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　　Generalappliedmath,

　　Statistics

　　Performsk-meansclusteringviatheHartiganandWongAS-136algorithm.

　　Availableinversion6.3.0andlater.

　　functionkmeans_aS136(

　　x:numeric,;floatordouble

　　k[1]:integer,

　　opt[1]:logical

　　return_val:floatordouble

　　Thereturnarray(say),clcnter,willcontainthecluster

　　centers.Itwillbedimensioned(k,N),whereN

　　collectivelyrepresentsthe'variable'dimension(s).

　　clcnterwillhavethefollowingattributesassociatedwithit:

　　id-aone-dimensionalintegerarrayof

　　sizeMindicatingtheclustertowhicheachobservationis

　　assigned.

　　npts-aone-dimensionalintegerarrayof

　　sizekcontainingthenumberofpointsineachcluster.

　　ss2-aone-dimensionaldoublearrayof

　　sizekcontainingthewithin-clustersumofsquares.

　　K-meansisacentroid-basedclustermethod.

　　Theobservationsareallocatedtokclustersinsuchawaythatthe

　　within-clustersumofsquaresisminimized.K-meansclusteringrequiresthat

　　thenumberofclusterstobeextractedbespecifiedinadvance.

　　Asnotedby

　　"Thenumberofclustersshouldmatchthedata.Anincorrectchoiceofthenumberofclusterswillinvalidatethewholeprocess.AnempiricalwaytofindthebestnumberofclustersistotryK-meansclusteringwithdifferentnumberofclustersandmeasuretheresultingsumofsquares."

　　Thek-meansalgorithmworksreasonablywellwhenthedatafitstheclustermodel:

　　Thenumberofclustersis'consistent'withthedata.

　　Thedatapointswithinaclusterarecenteredaroundthatcluster

　　Thespread/varianceoftheclustersissimilar,ieeachdatapointbelongstotheclosestcluster

　　Limitations:K-meansmayhaveproblemswhenclustersareofverydifferingsizes;

　　outliersarepresent;oremptyclustersexist.

　　TheoriginalcodeiscreatedforCartesiangrids.Iftheapplicationrequiresusinggridpoints

　　orstationslocatedathighlatitudes,itissuggestedthat

　　css2cbeused

　　tointerpolatetoCartesiancoordinates.Thesebetterreflectthetruedistancesandshouldbeinputtothefunction.

　　Themodifiedcodeusedbythisfunctionwasdownloadedfrom

　　JohnBurkardt'swebsite.

　　TheoriginalHartigan&WongFortrancodewasfrom:

　　JohnHartigan,ManchekWong瑞典AS136钢材,

　　AlgorithmAS136:

　　AK-MeansClusteringAlgorithm,

　　AppliedStatistics,

　　Volume28,Number1,1979,pages100-108.

　　Example1:Thesourceofthisexampleis

　　Defaultoptionsareused.

　　v0(/1.0,1.5,3.0,5.0,3.5,4.5,3.5/);1stvariable

　　v1(/1.0,2.0,4.0,7.0,5.0,5.0,4.5/);2ndvariable

　　mdimsizes(v1);#observations

　　n2;#variables

　　k2;#clusters(userspecified)

　　xnew((/n,m/),typeof(v1),"No_FillValue")

　　x(0,:)v0

　　x(1,:)v1

　　clcntrkmeans_as136(x,k,False);usedefaultoptions

　　print(clcntr);(1.25,1.5)and(3.9,5.1)

　　Aneditedversionoftheoutputfollows:

　　Variable:clcntr

　　Type:float

　　TotalSize:16bytes

　　4values

　　NumberofDimensions:2

　　Dimensionsandsizes:[2]x[2](kcX(:,{-30:30},:);x(time,lat,lon)

　　;reorderviaNCL'snameddimensionreordering

　　xrx(lat|:,lon|:,time|:);make'time'(observations;M)therightmostdimension

　　;thelat,lonarethe'variables'(N)

　　k3;#clusters(userspecified)

　　optTrue

　　opt@iseed1

　　clcntrkmeans_as136(xr,k,opt);inputthereorderedarray

　　:;clcntr(3,nlat,mlon)

　　delete(xr);deleteifnolongerneeded(notnecessary)苏州东锜公司始终坚持质量求生存、用户至上的信念和“追求卓越、打造精品”的经营理念，诚信、实力和产品质量获得业界的认可。以优质的产品、合理的价格，竭诚为广大客户提供优良的服务并和大家取得更好的经济效益，欢迎各界朋友莅临参观、指导和业务洽谈，我们将竭诚为你服务，共创美好的未来。

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