02 沈华伟 - 中国科学院计算技术研究所研究员 - Graph convolutional neural networks.pdfVIP免费

沈华伟shenhuawei@ict.ac.cn微博:沈华伟_ICT中国科学院计算技术研究所GraphConvolutionalNeuralNetworksConvolutionalNeuralNetworkConvolutionalneuralnetwork(CNN)gainsgreatsuccessonEuclideandata,e.g.,image,text,audio,andvideoImageclassification,objectdetection,machinetranslationThepowerofCNNliesinitsabilitytolearnlocalstationarystructures,vialocalizedconvolutionfilter,andcomposethemtoformmulti-scalehierarchicalpatterns2M.M.Bronstein,J.Bruna,Y.LeCun,A.Szlam,P.Vandergheynst.Geometricdeeplearning:goingbeyondEuclideandata.IEEESignalProcessingMagazine,18-42,2017.TemporalconvolutionalnetworkConvolutionalneuralnetworksonimageConvolutionalNeuralNetworkLocalizedconvolutionalfiltersaretranslation-orshift-invariantWhichareabletorecognizeidenticalfeaturesindependentlyoftheirspatiallocationsOneinterestingproblemishowtogeneralizeconvolutiontonon-Euclideandomain,e.g.,graph?Irregularstructureofgraphposeschallengesfordefiningconvolutionforgraphdata3LeCun,Y.,Bengio,Y.,andHinton,G.Deeplearning.Nature,521(7553):436,2015101010101101010101101010101TemplateMatchingX-ShapeFromCNNtographCNNConvolutioniswelldefinedinEuclideandata,grid-likenetworkNotstraightforwardtodefineconvolutiononirregularnetwork,widelyobservedinrealworld4Grid-likenetworkIrregularnetworksConvolutionConvolutionisamathematicaloperationontwofunctions,𝒇and𝒈,toproduceathirdfunction𝒉.Definedastheintegral,incontinuouscase,orsum,indiscretecase,oftheproductofthetwofunctionsafteroneisreversedandshifted.5ℎ𝑡=𝑓∗𝑔𝑡≝𝑓𝑡𝑔𝑡−𝜏ⅆ𝜏ℎ𝑥,𝑦=𝑓∗𝑔𝑥,𝑦≝𝑚,𝑛𝑓𝑥−𝑚,𝑦−𝑛𝑔𝑚,𝑛𝑔=𝑔1,11𝑔0,10𝑔−1,11𝑔1,00𝑔0,01𝑔−1,00𝑔1,−11𝑔0,−10𝑔−1,−11ContinuouscaseDiscretecase𝒇𝒉𝑥𝑦ExistingmethodstodefineconvolutionSpectralmethods:defineconvolutioninspectraldomainConvolutionisdefinedviagraphFouriertransformandconvolutiontheorem.Themainchallengeisthatconvolutionfilterdefinedinspectraldomainisnotlocalizedinvertexdomain.Spatialmethods:defineconvolutioninthevertexdomainConvolutionisdefinedasaweightedave...