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Semi-Supervised Classification Based on Graph Filtering Jie Fan, Cihan Tepedelenlioglu, Andreas Spanias SenSIP Center, School of ECEE, Arizona State University MOTIVATION q Graphs can capture complex relational characteristics. q Signal processing on graphs extends the classical discrete signal processing theory to signals indexed by vertices of a graph. GRAPH FILTER DIAGRAM MONTE CARLO SIMULATION RESULTS Sensor Signal and Information Processing Center http://sensip.asu.edu • [1] S. Chen, A. Sandryhaila, J. M. Moura and J. Kovacevic, “Adaptive graph filtering: Multiresolution classification on graphs,” IEEE GlobalSIP,2013, pp. 427–430. • [2] S. Chen, F. Cerda, P. Rizzo, J. Bielak, J. H. Garrett, and J. Kovacevic, “Semi-supervised multiresolution classification using adaptive graph filtering with application to indirect bridge structural health monitoring,” IEEE Trans. on Signal Processing, vol. 62, pp. 2879– 2893, 2014. • [3] G. Caldarelli, A. Chessa, F. Pammolli, A. Gabrielli, and M. Puliga, “Reconstructing a credit network,” Nature Physics, vol. 9, no. 3, pp. 125–126, 2013. This work is funded in part by the NSF award ECSS 1307982, NSF CPS award 1646542 and the SenSIP Center. POTENTIAL APPLICATIONS q A well designed graph filter works as a semi-supervised classifier. q The proposed filter designing method provides lower error rate than the conventional one when feature data is incomplete. q Our method is especially suitable for practical application that the initial information is insufficient or quite correct due to privacy policies and measuring difficulties. q A classifier for data labeling. q An error detector for network analysis. q A simple representation for images in computer vision. q A pre-process of neural networks for reducing computation and mitigating overfitting risk. PROBLEM STATEMENT GRAPH FILTERING PROCEDURE q A partially labeled dataset with graph encoded inner interaction. Graph vertices: data points. Graph edges: relationships among the vertices. q A graph shift matrix is generated from the dataset. q The features of vertices is not completely collected. q Eigenvalues and eigenvectors need to be updated. ACKNOWLEDGEMENTS REFERENCES CONCLUSION q Graph Filtering: q Conventional Graph Filter Design Method: q Proposed Graph Filter Design Method: Y = H ⋅ X = QΛQ −1 ( ) ⋅ X H = Qh 0 + h 1 Λ + h 2 Λ 2 + ! + h L Λ L ( ) Q −1 H k + 1 = H k ! R k A i , j = exp − X i − X j 2 σ ( ) exp − X i − X j 2 σ ( ) i ∑ R k = f X , H k ( )

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Page 1: Poster Print Size: Change Color Theme: Semi-Supervised ... · 150-200 pixels per inch in their final printed size. For instance, a 1600 x 1200 pixel photo will usually look fine up

PosterPrintSize:Thispostertemplateis24”highby36”wide.Itcanbeusedtoprintanyposterwitha2:3aspectratioincluding36x54and48x72.

Placeholders:Thevariouselementsincludedinthisposterareonesweoftenseeinmedical,research,andscientificposters.Feelfreetoedit,move,add,anddeleteitems,orchangethelayouttosuityourneeds.Alwayscheckwithyourconferenceorganizerforspecificrequirements.

ImageQuality:YoucanplacedigitalphotosorlogoartinyourposterfilebyselectingtheInsert,Picturecommand,orbyusingstandardcopy&paste.Forbestresults,allgraphicelementsshouldbeatleast150-200pixelsperinchintheirfinalprintedsize.Forinstance,a1600x1200pixelphotowillusuallylookfineupto8“-10”wideonyourprintedposter.Topreviewtheprintqualityofimages,selectamagnificationof100%whenpreviewingyourposter.Thiswillgiveyouagoodideaofwhatitwilllooklikeinprint.Ifyouarelayingoutalargeposterandusinghalf-scaledimensions,besuretopreviewyourgraphicsat200%toseethemattheirfinalprintedsize.

Pleasenotethatgraphicsfromwebsites(suchasthelogoonyourhospital'soruniversity'shomepage)willonlybe72dpiandnotsuitableforprinting.

[Thissidebarareadoesnotprint.]

ChangeColorTheme:Thistemplateisdesignedtousethebuilt-incolorthemesinthenewerversionsofPowerPoint.Tochangethecolortheme,selecttheDesigntab,thenselecttheColorsdrop-downlist.

Thedefaultcolorthemeforthistemplateis“Office”,soyoucanalwaysreturntothataftertryingsomeofthealternatives.

PrintingYourPoster:Onceyourposterfileisready,visitwww.genigraphics.comtoorderahigh-quality,affordableposterprint.EveryorderreceivesafreedesignreviewandwecandeliverasfastasnextbusinessdaywithintheUSandCanada.Genigraphics®hasbeenproducingoutputfromPowerPoint®longerthananyoneintheindustry;datingbacktowhenwehelpedMicrosoft®designthePowerPoint®software.

USandCanada:1-800-790-4001Email:[email protected]

[Thissidebarareadoesnotprint.]

Semi-SupervisedClassificationBasedonGraphFiltering JieFan,CihanTepedelenlioglu,AndreasSpanias

SenSIPCenter,SchoolofECEE,ArizonaStateUniversity

MOTIVATION

q Graphscancapturecomplexrelationalcharacteristics.q Signalprocessingongraphsextendstheclassicaldiscretesignalprocessingtheorytosignalsindexedbyverticesofagraph.

GRAPHFILTERDIAGRAM

MONTECARLOSIMULATIONRESULTS

SensorSignalandInformationProcessingCenterhttp://sensip.asu.edu

•  [1]S.Chen,A.Sandryhaila,J.M.MouraandJ.Kovacevic,“Adaptivegraphfiltering:Multiresolutionclassificationongraphs,”IEEEGlobalSIP,2013,pp.427–430.

•  [2]S.Chen,F.Cerda,P.Rizzo,J.Bielak,J.H.Garrett,andJ.Kovacevic,“Semi-supervisedmultiresolutionclassificationusingadaptivegraphfilteringwithapplicationtoindirectbridgestructuralhealthmonitoring,”IEEETrans.onSignalProcessing,vol.62,pp.2879–2893,2014.

•  [3]G.Caldarelli,A.Chessa,F.Pammolli,A.Gabrielli,andM.Puliga,“Reconstructingacreditnetwork,”NaturePhysics,vol.9,no.3,pp.125–126,2013.

ThisworkisfundedinpartbytheNSFawardECSS1307982,NSFCPSaward1646542andtheSenSIPCenter.

POTENTIALAPPLICATIONS

q  Awelldesignedgraphfilterworksasasemi-supervisedclassifier.q Theproposed filterdesigningmethodprovides lowererror rate than the

conventionalonewhenfeaturedataisincomplete.q  Ourmethodisespeciallysuitableforpracticalapplicationthatthe initial

information is insufficient or quite correct due to privacy policies andmeasuringdifficulties.

q Aclassifierfordatalabeling.q Anerrordetectorfornetworkanalysis.q Asimplerepresentationforimagesincomputervision.q Apre-processofneuralnetworksforreducingcomputationandmitigatingoverfittingrisk.

PROBLEMSTATEMENT

GRAPHFILTERINGPROCEDURE

q Apartiallylabeleddatasetwithgraphencodedinnerinteraction.Graphvertices:datapoints.Graphedges:relationshipsamongthevertices.

q Agraphshiftmatrixisgeneratedfromthedataset.q Thefeaturesofverticesisnotcompletelycollected.q Eigenvaluesandeigenvectorsneedtobeupdated.

ACKNOWLEDGEMENTS

REFERENCES

CONCLUSIONq GraphFiltering:

q ConventionalGraphFilterDesignMethod:

q ProposedGraphFilterDesignMethod:

Y = H ⋅ X = QΛQ−1( ) ⋅ X

H =Q h0 + h1Λ + h2Λ2 +!+ hLΛ

L( )Q−1

Hk+1 = Hk !Rk

Ai , j =exp − Xi − X j 2

σ( )exp − Xi − X j 2

σ( )i∑

Rk = f X ,Hk( )

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