四元数域中基于根幂均值的神经元聚合(IJISA-V10-N7-2)

I.J.IntelligentSystemsandApplications,2018,7,11-26PublishedOnlineJuly2018inMECS()DOI:10.5815/ijisa.2018.07.02Copyright©2018MECSI.J.IntelligentSystemsandApplications,2018,7,11-26OntheRoot-PowerMeanAggregationBasedNeuroninQuaternionicDomainSushilKumarHarcourtButlerTechnicalUniversity/DepartmentofComputerScience&Engineering,Kanpur,208002,IndiaE-mail:[e-mail]chnicalUniversity/DepartmentofComputerScience&Engineering,Kanpur,208002,IndiaE-mail:[e-mail]:27June2017;Accepted:15September2017;Published:08July2018Abstract—Thispaperillustratesthenewstructureofartificialneuronbasedonroot-powermeans(RPM)forquaternionic-valuedsignalsandalsopresentedanefficientlearningprocessofneuralnetworkswithquaternionic-valuedroot-powermeansneurons(ℍ-RPMN).Themainaimofthisneuronistopresentthepotentialcapabilityofanonlinearaggregationoperationonthequaternionic-valuedsignalsinneuroncell.AwidespectrumofaggregationabilityofRPMinbetweenminimaandmaximahasabeautifulpropertyofchangingitsdegreeofcompensationinthenaturalwaywhichemulatesthevariousexistingneuronmodelsasitsspecialcases.Further,thequaternionicresilientpropagationalgorithm(ℍ-RPROP)witherror-dependentweightbacktrackingstepsignificantlyacceleratesthetrainingspeedandexhibitsbetterapproximationaccuracy.Thewidespectrumsofbenchmarkproblemsareconsideredtoevaluatetheperformanceofproposedquaternionicroot-powermeanneuronwithℍ-RPROPlearningalgorithm.IndexTerms—Quasi-arithmeticmeans,Root-powermeansinquaternionicdomain(ℍ),Quaternionic-valuedmultilayerperceptron,Quaternionic-valuedbackpropagation,Quaternionicresilientpropagation,3Dfacerecognition.I.INTRODUCTIONTheinformationprocessingincellbodyisanimportantfunctionofaneuron,whichemulatesthecomputationalpowerofaneuron[1-4].Inlastfewyears,variousneuro-computingresearchershaveconfirmedthecomputationalcapabilityofaneuronwithnonlinearaggregationoperationsonsynapticinputs[1,2,5-8]andpresentedvarioushigherorderneuronsbasedonthenonlinearcorrelationamongdifferentimpingingsignals.Theseattemptsresultedinthevariousclassofneuralstructureaspi-sigma[9,10]secondorderneuron[11],compensatoryneuron[12],andotherhigherorderneurons[13-16,54].However,thehigherorderneuronshaveprovedtobeefficient,buttheyfacetheproblemofexplosionoftermsasthenumberofinputsincreaseshencedemandingsparsenessinrepresentation.Theproblemworsenswhenneuronsareimplementedinhighdimension.Itishighlydemandingtoinvestigateaneuronmodellikeaconventionalneuroninhigherdimensionbutisfreefromtheproblemofhigherorderneurons.Thispaperpresentsaneuronmodelwithacompletespecificationforquaternionic-valuedthatemploysthenonlinearcorrelationamonginputcomponents,butitisfreefromaboveproblemevenwhenthereisanincreaseinthedegreeofapproximation.Thecorrespondingneuralnetworkwithlearningalgorithminthequaternionicdomain(ℍ)providesabetterlearningandgeneralizationopportunityforproblemsinthreeorfourdimension.Theweightedroot-powermeancoversthevariousclassesofaggregationintheintervalbetweenminimatomaximaoperations[18,19].Itprovidestheflexibilitytoapproximateappropriateoperationinthewiderangeofaggregationthroughvariationofpowercoefficient.Theweightedroot-powermeanasanaggregationfunctionoftheproposedneuronmodelwithquaternionic-valuedsignalsexhibitsthenaturalandgeneralmodelthatpresentsthevariousexistingneuronmodelsasitsspecialcases,dependingonthedomainofinputsignalsandvalueofpowercoefficient.However,thequaternionic-valuednetworkswithconventionalneuronsareusedinPolSARLandclassification[55]andspokenlanguageunderstanding[53].Thebackpropagation(BP)learningalgorithmhasgainedpopularlyduetoitssimplicity,buttheslowerconvergenceandgettingstuckintolocalminimaarethemajorweaknessesfordegradingitsperformance.Therefore,someofotherproposalshavebeengiven,likemodifiederrorfunction[20,21],additionofvariablelearningrate[22,23],additionofmomentum[24,25],delta-bar-deltaalgorithm[26,27],LevenbergMarquardt(LM)algorithm[51],GA-MLPhybridalgorithm[56],andquickprop[28],toovercometheaboveissues,buttheyhavenotacceleratedtheconvergencetoasignificantamount.Thefastconvergencewithefficaciousperformancealongwithlesscomplexityofneuralnetworkistheimportantmatterforthevarietyofapplications.Theresilientpropagationalgorithm12OntheRoot-PowerMeanAggregationBasedNeuroninQuaternionicDomainCopyright©2018MECSI.J.IntelligentSystemsandApplications,2018,7,11-26(RPROP)hasbeenshowntheextremelearningcapabilityinreal[29-31],complexdomain[17,32],andquaternionicdomain[52].TheRPROPwasdevelopedforfasterconvergencewhichproveditslearningandgeneralizationcapabilitiesinmanyapplicationssuchasweightedgeometricdilutionofprecisionandmobilelocation[33],speechqualityprediction[34].Thisalgorithmeliminatestheharmfulinfluencesofthesizeofthepartialderivativeoferrorfunctiononweightupdatebecauseadaptationdependsonthesignsofconsecutivepartialderivatives.TheRPROPinthequaternionicdomain(ℍ-RPROP)hasbeenthoroughlyinvestigatedwithproposedquaternionic-valuedrootpowermeanneuron(ℍ-RPMN)andcomparedwithconventionalneuronandBPlearn