulatestheexistenceofoutliersandoverlappingclusters ToIdentifytheoptimalstructure 11

  12. Methodology- Idea N=64,max#ofcluster=,8 qisrelatedtothedensitiesoftheclusters Eachclusterstructurecorrespondstoanintervalofq Identifytheoptimalstructureisequivalenttofindingthelargestinterval 12

  13. Methodology- Problem Howtolocateoverallsearchrangeofq Howtodetectoutliers/noises Howtoidentifythelargestinterval 13

  14. Methodology – Locaterangeofq • Lowerbound • Upperbound:EmployK-Meanstogetclusters,andgetvarianceofeachclustersvi Ascendingorder:clustersize n=3,thebiggest3clusters’variance 14

  15. Methodology – Outlier Detection singleton outlier AndwegetCopt,removethese outlier Setq=qmax,thetightestofq 15

  16. Methodology – the largest interval qopt 16

  17. Methodology – the largest interval • Fibonaccisearch:locatetheintervalwheretheclusterstructureisthesame • Bisectionsearch • n:iteration 17

  18. Methodology– Overview Locaterangeofq the largest interval Outlier Detection 18

  19. Experiments - Benchmark and Artificial Examples 19

  20. Experiments - Outlier Copt 20

  21. Experiments ？ 21

  22. Conclusions • Anewmeasure: • Inspiredfromtheobservationsofq • DeterminetheoptimalclusterstructurewithitscorrespondingrangeofqandC q C

  23. Comments • Advantage • Inspiredfromobservationofparameter • Drawback • … • Application • SVC • DBSCAN:MinPts/Eps

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