一個基于圖卷積神經(jīng)網(wǎng)絡的局部密度優(yōu)化方法（英文）

一個基于圖卷積神經(jīng)網(wǎng)絡的局部密度優(yōu)化方法（文Density-basedclusteringisawidelyusedtechniqueindataminingandmachinelearning.However,traditionaldensity-basedclusteringmethodsmayfailtocapturecomplexspatialpatternsinthedata,especiallywheninvolvinghigh-dimensionalfeatures.Inthispaper,weproposealocaldensityoptimizationmethodbasedongraphconvolutionalneuralnetworks(GCNNs).TheproposedmethodutilizesthepowerofGCNNstolearnahierarchicalrepresentationofthedata,andoptimizesthelocaldensitybyincorporatingthelearnedfeaturerepresentation.Experimentalresultsonseveralreal-worlddatasetsindicatethatourproposedmethodoutperformsexistingdensity-basedclusteringtechniquesintermsofclusteringaccuracyandrobustness.Density-basedclusteringisafundamentaltechniqueinunsupervisedlearningthathasbeenextensivelystudiedandappliedinvariousdomains,suchasimagesegmentation,communitydetection,andanomalydetection.Thebasicideaofdensity-basedclusteringistogroupdatapointsthatareclosetogetherinthedensityspace,whileseparatingthosethatarefarapart.Theadvantagesofdensity-basedclusteringmethodsincludetheirabilitytohandlearbitrary-shapedclustersandnoisydata,andtheirrobustnesstooutliers.However,traditionaldensity-basedclusteringmethodsmayfailtocapturecomplexspatialpatternsinthedata,especiallywheninvolvinghigh-dimensionalfeatures.Moreover,theperformanceofdensity-basedclusteringmethodsheavilyreliesonthedefinitionofthelocaldensityandthechoiceofthedistancemetric.Recently,deeplearninghasdemonstratedremarkablesuccessinawiderangeofmachinelearningtasks,includingclustering.Inparticular,graphconvolutionalneuralnetworks(GCNNs)havegainedincreasingattentionduetotheirabilitytolearnrepresentationsofgraph-structureddata.GCNNsextendthetraditionalconvolutionoperationtothegraphdomainandallowthemodeltocapturelocalandglobalfeaturesofthegraph.Therefore,GCNNsarewell-suitedfordealingwithhigh-dimensionalandcomplexdata.Motivatedbytheadvantagesofdensity-basedclusteringandthepowerofGCNNs,weproposealocaldensityoptimizationmethodbasedonGCNNs.Specifically,ourmethodutilizesthelearnedfeaturerepresentationbyGCNNstooptimizethelocaldensityestimation,whichinturnimprovestheclusteringquality.Ourproposedmethodconsistsoftwostages:featurelearningbyGCNNsandlocaldensityoptimization.Inthefirststage,weuseaGCNNtolearnahierarchicalrepresentationofthedata.AGCNNtakesasinputagraphwithnodefeaturesandlearnsasetoffiltersthatextractlocalandglobalfeaturesofthegraph.TheoutputoftheGCNNisanewsetofnodefeaturesthatbetterrepresenttherelationshipsbetweennodesinthegraph.Thelearnedfeaturerepresentationisthenusedinthesecondstagetooptimizethelocaldensityestimation.Inthesecondstage,weusethelearnedfeaturerepresentationtoestimatethelocaldensityofeachdatapoint.Specifically,wedefineakernelfunctionthatmeasuresthesimilaritybetweentwodatapointsinthelearnedfeaturespace.Weusethiskernelfunctiontocomputethelocaldensityofeachdatapointbasedonitsneighboringpoints.Thelocaldensityisthenoptimizedbyagradientdescentalgorithm,whichaimstominimizealossfunctionthatpenalizesthedifferencebetweentheestimatedandtruelocaldensities.Weevaluatetheperformanceofourproposedmethodonseveralreal-worlddatasets,includingtheMNISThandwrittendigitsdataset,theCIFAR-10imagedataset,andtheUCIadultincomedataset.Wecompareourmethodagainsttwostate-of-the-artdensity-basedclusteringmethods,namelyDBSCANandHDBSCAN.Experimentalresultsshowthatourproposedmethodachieveshigherclusteringaccuracyandrobustnessthanthetwobaselinemethodsonalldatasets.Inparticular,theproposedmethodoutperformsthebaselinemethodswhenthedatafeaturesarehigh-dimensionalorthedatacontaincomplexpatterns.Theproposedmethodisalsomorerobusttothechoiceofthedistancemetricandthedensityparameter.Inthispaper,wehaveproposedalocaldensityoptimizationmethodbasedongraphconvolutionalneuralnetworksfordensity-basedclustering.TheproposedmethodutilizesthepowerofGCNNstolearnahierarchicalrepresentationofthedataandoptimizesthelocaldensityestimationusingthelearnedfeatures.Experimentalresultsonseveralreal-worlddatasetsdemonstratethatourproposedmethodoutper