廣義多維云模型及在空間聚類中的應(yīng)用-以廣東湛江市為例-英文-

J.Geogr.Sci.2010,20(5):787-798

DOI:007/s11442-010-0811-8

?2010

ScienceChinaPress

Springer-Verlag

Generalmultidimensionalcloudmodelandits

applicationonspatialclusteringinZhanjiang,Guangdong

DENGYu1,4,*LIUShenghe1,ZHANGWenting2,WANGLi3,4,WANGJianghao1,4

1.InstituteofGeographicSciencesandNaturalResourcesResearch,CAS,Beijing100101,China;

2.SchoolofResourcesandEnvironmentScience,WuhanUniversity,Wuhan430079,China;

3.InstituteofPolicyandManagement,CAS,Beijing100080,China;

4.GraduateUniversityofChineseAcademyofSciences,Beijing100049,China

Abstract:Traditionalspatialclusteringmethodshavethedisadvantageof“hardwaredivision”,

andcannotdescribethephysicalcharacteristicsofspatialentityeffectively.Inviewoftheabove,thispapersetsforthageneralmulti-dimensionalcloudmodel,whichdescribesthecharacteristicsofspatialobjectsmorereasonablyaccordingtotheideaofnon-homogeneousandnon-symmetry.Basedoninfrastructures’classificationanddemarcationinZhanjiang,adetailedinterpretationofclusteringresultsismadefromthespatialdistributionofmembershipdegreeofclustering,thecomparativestudyofFuzzyC-meansandacoupledanalysisofresidentiallandprices.Generalmulti-dimensionalcloudmodelreflectstheintegratedchar-acteristicsofspatialobjectsbetter,revealsthespatialdistributionofpotentialinformation,andrealizesspatialdivisionmoreaccuratelyincomplexcircumstances.However,duetothecomplexityofspatialinteractionsbetweengeographicalentities,thegenerationofcloudmodelisaspecificandchallengingtask.

Keywords:multi-dimensionalcloud;spatialclustering;datamining;membershipdegree;Zhanjiang

1

Introduction

Withtherapiddevelopmentofmodernscienceandtechnology,thecapacityofaccessing

datahasbeengreatlyimproved.However,thecomplexityofmassivedataandthetimelinessofdataprocessinghaspreventedtheeffectiveuseofdata,wegetintoacontradictionin“richdata,meagerknowledge”(Liu,2007).Inordertosearchformorevaluableknowledge,DataMiningandKnowledgeDiscoveryemerges,whichhasbecomethefocusofinterna-tionalresearchandapplications(Macqueen,1967).Spatialclusteringisoneoftheimportantmethodsappliedtospatialdataminingandknowledgediscovery.Therearemanymethodsofspatialclusteringincludingpartitioningmethod(KaufmanandRousseeuw,1990),hier-

Received:2010-02-06Accepted:2010-04-16

Foundation:NationalNaturalScienceFoundationofChina,No.40971102;KnowledgeInnovationProjectoftheChineseAcademyofSciences,No.KZCX2-YW-322;SpecialGrantforPostgraduates’ScientificInnovationandSo-cialPracticein2008

Author:DengYu(1985–),Ph.DCandidate,specializedinurbandevelopmentandlanduse.E-mail:

HYPERLINKmailto:rain00788@163

rain00788@163

*Correspondingauthor:LiuShenghe,Professor,E-mail:

HYPERLINKmailto:liush@igsnrr.ac

liush@igsnrr.

scichina

springeom

archymethod(Berkhin,2000;Zhangetal.,1996;KarypicandHan1999),methodbasedon

network(Wangetal.,1997;Sheikholeslamietal.,1998),andmethodbasedondensity(Es-teretal.,1996;Ankerstetal.,1999).Traditionalmethodsofspatialclusteringcannotover-comethedefectofhardwaredivisioneffectively,aswellasareasonableexpressionofdy-namicchange.Therefore,itisparticularlyurgenttolookfornewmethodsofspatialcluster-ing.

Thecloudmodel,whichwasintroducedtoChinabyLiDeyi,isaqualitativeandquanti-tativeuncertaintyconversionmodelwhichwasbuiltonthebasisoftraditionalfuzzysettheory,probabilityandstatistics.Itorganicallycombinesfuzzinessandrandomnessofun-certainconceptandrealizestheconversionbetweenuncertainlanguagevalueandquantita-tivevalue(Lietal.,1995).Subsequently,LiDeyidiscussedtheuniversalnatureofnormalcloudmodelandbroadenedthescopeofitsapplications(LiandLiu,2004).Inordertoraisetheawarenessofcloudmodelanditsapplicationlevel,LiuChangyuanalyzedthestatisticalsignificanceandparameterscharacteristicsofthenormalcloudmodel(Liu,2005).Onthisbasis,thecloudmodeliswidelyusedinspatialgeneralizedknowledgeandassociationrulesmining,foundedknowledgeexpression,continuousdatadiscretization,spatialdatabaseun-certaintyqueryandinference,remotesensingimageinterpretationandidentification(Lietal.,1997;Lietal.,1998;Dietal.,1999;Liuetal.,2004).Astheapplicationdeepens,cloudtheorysystemisincreasinglymature,suchascloudmodel,virtualcloud,cloudcomputing,cloudtransform,uncertaintyreasoningandsoon(LiandLiu,2004;Li,2000).Moreover,theoreticalresearchhasinstructivesignificanceonpracticalapplications.

Cloudmodelwakenednewinterestintheapplicationofclusteringbecauseitappliesfuzzinessandrandomnessofclouddropstoretaintheuncertaintymembershipofspatialinformation.Itcanovercomemanyproblemssuchasavoidingthedefectofhardwaredivi-sioneffectively,aswellasexpressingtheprocessofdynamicchangeofspatialobjectsrea-sonably(Tang,1986;Chen,1998;Houetal.,2008),andreallyimplement“softdivision”,whichtraditionalspatialclusteringmethodscannotachieve.QinKun(2006)appliedcloudmodelinimageclassificationandclustering,whichwasthefirstattemptofpracticalappli-cation(Qin,2006).Wangclassifiedthespatialobjectsuccessfullyusingcloudmodel(Wang,

2007a).Wangdidclusteringresearchonthespatialobjectafter“potentialtransform”(Wang,

2007b),whichmadesomeprogressaswell.However,allofthemdidnotfullyreflectthemulti-dimensionalcharacteristicsofspatialdata.Thesemethodswhichachievethepurposeofdimensionalityreductiononlyrelyingondataintegrationstillhavemanydefects,whileweightingascertainmentistoosubjective.Moreover,theerrorproducedbynormalatomiccloudfittingcannotbecontrolledeffectivelywhentheleafnodesinpanconcepttreegener-ates,andthismethodcannotexpressthecomplexityofthecharacteristicsofspatialobjectsaccurately.

Inviewoftheabove,thispapersetsforthageneralmulti-dimensionalcloudmodel,thismodeldescribesthecharacteristicsofspatialobjectsmorereasonablyaccordingtotheideaofnon-homogeneousandnon-symmetry,thereforethenewmethodismoreaccordanttopractice.Onthisbasis,thispaperanalyzesthespaceobjectwithclustersbyapplyinggeneralmulti-dimensionalcloudmodel.Themethodavoidedtheissueofindexweightascertain-ment(LiandZheng,2004;Zhangetal.,2004),anditsclusteringresultsembodiedtheinte-gratedcharacteristicsofspaceobjects,reflectedthespatialdistributionofthepotentialin-

DENGYuetal.:GeneralmultidimensionalcloudmodelanditsapplicationonspatialclusteringinZhanjiang

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formation,andrealizedspatialdivisionmoreaccuratelyincomplexcircumstances.There-

fore,generalmultidimensionalcloudmodelcanbewidelyappliedtotheresearchonspatialdataminingandknowledgediscovery.

2 Cloudmodelandgeneralmultidimensionalcloudmodel

Cloudmodel

Cloudmodeltakesexpectationvalue(Ex),entropy(En)andsuper-entropy(He)asatoken

ofqualitativeconcept.Itcombinesfuzzinessandrandomnesstogetherduringqualitativetransform.Exreflectsthecloudcenteroftheclouddrops.Enrevealsthefuzzinessofthe

rangeofconceptnumerical.ThevalueofHereflects

DigitalcharacteristicsofcloudareshownasFigure1.

the

discretedegreeof

cloud

drops.

Figure1 Digitalcharacteristicsofcloud

Ithasbeendemonstratedthatatomiccloudisuniversallyadaptable(LiandLiu,2004).

However,incomplexrealworld,thishomogeneityandsymmetryaredifficulttomeet.Inordertoportraytheobjectivethingsmoreaccurately,generalmultidimensionalcloudmodelemerged.Figure2isacomparisondiagramofastandardone-dimensionalandageneralmultidimensionalcloudmodel.

Figure2 Comparisondiagramsof1Dnormalcloudandgeneralcloud

Generalmultidimensionalcloudmodel

Generalcloudovercomestheshortcomingsofunreasonablespatialdivision,ithasseveral

non-equilibriumandnon-symmetricforms;ontheotherhand,theheterogeneouscharacter-isticsofgeneralmulti-dimensionalcloudmodelhasgreatsuperiorityinsimulatingcomplexphenomena.Forexample,thedelimitationofinfluenceradiusofbusinessservicecenterusuallyspreadalongthetrafficroute,orspreadtoresidentialareasinacertaindirectionun-symmetrical.Inordertodealwithsuchproblemseffectively,thepresentationofgeneralcloudmodelseemsparticularlyimportant.

Whennecessary,usingtherelativepositiontothe“cloudcores”todescribethedirectionrange,andselectingappropriatenormalcloudfunctioncanmeettherequirementsofcom-plexsituations.Generalcloudmodelissubstantiallypiecewise,anditsbasicformulaisshowninFigure3(takingtwo-dimensionalcloudmodelasanexample):

?

1?(x1?Ex1)2(x2?Ex2)2?

?

+

?

?

??

?

(En11)2 (En21)2

2??

?e

x1<Ex1andx2>Ex2

μi=?

(1)

1?(x1?Ex1)2(x2?Ex2)2?

??

+

?

?

??others

2??(En12)2

(En22)2

?e

?

whereμiisdegreeofmembership,xiisabscissavalueofrandomdot,andx2isordinate

valueofrandomdot.(Ex1,Ex2)isexpectationpairoftwo-dimensionalcloudmodel.(En11,

En21)isentropypairofonedirection,and(En12,En22)isentropypairoftheotherdirection.

Figure3 Comparisondiagramof2Dnormalcloudandgeneralcloud

3

Studyofclusteringbasedongeneralmultidimensionalcloudmodel

Thebasicideainspatialclusteringmethodbasedongeneralmultidimensionalcloudmodel

isasfollows:Firstofall,determinereasonablemultidimensionalcloudmodelparametersaccordingtotheradiationrangeandattributedimensionaswellasrelatedcharacteristicsofaspatialobject,andthengenerateatomicclouds,thatis,leafnodeinpan-concept-tree.Secondly,raisethelowerconceptualfinenesstoahigherlevelaccordingtosyntheticopera-torofamultidimensionalcloudmodel.Stopthisstepwhenthenumberofconceptsequalstothenumberofclassificationgrades.Finally,getthemembershipdegreeofeachspatialob-jectsfromahigher-levelconcept.Theconceptwiththehighestmembershipdegreetoanobjectistherelatedconceptofthatobject.

DENGYuetal.:GeneralmultidimensionalcloudmodelanditsapplicationonspatialclusteringinZhanjiang

791

Generationofatomiccloud

Spatialobjectsarerepresentedbyconcept,whileatomiccloudisthesmallestconceptparti-

cle.Thesingleobjectcanbeconsideredasatomiccloud,andthushowtodeterminetherelevantparametersisespeciallyimportantaccordingtothecomplexityandcomprehen-sivenessofspatialobjects.

Expectationvalue(Ex)reflectsthehorizontallocationoftheatomiccloud,areflectionoftheconceptof“core”.Themembershipdegreeofthelocationwhereexpectationstandsis1,anditdecreasesgraduallywiththedistance.Entropy(En)hasanexplicitgeographicmean-ing,itisametricofspatialradiationrangeaccordingtotheattributevalueofspatialobjects.

?1

Rmax?Rmin

Ai≠Amin

Ai=Amin

?(Ai?Amin)?

?

Eni=?3

??b

Amax?Amin

(2)

whereAistheattributevalueofspatialobject,Amin,Amaxaretheminimumandmaximumof

attributevalues;Rmin,Rmaxaretheminimumandmaximumofradiationdistance;bisaun-

determinedconstant;constant isobtainedbytheformulaen＝1R.

1

3

3

Basedonthenon-homogeneousandnon-symmetryattributesofspatialobjects,entropyalsohaspiecewisefeatures,thatis,anisotropy.Thusweshouldintroduceacorrectionα,

whichcandepictthecomplexgeographicphenomenonmoreaccurately.Theexpressionisasfollows:

?Eni

En＝?

(3)

?(1+α)?Eni

Thenormalcloudisanormaldistributedcloudwhosedeviationdegreefromthenormal

distributionismeasuredbysuperentropyHe.IfHe=0,cloudmodeldegenerateintoordi-narynormaldistribution.Inordertoshowthedynamicchangesofradiationrange,andcon-trolthefuzzydegreeof“BothThisandThat”characteristic,thesettingofHeisveryimpor-tant.Takeallfactorsintoconsideration,thesettingofHeis0.1(Qinetal.,2006).

Afterparametersetting,theatomiccloud--thegenerationofleafnodesofpanconcepttreeterminated.Thismethodtakesconsiderationofboththeaccurateexpressionofcentralcon-ceptandthecharacteristicsofedgedynamicchanges.

Climbingofuniversalconceptualnumber--Cloudcomputing

Atomiccloudisraisedfromextendedmultidimensionalcloudmodeltoahigherlevelcon-

ceptualfinenessgraduallybycomprehensiveoperations.Theconceptualtreebuiltbycloudmodelhaspropertyofuncertainty,andtheboundarybetweenconceptsisvague.Conceptfinenessinlowerlevelcanclimbtoahighleveltogeneratetheneededleafnodesinpanconcepttree.Thenumberoftypesdecidesthenumberofrootnodes.Piecewiseandmulti-formationcharacteristicofatomiccloudhaveraisedahigherdemandforcloudopera-tion.Superpositionofdifferentatomiccloudscanbetreatedflexibly,andatomiccloudsinthesamemembershipintervalaredescribedasfollows:

C(Ex1,Ex2,En1,En2,He1,He2),

A2(Ex21,Ex22,En21,En22,He21,He22),...,

Am(Exm1,Exm2,Enm1,Enm2,Hem1,Hem2)

Applying“Soft-Or”method,cloudsyntheticalgorithmcanbeamelioratedsentedasfollows(Jiangetal.,2000):

and

repre-

WhenthedistancebetweenA1andA2istheminimum,thatisDmin=A1,A2

Ex1=(Ex11+Ex21)/2+(En21?En11)/4;Ex2=(Ex12+Ex22)/2+(En22?En12)/4;En1=(Ex21?Ex11)/4+(En11+En21)/2;En2=(Ex22?Ex12)/4+(En12+En22)/2;

He1=max(He11,He21);

He2=max(He12,He22);

:

(4)

(5)(6)(7)(8)

(9)

Conceptpromotingistogetthedifferencebetweenconceptfinenessinthesamelevel,the

mostcommonofwhichisEuclideandistance,andtocombinetheconceptwithminimalex-pectationdifference.Usingmulti-dimensionalcloudsyntheticoperatormentionedabove,thelevelofnodesinpan-concept-treecanberaisedstagebystage.Itisworthemphasizingthatweshouldemploytheunionofdifferentscope,whenfacingconceptsinthesamelevelwithdifferentdirection.

3.3

Determiningclass--X-conditiongenerators

Whenthenumberoffatherconceptualcloudsinthehighestlevelreachesthenumberof

classificationcategories,pan-concept-treebasedoncloudmodelhasbeenbuilt,andthecloudsynthesisfinishes.Then,themembershipdegreeofeachorderedsettoitsrelevantconceptinahigherlevelisgainedonthebasisofanX-conditionnormalcloudmodel.Amongallclasses,theonewiththehighestmembershipdegreeisdefinedasthemember-shipanalysisresultofitsrelevantobject.Thespecificalgorithmcanbedescribedinthefol-lowingsteps:

Step1:Estimatethepositionalmembershipbetween(x1,x2)and(Ex1,Ex2),findoutthecorrespondingcloudfunction

Step2:Computeformula(P1i,P2i)=R1(Ex1,Ex2,En1,En2),andget(P1i,P2i)asarandom

numberundernormaldistributionwithEnasitsexpectationvalueandHeasitsstandardiza-tiondifference.

1?(x1?Ex1)2(x2?Ex2)2?

?

+

?

?

??

(P1i)2 (P2i)2

2??

Step3:Computeformulaμi=e

(10)

Step4:ComputeMaxμi,andtheobjectthatisbeingstudiedfallsintotherelevantClassi.

4

ApplicationonacasestudyinZhanjiang

AccordingtotheGeneralMultidimensionalCloudModelanditsbasicideasintheSpatial

ClusteringResearch,thispaperusestheclusteringofhighschoolsinZhanjiangcityasastudycase.ZhanjiangliesinthewestofGuangdongProvince,whichisoneofthefirstbatchofopencoastalcities.Owingtoitspredominantgeologicallocation,Zhanjianghashadarapiddevelopmentofsocietyandeconomy.Theauthorhasparticipatedinthemultiple-indexlandpriceevaluationofZhanjiangandmasteredthebasicdataandserviceconditionsof

DENGYuetal.:GeneralmultidimensionalcloudmodelanditsapplicationonspatialclusteringinZhanjiang

793

variousinfrastructuresincludinghighschools.Therefore,therelatedmeasurementresults

andspatialmodificationinformationinthebaselandvalueevaluationreportofZhanjiangcanbeusedtoascertaintheconceptionalparameterofthegeneralcloudmodel.Furthermore,comparativeanalysisoftheclusteringresultsandresidentialstandardlandpricedistributionmapcanbeusedtofurtherembodythevalueandadvantageofgeneralcloudmodel.Dividetheresearchareainto120×120gridsandeachofthegridsis250×250m2.Figure4showsthedistributionmapofthegeneralcloudmodeldefinedbythebasicdataofthehighschools

intheresearcharea.

Wecantentativelydividespatialpatternofhighschools’servicezoneintofourareas.Theneveryschoolmaybelongtoacertainzoneaccordingtotheclassification.Figure5showstheclusteringresultsoperatedbythecloudsyntheticoperator,andthenumberoftheclassescanbedifferentwithdifferentsituations.WecanseefromFigure5thattheresultoftheclusteringcloudisobviouslyanisotropic,andthedivisionofthespatialclassescanbereflectedbythespatialcoveragerangeoftheclasses.Itisnoteworthythatnoneofthespatialentitiestotallybelongtoacertainclass,thatistosay,thedivisionoftheclassesis“Both

ThisandThat”.However,eachentityhasthemaximummembershipdegreeaccording

itself.

to

Figure4

Distributionofcloudmodel

Figure5

Resultsofclassification

JustaswhatFigure6shows,therearefourclusterdistrictsofmembershipdegreeinspace,

themaximummembershipdegreeisoclinesattenuatefromthecentertotheperipheralarea

ofeachclass.Duetothecorrectionofthecalculationofhighschools’serviceradius,the

membershipdegreechangessharplyinthedirectionofnorthwest,whileattenuatingsmoothlyinotherdirections.Thisresultsinthenoncontinuousdistributionofthemember-shipdegreeinthedirectionofnorthandwest.Wecanclassifythesehighschoolsaccordingtothemaximummembershipdegreeprinciple,andfinishthespatialclusteringwork.

Figure6

Regionalisolinedistributionofthelargestmembership

Furtherinvestigatethemembershipbetweenmembershipdegreeandspatialpositionofeachtypeofobjects,asshowninFigure7,thereisagoodcorrelationbetweenthem：The

correlationcoefficientswithdifferentzonesare:1(west,F=167,sig=0.00),7(south,F=39,sig=0.00),0.98(north,F=26,sig=0.01),and0.99(east,F=2800,sig=0.00).Westzoneincludes17objects,andthemaximumcoveringdistanceis9807m.ComparedwiththemarkofthespatialobjectinFigure6,objectsa1,a2anda3inwestzonearefarawayfromthecenter,whichisresultedfromtheextensionoftheserviceradiusinthedirectionofsoutheast.Southzoneincludes22objects,themostdistantobjectb1whichclassisnotinthedirectionofnorthwest,inthecontrary,thecloserobjectb2isinthisarea,andthusmembershipdegreeofb2issmaller.Northzoneandeastzonehavefewerobjects,thusthefittingresultsaremoresatisfactory.

Figure8revealsthefundamentalsimilarinformationfromtheaspectoffittingerror.Insouthzone,themaximalerrorisupto62%becauseoftheexistenceofb2,whichisthere-flectionoftheanisotropyofspatialobjects’radiation.Overall,membershipdegreeofobjectsdecreaseswiththeincreaseofthedistancetotheclasscenter.Thespatialinfluenceamongobjectscausestheunbalanceddecreaseofthemembershipdegree,whichreflectstheactualsituationmorerationally.

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Figure7 Changingtrendsofmembershipofdifferenttypes

Figure8 Residualofmembershipofdifferenttypes

Inordertorepresenttheadvantagesofclusteringmethodbasedongeneralmultidimen-

sionalcloud,hereweanalyzetheclusteringresultsandFCMcomparatively.FCMisaclus-teringalgorithmwhichdeterminesthesubjectiondegreetoacertainclassaccordingtomembershipdegree.Membershipfunctiondescribesthesharinglevelofmodelsbetweenfuzzyclasses.FCMwasputforwardinordertoabsorbtheadvantagesoftraditionalC-meansclustering,suchasitsconvergentspeed,insensitivitytoinitializationandabilitytoshowthesimilarinformationamongsamples.Thefuzzypartitionmatrix(U)isnotonlypartlyexplicitbutalsomaintainsthefuzzinessofsamples’spatialdistributiontherebyin-creasestheaccuracyofclassification(Bezdek,1981).TheclusteringresultbasedonFCMisshowninFigure9.Comparedwiththemethodinthispaper,a1,a2,a3andb1areallclassi-fiedasnorthzone.AlthoughFCMcanensurethesmallestdifferencesamongclasses,itstillcouldnotconsidereffectcharacteristicsofallthespatialobjectsinacomplexgeographicworld.Therefore,FCMishardtomeettherequirementsofscientificclassificationundertheconstraintsofcomprehensivefactors.

Figure9 ClusteringresultsoffuzzyC-means

Figure10showsthedistri-

butionofresidentialaffectingfactorsvalueofZhanjiangcity.Theassessmentcoverageof

the

notthe

spatialdistributiondoes

completelycoincidewith

city

boundaries.Conse-

quently,

havean

clustering

classes

obviousaggregation

withthefourextremeareasof

landvaluedistributions.65%ofspatialobjectsarelocatedintheregionsofhighlandprices,only8%isdistributedinre-gionsoflowlandprices.Thehigherthelandpricesoftheregion,themoreintensivethedistributionofthespatialob-jects.Theregionswithasmallmembershipdegreeoftenhave

Figure10

Relationshipofhousepriceandclusteringresultsin2008

DENGYuetal.:GeneralmultidimensionalcloudmodelanditsapplicationonspatialclusteringinZhanjiang

797

alowlandpriceseither,especiallyinthepricelowlandbetweenclasses,justasthespatial

objecta1,a2,a3andb1inFigure6,whichreflectthefiercecompetitionforspaceobjectsbetweenclasscenters.Thepricelowlandsrevealthecharacteristicsofweaklyabsolutecon-trollingforceofalltheclassesoverobjects,andtheclusteringresultismostlyinfluencedbytheseregions.

5 Conclusionsanddiscussion

(1)Cloudmodelhasdualcharacteristicsoffuzzynessandrandomness,anditshowsgreatsuperiorityintheexpressionofconceptualfineness.One-dimensionalcloudmodelcannotaccuratelyreflectmulti-attributecharacteristicsofthereal-world,andessentialinformationofspatialobjectswaslostduringtheprocedureofsimpledatafusion.Standardtwo-dimensionalcloudmodelovercomessomeshortcomingsofone-dimensionalcloud,butitstillcannotmeettheneedsofsimulatingthenon-homogeneousandnon-symmetrychar-acteristicsofcomplexgeographicalphenomena.Thispaperputsforwardageneralmulti-dimensionalcloudmodel,andtheproblemsabovewereresolvedeffectivelyandfac-tually.

(2)Basedonthedemonstrativestudy,adetailedinterpretationofclusteringresultsismadefromtheintegratedperspectiveofthespatialdistributionofmembershipdegreeofspatialclustering,andthecomparativestudyofFCMandacoupledanalysisofresidentiallandprices.Generalmulti-dimensionalcloudmodelcouldreflecttheintegratedcharacteris-ticsofspatialobjectsbetter,whilethespatialclusteringresultscanrevealthepotentialin-formationofspatialdistribution,andrealizespatialdivisionmoreaccuratelyincomplexcircumstances.

(3)Thepracticalvalueofgeneralmulti-dimensionalcloudmodelinspatialclusteringisnotable.However,parametersetting,theaccuracyanduncertaintyofthemodelareprob-lemstobeovercome.Thecharacteristicofthemodelisthatalltheparametershaveappro-priategeographicalmeanings.Thismakesthedescriptionofgeographicalphenomenamorereasonable.Duetothecomplexityofspatialinteractionsamonggeographicalentities,thegenerationofacloudmodelisstillaspecificandchallengingtask.

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