资源描述：
《sparsity-exploiting robust multidimensional scaling》由会员上传分享，免费在线阅读，更多相关内容在工程资料-天天文库。
1、4118IEEETRANSACTIONSONSIGNALPROCESSING,VOL.60,NO.8,AUGUST2012Sparsity-ExploitingRobustMultidimensionalScalingPedroA.Forero,StudentMember,IEEE,andGeorgiosB.Giannakis,Fellow,IEEEAbstract—Multidimensionalscaling(MDS)seeksanembeddingrendertheclassicalMDSsolution
2、oflimiteduse.Inparticular,ofobjectsinadimensionalspacesuchthatinter-vectordoublecenteringspreadstheeffectofanoutliertotheentiredistancesapproximatepairwiseobjectdissimilarities.Despitedouble-centereddistancematrix,seee.g.,[6].Analternativetotheirpopularity,M
3、DSalgorithmsaresensitivetooutliers,yieldingMDS,whichcanaccommodatetransformationsonthedissimi-grosslyerroneousembeddingseveniffewoutlierscontaminatetheavailabledissimilarities.ThisworkintroducesrobustMDSap-laritiesaswellasmissingdata,reliesonstressfunctions[
4、2,ch.proachesexploitingthedegreeofsparsityintheoutlierspresent.11].Apopularalgorithmtominimizetheso-calledrawstressLinkswithcompressivesamplingleadtorobustMDSsolversis“scalingbymajorizingacomplicatedfunction,”whichiscapableofcopingwithunstructuredandstructur
5、edoutliers.TheabbreviatedasSMACOF[10].Thestressfunctionisaweightednovelalgorithmsrelyonamajorization-minimizationapproachsumofsquared-errorsbetweendissimilaritiesandembeddingtominimizearegularizedstressfunction,wherebyiterativeMDSsolversinvolvingLassoandspar
6、segroup-Lassooperatorsareinter-vectordistances.Unfortunately,thedependencyofstressobtained.Theresultingschemesidentifyoutliersandobtainthefunctionsontheleast-squares(LS)criterionrendersSMACOFdesiredembeddingatcomputationalcostcomparabletothatofandrelatedstre
7、ss-basedMDSschemessensitivetooutlierstheirnonrobustMDSalternatives.TherobuststructuredMDSal-[17].gorithmconsidersoutliersintroducedbyasparsesetofobjects.InDespitethepopularityofMDSinvariousapplications,thiscase,twotypesofsparsityareexploited:i)sparsityofoutl
8、iersinthedissimilarities;andii)sparsityoftheobjectsintroducingdealingwithoutliershasbeenrelegatedtopre-andpost-pro-outliers.Numericaltestsonsyntheticandrealdatasetsillustratecessingtasks,whichre
