聚类的R语言实现外文.docx

聚类的R语言实现外文.docx

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聚类的R语言实现外文

ClusterAnalysis:

TutorialwithR

JariOksanen

January26,2014

Contents

1Introduction1

2HierarchicClustering1

2.1DescriptionofClasses........................42.2NumbersofClasses..........................42.3ClusteringandOrdination......................52.4ReorderingaDendrogram......................62.5MinimumSpanningTree.......................72.6CopheneticDistance.........................8

3InterpretationofClasses8

3.1EnvironmentalInterpretation....................93.2CommunitySummaries.......................10

4OptimizedClusteringataGivenLevel11

4.1OptimumNumberofClasses....................11

5FuzzyClustering12

1Introduction

Inthistutorialweinspectclassification.Classificationandordinationareal-ternativestrategiesofsimplifyingdata.Ordinationtriestosimplifydataintoamapshowingsimilaritiesamongpoints.Classificationsimplifiesdatabyputtingsimilarpointsintosameclass.Thetaskofdescribingahighnumberofpointsissimplifiedtoaneasiertaskofdescribingalownumberofclasses.

2HierarchicClustering

TheclassificationmethodsareavailableinstandardRpackages.Theveganpackagedoesnothavemanysupportfunctionsforclassification,butwestill

loadvegantohaveaccesstoitsdatasetsandsomeofitssupportfunctions.1

1Ifyoudonothaveapackage,butgetanerrormessage,youmustinstallpackageusinginstall.packages（"vegan"）ortheinstallationmenu.

1

AA

A

AA

B

B

B

BBB

B

A

A

A

A

+

A

B

+

B

B

B

B

B

BB

Figure1:

DistancebetweentwoclustersAandBdefinedbysingle,completeandaveragelinkage.Markeachofthelinkagetypesintheconnectingline.Thefusionlevelintheclusterdendrogramwouldbethelengthofthecorrespondingconnectinglineofthelinkagetype.

R>library（vegan）

R>data（dune）

Hierarchicclustering（functionhclust）isinstandardRandavailablewith-outloadinganyspecificlibraries.Hierarchicclusteringneedsdissimilaritiesasitsinput.StandardRhasfunctiondisttocalculatemanydissimilarityfunctions,butforcommunitydatawemaypreferveganfunctionvegdistwithecologically

usefuldissimilarityindices.ThedefaultindexinvegdistisBray-Curtis:

R>d<-vegdist（dune）

Ecologicallyusefulindicesinveganhaveanupperlimitof1forabsolutelydiferentsites（nosharedspecies）,andtheyarebasedondiferencesofabun-dances.Incontrast,thestandardEuclideandistancehasnoupperlimit,butvarieswiththesumoftotalabundancesofcomparedsiteswhentherearenosharedspecies,andusessquaresofdiferencesofabundances.Therearemanyotherecologicallyusefulindicesinvegdist,butBray-Curtisisusuallynotabadchoice.

Thereareseveralalternativeclusteringmethodsinthestandardfunctionhclust.Weshallinspectthreebasicmethods:

singlelinkage,completelinkageandaveragelinkage.Allthesestartinthesameway:

theyfusetwomostsim-ilarpointstoacluster.Theydiferinthewaytheycombineclusterstoeachother,ornewpointstoexistingclusters（Fig.1）.Insinglelinkage（a.k.a.near-estneighbour,orneighbourjoiningtreeingenetics）thedistancebetweentwoclustersistheshortestpossibledistanceamongmembersoftheclusters,orthebestofthefriends.Incompletelinkage（a.k.a.furthestneighbour）thedistancebetweentwoclustersisthelongestpossibledistancebetweenthegroups,ortheworstamongthefriends.Inaveragelinkage,thedistancebetweentheclusters

2

isthedistancebetweenclustercentroids.Thereareseveralalternativewaysof

definingtheaverageanddefiningthecloseness,andhenceahugenumberofaveragelinkagemethods.Weonlyuseoneofthesemethodscommonlyknown

asupgma.Thelectureslidesdiscussthemethodsinmoredetail.

Inthefollowingwewillcomparethreediferentclusteringstrategies.Ifyou

wanttoplotthreegraphssidebyside,youcandividethescreenintothree

panelsby

R>par（mfrow=c（1,3））

Thisdefinesthreepanelssidebyside.Youprobablywanttostretchtheplotting

windowifyouareusingthisoption.Alternatively,youcanhavethreepanels

aboveeachotherwith

R>par（mfrow=c（3,1））

Youcangetbacktothesinglepanelmodewith

R>par（mfrow=c（1,1））

Youmayalsowishtousenarroweremptymarginsforthepanels:

R>par（mar=c（3,4,1,1）+.1）

Themarcommanddefinesplotmarginsinorderbottom,left,up,rightusing

rowheight（textheight）asaunit.

Thesinglelinkageclusteringcanbefoundwith:

R>csin<-hclust（d,method="single"）

R>csin

Thedendrogramcanbeplottedwith:

R>plot（csin）

Thedefaultistoplotaninvertedtreewiththerootatthetop,andbranches

hangingdown.Youcanforcethebranchesdowntothebaselinegivingthehang

argument:

R>plot（csin,hang=-1）

Ifyouplottedthecsintreetwiceyouconsumedtwopanelsoutofthreeyou

have,andtherewillnotbespaceforthenexttwotreesinthesameplot.Inthatcaseyoucanstartanewplotbyissuingagainthemfrowcommandandthendrawingcsinagain.

Thecompletelinkageandaveragelinkagemethodsarefoundinthesame

way:

R>

R>R>R>

ccom<-hclust（d,method="complete"）

plot（ccom,hang=-1）

caver<-hclust（d,method="aver"）

plot（caver,hang=-1）

Theverticalaxesoftheclusterdendrogramshowthefusionlevel.Thetwo

mostsimilarobservationsarecombinedfirst,andtheyareatthesamelevelinalldendrograms.Attheupperfusionlevels,thescalesdiverge:

theyaretheshortestdissimilaritiesamongclustermembersinsinglelinkage,thelongestpossibledissimilaritiesincompletelinkage,andthedistancesamongclustercentroidsinaveragelinkage（Fig.1）.

3

Figure2:

VegemiteisanAustraliannationaldelicacymadeofyeastextract.The

vegemitefunctionwasnamedbecauseitsoutputisjustasdenseasVegemite.

2.1DescriptionofClasses

Oneproblemwithhierarchicclusteringisthatitgivesaclassificationofob-

servations（plots,samplingunits）,butitdoesnottellhowtheseclassesdiferfromeachother.Forcommunitydata,thereisnoinformationhowthespeciescompositiondifersbetweenclasses（wereturntothissubjectinChapter3.2）.

Theveganpackagehasfunctionvegemite（Fig.2）thatcanproducecom-pactcommunitytablesorderedbyadendrogram,ordinationorenvironmentalvariables.Withthehelpofthesetablesitispossibletoseewhichspeciesdifer

inclassification:

R>vegemite（dune,caver）

Thevegemitecommandwillalwaysuseone-charactercolumns.Iftheob-servedvaluesdonotfitonecharacter,thevegemiterefusestowork.Withar-gumentscaleyoucanrecodethevaluestoone-characterwidth.Thevegemitehasagraphicalsisterfunctiontabascothatisdescribedinsection2.4.

2.2NumbersofClasses

Thehierarchicclusteringmethodsproduceallpossiblelevelsofclassifications.

Theextremesareallobservationsinasingleclass,andeachobservationinitsprivateclass.Theusernormallywantstohaveaclusteringintoacertainnumberofclasses.Thefixedclassificationcanbevisuallydemonstratedwith

rect.hclustfunction:

R>plot（csin,hang=-1）

R>rect.hclust（csin,3）R>plot（ccom,hang=-1）

R>rect.hclust（ccom,3）

4

R>plot（caver,hang=-1）

R>rect.hclust（caver,3）

Singlelinkagehasatendencytochainobservations:

mostcommoncaseis

tofuseasingleobservationtoanexistingclass:

thesinglelinkisthenearestneighbour,andacloseneighbourismoreprobablyinalargegroupthaninasmallgrouporalonelypoint.Completelinkagehasatendencytoproducecompactbunches:

completelinkminimizesthespreadwithinthecluster.Theaveragelinkageisbetweenthesetwoextremes.

Wecanextractclassificationinacertainlevelusingfunctioncutree:

R>cl<-cutree（ccom,3）

R>cl

Thisgivesanumericclassificationvectorofclusteridentities.Theclustersare

numberedintheordertheobservationsappearinthedata:

thefirstitemwillalwaysbelongtocluster1,andthenumberingdoesnotmatchthedendrogram.

Wecantabulatethenumbersofobservationsineachcluster:

R>table（cl）

Wecancomparetwoclusteringschemesbycross-tabulationwhichgivesasa

confusionmatrix:

R>table（cl,cutree（csin,3））

R>table（cl,cutree（caver,3））

Theconfusionmatrixtabulatestheclassificationsagainsteachother.Therows

givethefirstclassification,andthecolumnsthesecondclassification.Iftheclassificationsmatchandthereisno"confusion",eachrowandeachcolumnhasonlyonenon-zeroentry,butiftheclassesaredividedbetweenseveralclassesinthesecondclassification,therowhasseveralnon-zeroentries.

2.3ClusteringandOrdination

Wecanuseordinationtodisplaytheobserveddissimilaritiesamongpoints.

Anaturalchoiceistousemetricscalinga.k.a.principalcoordinatesanalysis（PCoA）thatmapsobserveddissimilaritieslinearlyontolow-dimensionalgraphusingthesamedissimilaritieswehadinourclustering.

ThemetricscalingcanbeperformedwithstandardRfunctioncmdscale:

R>ord<-cmdscale（d）

Wecandisplaytheresultsusingveganfunctionordiplotthatcanplot

resultsofanyveganordinationfunctionandmanynon-veganordinationfunc-tions,suchascmdscale,prcompandprincomp（thelatterforprincipalcompo-

nentsanalysis）:

R>ordiplot（ord）

Wegotawarningbecauseordiplottriestoplotboth