AssessingConceptualSimilarity to Support ConceptMapping�

David B. Leake and Ana MaguitmanComputerScienceDepartment

Lindley Hall, IndianaUniversity150S.Woodlawn Avenue

Bloomington,IN 47405,U.S.A.�leake,anmaguit� @cs.indiana.edu

Alberto CanasInstitutefor HumanandMachineCognition

Universityof WestFlorida11000UniversityParkway

Pensacola,FL 32514,U.S.A.acanas@ai.uwf.edu

AbstractConceptmapscaptureknowledgeabout the conceptsandconceptrelationshipsin a domain,usinga two-dimensionalvisually-basedrepresentation.Computertools for conceptmappingempower experts to directly construct,navigate,share,andcriticize rich knowledgemodels.This paperde-scribesongoingresearchon augmentingconceptmappingtools with systemsto supportthe userby proactively sug-gestingrelevantconceptsandassociatedresources(e.g.,im-ages,video, and text pages)during conceptmapcreation.Providing suchsupportrequiresefficientandeffectivealgo-rithms for judging conceptsimilarity and the relevanceofprior conceptsto new conceptmaps.We discusskey issuesfor suchalgorithmsandpresentfour new approachesdevel-opedfor assessingconceptualsimilarity for conceptsin con-ceptmaps. Two useprecomputedsummariesof structuralandcorrelationalinformationto determinetherelevanceofstoredconceptsto selectedconceptsin a new conceptmap,andtwo useinformationaboutthecontext in which these-lectedconceptappears.We closeby discussingtheir trade-offs andtheir relationshipsto researchin areassuchasin-formationretrieval andanalogicalreasoning.

Intr oductionCapturingexpert knowledgeis an essentialcomponentofthe knowledgemanagementprocess.Oncemodelsof ex-perts’ domainknowledgeareavailable,they canprovide avaluableresourcefor knowledgecomparison,refinement,and reuse. However, a difficult questionis how to obtainthe requiredknowledgemodels. Hand-craftingis expen-sive; machinelearningtechniquesmaynot beeffective. Weare investigatingan alternative approach:developingtoolsto enableexperts themselves to constructmodelsof theirknowledge.Our approachbuilds on conceptmapping(No-vak & Gowin 1984), in which subjectsconstructa two-dimensional,visually-basedrepresentationof conceptsandtheir relationships.Conceptmappingwasfirst proposedineducationalsettings,to helpassessstudents’understandingand to aid their knowledge-building, comparison,and re-�

This researchis supportedin partby NASA underawardNoNCC2-1216.Copyright c

�2002, AmericanAssociationfor Artificial Intelli-

gence(www.aaai.org). All rightsreserved.

finement. In the conceptmappingview, expertswho buildconceptmapsarenotsimplyexternalizingpre-existinginter-nal knowledge,but arealsodoingknowledgeconstruction.Thus tools to provide relevant knowledgeto considerandcompareduring conceptmappingcould facilitatenot onlyknowledgecapture,but knowledgegeneration.

The Institute for Human and Machine Cognition hasdeveloped a set of publicly-available tools for conceptmapping,availableat http://cmap.coginst.uwf.edu/.Thesewidely-usedsystemssupportgeneratingandmodifyingcon-ceptmapsin electronicform, aswell asannotatingconceptmapswith additionalmaterialsuchasimages,diagrams,andvideoclips. They provide thecapabilityto storeandaccessconceptmapson multiple servers, to supportknowledgesharingacrossgeographically-distantsites.We have devel-opedaninitial implementationof asuggestersystemthatau-tomaticallyextractsinformationfrom a conceptmapunderconstructionandusesthatinformationto retrieveprior con-ceptmaps,associatedresources,and relatedconceptsthatthe usercan compareand possiblyinclude in the conceptmapbeingconstructed.Figure1 shows a screenshotof theconceptmappingtoolsbeingusedfor knowledgemodelingaboutMars, with the suggesterproposingnew conceptstolink to the “spaceexploration” node(to fill in the not-yet-specifiedconceptnodedesignatedby “????”).

The effectivenessof a suggestersystemdependson ef-ficient algorithmsfor judging similarity and relevanceofstoredconceptsto the conceptscurrentlyunderconsidera-tion. This paperdescribesfour approachesthat we haveimplementedand are now testing, two of which focus ondeterminingthe relevanceof a prior conceptto a new con-cept,basedon summariesof structuralandcorrelationalin-formationpreviouslygeneratedfor theconceptmaplibrary,andtwo of which directlycomparethecontext in which theconceptappears—itsconceptmap—toconceptmapsin theconceptmaplibrary. We comparethe complexity of theseapproaches,discusspilot studiesof their effectiveness,andtherelationshipof thiswork to previousapproaches.

ConceptMaps for KnowledgeModelingConceptmappingwas designedboth to enablethe exam-inationof humanconceptualizations,andto furtherhumanknowledgeconstruction.As shown in thecenterof Figure1,conceptmapsarea two-dimensionalvisual representations

Figure1: A screenshotof thesuggesterproposingresourcesrelevantto a currentconcept,in thecontext of aconceptmap.

containingnodesfor concepts,connectedwith namedlinksexpressingconceptrelationships(e.g.,thatEarthis a neigh-bor of Jupiter). Conceptmapsappearsimilar to semanticnetsbut havenofixedsemanticsandvocabulary—they sim-ply make explicit any set of conceptsand relationshipsinany vocabulary thattheexpertchooses.

In electronicconceptmaps,nodescanbeassociatedwithresourcessuch as photographsand textual passages(asshown in the backgroundof Figure 1), diagrams,or evenpointersto additionalconceptmapsto definea hierarchi-cal conceptstructure.The resultis a rich andflexible con-ceptrepresentationto helphumansunderstanddomainsandrevise their domainknowledge. Conceptmappinghasre-ceived widespreaduse for knowledge modeling, sharing,andrefinementby expertsandnovices(e.g.,in theQuorumproject,involving over a thousandschoolsin SouthAmer-ica (Canaset al. 1995)).As increasingnumbersof conceptmapsarecapturedin electronicform, they provide a grow-ing sourceof datafor studyinghumanconcepts,for enablingknowledgesharing,andfor helpingto refinetoolsto supporthumanconcept-mapping.

SomeCentral IssuesDeveloping methodsfor assessingconceptmap similarityrequiresaddressingissuesfor bothcognitivescienceandAI:� The rolesof contentand structur e in similarity assess-

ment: Modelsof conceptualsimilarity in conceptmapsmustconsiderboth conceptlabels,andhow the labeledconceptsarerelatedto otherconcepts.� Assessing similarity and relevance for non-standardized representations: Labels on conceptmap nodesprovide namesfor the conceptsthat they

represent,but not in the more formal, standardizedrepresentationsassumedin muchAI research.Nodeandlink labelsmay be ambiguousor inconsistentwith thenamesusedin other conceptmaps. Thus determiningrelated conceptsrequires more than simple keywordmatching,andsimilarity assessmentmustbesufficientlyrobustto dealwith representationaldifferences.� Efficient use of structural information: If link labelscannotbematchedreliably, matchingconceptmapstruc-turereducestographmatching.Becausethisis expensive,methodsareneededto summarizestructuralinformationandusethosesummariesto guidematching.� Exploiting contextual information: Context may becrucialin determiningtherelevanceof conceptswith dif-ferent labels,becausethe meaningof eachconceptin aconceptmap is partially capturedby its connectionstootherconcepts.Context may be crucial even for deter-mining relevanceof identicalconcepts:A rocket enginedesignerwho entersa nodelabeled“hydrogenperoxide,”linked to conceptsfor fuel andpropulsion,would not beinterestedin retrievingaconceptmaponfirst-aidthathap-pensto includehydrogenperoxideaswell.� Facilitating representational standardization: Theusefulnessof conceptualinformation for reasoningsys-tems increaseswith standardization.To increasestan-dardizationwithout increasingtheburdenonusers,meth-odsareneededto helpidentify to reuseexisting labels.

Methodsfor ComputingRelevance,Similarity , and Usefulness

We arestudyingtechniquesfor assessingthe relevanceofa new conceptasa candidate“conceptextension”(related

conceptto considerlinking to a selectedconceptin a con-ceptmap),aswell asto suggestrelevant vocabulary itemsfor possiblereuse. This sectionintroducesand comparesfour techniquesfor determiningtherelevanceof a new con-ceptto aconceptunderconsideration.Thefirst two rely pri-marilyonprecomputedglobalinformation,while thesecondtwo usethecontext of theconceptmapin whichtheconceptappears.We begin with definitionsthat will be useful forunderstandingthefollowing algorithms.

Preliminary DefinitionsConceptshave different importancesin conceptmaps,andthe conceptmap layout often providesuseful informationfor assigningconceptweights.For example,amainconceptusuallyappearsat the top of eachconceptmap,specifyingthemain topic. In (Canas,Leake, & Maguitman2001)weproposedthatasmallsetof topologicaldimensionscanuse-fully summarizeconceptroles:� Authorities: Conceptsto which otherconceptsconverge.

Thesehave the largestnumberof incoming links from“hub nodes”(definedbelow).� Hubs(centersof activity): Conceptswith thelargestnum-berof outgoinglinks endingatauthoritynodes.� UpperNodes:Conceptsthatappeartowardsthetopof themapin its graphicalrepresentation.� Lower Nodes:Conceptsthat appeartowardsthe bottomof theconceptmapin its graphicalrepresentation.

Our algorithmsto computetheseweightsareadaptedfromresearchon determininghubandauthoritiesnodesin a hy-perlinked environment(Kleinberg 1999). We definefourweights,a-weight, h-weight, u-weightandl-weight, in [0,1],representingthe degreeto which a conceptbelongsto theabovecategoriesin a particularconceptmap.Detaileddefi-nitionsarepresentedin (Canas,Leake,& Maguitman2001).For a givenconceptmap,theseweightscanbecomputedin������

time, where

is the numberof conceptsin a map.They needonly becomputedonce,whentheconceptmapisindexed,andstoredwith eachconcept.

To describeindividualconcepts,ourmethodsextractkey-wordsfrom theconceptlabels(“stopwords”aredeletedbe-foreprocessing),andweightthekeywordsin termsof thesefour typesof weights,usingtheweightsof the conceptsinwhich they appear. Conceptmapsare then comparedac-cordingto their weightedkeywords. (In the following for-mulas,wesometimesrefertoapplyingsetoperationssuchasintersectionanddifferenceto conceptmaps;this is a short-handfor applyingthoseoperationsto the setsof keywordsextractedfrom theconceptmaps.)Givena keyword � andconceptmap library � , ���� standsfor the set of conceptmapsin � containingkeyword � . For simplicity weassumethat � is fixedanduse � � to denoteall conceptmapscon-taining keyword � . It may be useful to refer to the globalweightof a keyword in a setof conceptmaps.If � is a setof conceptmaps,� is akeyword,andw is aweightfunction,theglobalweight ��� � ����� of � in � is definedby:� � � ����� �����! #"%$ � �&��' )(

Someof our algorithmscomputethe averageof the

highestvaluesof a setof values.For a setof values* , wewill usethenotation+ �, �-* to referto thesumrestrictedtothe

highestvaluesof * , dividedby

. In thespecialcase

when * is empty, thereturnedvalueis 0.

Estimating Relevanceby Global CorrelationsOur first two methodsuseglobal correlationmetricsto re-trieve conceptmapscontainingconceptsthat tend to co-occurwith conceptsfrom thecurrentconceptmap.Becausethis allows correlatedkeywords to matcheachother, it ismoreflexible thanusingkeywordmatchingalone.Correla-tion informationis combinedwith theweighteachkeywordhasonthecorrespondingmaps—giving riseto weight-basedglobalcorrelationmetrics—orwith thedistancebetweenthetwo involved keywords in eachconceptmap—giving riseto distance-basedglobal correlationmetrics. (In a conceptmapthe notion of distancecanbe naturallydefinedastheminimumdistancebetweenconceptsin whichthekeywordsappear.) Both of theabove methodsareglobal in thesensethatthey assignconceptimportancesbasedon global infor-mationpre-computedfrom theentireconceptmaplibrary.

Method 1: Using weight-basedglobal correlations: Tocomputeweight-basedglobalcorrelationsbetweenasourceconcept. anda targetconcept/ , we first computetheset021 � .3�-/ of weight-basedcorrelation values. Writing �for ��4#56��798;:)<>= , wecalculate:?�@ � 8BA �DC @ E � � � � 8BA �DCF� G � � � � 8HA �DCF� I @ � 8 @ � @ �DC @ � � � � 8 � G � � � �DC�� I J G�KL.3�MINKO/�PRQThen we computethe weight-basedglobal correlation asS � .3�T/ !� + � � 021 � .3�T/ - , where

U�2� @ . @WVX@ / @ -YFZ .Method 2: Usingdistance-basedglobal correlations: Inorder to computedistance-basedglobal correlations westartby defining[ � � G��MI , whichstatesthedistancebetweenkeywordsG andI in theconceptmap ' . Thedistancemetric[ � � G\�BI canbe naturallydefinedasthe minimumnumberof links betweenconceptscontainingthosekeywords,or in-finity if G and I arenot both in ' . Considerthesetof key-words . and / . We begin by computingtheset ] 1 � .3�T/ of distance-basedcorrelationvalues:^_ ` ��! ba"dcHef"&gTh Z� @ � 8 @iVj@ � C @ � [ � � G\�BI J GkKl.!�BINKm/on pq (The distance-basedglobal correlation is then r � .3�T/ ��+ � ��] 1 � .3�-/ T , where

l�s� @ . @iVj@ / @ �YtZ .Estimating RelevanceBasedon ContextWhenproviding suggestionsto a userconstructinga con-ceptmap,it is appealingto retrieve conceptsthatappearincontextssimilar to themapunderconstruction.Wehavede-velopedtwo methodsto comparelocal contexts, thefirst ofwhich is asimilarity-basedapproach.It positsthatthemoresimilarthecontextsin whichtwo conceptsappear, thehigher

thelikely relevanceof oneconceptto theother. Thesecondis a usefulness-basedu approachthat favorsconceptsprovid-ing additionalinformationastheuserseeksto addnew con-ceptsto apartialconceptmap.

Method 3: Using contextual similarity: To comparetheconceptmapstructuresin which two conceptsappear, weconsiderthe four weightsobtainedfrom topologicalanaly-sis to summarizethe positioningof eachconcept,andusethatinformationto comparetheroleof eachrelatedconcept(i.e.,conceptwith overlappingkeywords)in its own conceptmapby calculatingthedistancesbetweenthesetsof associ-atedweights.Thustheweightsobtainedfrom thetopologi-cal analysisof a conceptmapareusedto definetopologicalsimilaritiesbetweentwo conceptsbelongingto two differentconceptmaps.For example,two conceptsthatappearat thetop of their correspondingconceptmapswill have similaru-weights, while two conceptsthatplaysimilar rolesashubnodesin theircorrespondingconceptmapswill havesimilarh-weights. Basedon theseintuitions we cancomparetwomaps'wv and 'kx by first computing/�. � 'wvd�\'yx , thesetoftopological similarity valuesasfollows:^zz_ zz`w{ |~}���{ � �� � ��� �M���O�%��� |d�������M���T�!�&�9�{ ��� {��3� � |d�9�y� � |l�N� � �M����� � n

zzpzzqwhere��� � .3�T/ ��s� @ . @iVj@ / @ �YtZ ,��� 0 =

� � a-weight,� h-weight,� u-weight,� l-weight� ,and��� $ � .3�\' v �-/D��' x k�2� $ � .3�\' v d� $ � /D�\' x T E , and $ isoneof thefour weights.

Wethencomputethetopologicalsimilaritybetweenconceptmaps ' v and ' x , as � � ' v ��' x �� + � �-/�. � ' v ��' x - ,where

m�s� @ 'wv @>VX@ 'yx @ -YFZ .Method 4: Using context and novelty of information:Theconceptmapthat is themostsimilar to thesourcemapmay not be mostusefulfor suggestinginformationto con-nectto a new concept.For finding new connections,usefulprior conceptmapsarethosethatboth includesimilar con-ceptsandsuggestnew connections.Consequently, we arealsoexploringmethodsthatfavor bothcommonalityandtheexistenceof new materialin thestoredconceptmap.

A simpleusefulnessmeasurebetweena sourceconceptmap ' v anda targetconceptmap ' x canbecomputedby:� � 'wv���'yx �� � � @ ' v A 'yx @VN¡ � @ 'kx � ' v @ ��¢ � @ ' v � 'kx @where � ,

¡and

¢areconstantsthat adjustthe balancebe-

tweenoverlapandnovelty. (�

neednot besymmetric,so itis a measure, ratherthana metric.) We arealsoinvestigat-ing measuresthat considerthe correlationsbetweentargetandthesourcekeywordsfor moreflexible matchingof non-identical terms. For example,applyingthe distance-basedcorrelationmeasurefrom Method 2, we can computetheusefulnessmeasure:

��£ � ' v �\' x �� � � @ ' v A ' x @ V¡ � r � ' v ��' x � ' v � @ ' x � ' v @ �¢ � ��¤¥� r � 'yx!��'wv � 'yx T � @ 'wv � 'yx @ (Discussionof MethodsAssessingthe previous methodsrequiresconsideringtheircostandthequalityof their relevancepredictions.

Cost: Methods1 and2, theglobalcorrelationmetrics,areefficientto compute.Computingtheglobalweightfor akey-word (Method1) is linear in the numberof conceptmapsinvolved. Computingthe weight-basedcorrelationvaluesfor keywords G andI involvescountingtheconceptmapssi-multaneouslycontainingthosekeywords,whichcanbedonein timesfrom

��� @ � 8 @ to��� @ � 8 @ � @ �DC @ , dependingon the

underlyingindexing scheme.Weight-basedglobal correla-tionsmustbecomputedfor eachpair of keywordsin sourceand target concepts,but becausethe numberof keywordsin conceptsis usually small, this is inexpensive in prac-tice. Computingdistance-basedglobalcorrelations(Method2) requirescomputingminimumdistancesbetweenpairsofkeywordsin conceptmaps,which is basicallythe shortestpath problem, and can be computedin

��� @ ¦o@ �N§¨W© @ 1 @ ,where

1is the numberof vertices(conceptsin our case)

and¦

is thenumberof edges(links in ourcase).Method3, thefirst context-basedmethod,requirescom-

putingtopologicalsimilarity betweeneachpair of conceptsin two conceptmaps.In principle,this canbequiteexpen-sive,but thesevaluesonly needto becomputedfor pairsofconceptsthathave at leasta keyword in common.Usuallytherearefew suchconceptsin any conceptmap,makingthisinexpensive in practice.Dependingon theindexing mecha-nismused,thebasictechniqueconsideringcontext andnov-elty (the first versionof Method4) canbe implementedintimes

���ªl to���,ª � � , where

ªand

arethe sizesof

the conceptmapsto be compared.The secondversionofMethod4, which addsglobal correlations,is significantlylessefficient. Its speedof calculatingglobalcorrelationsisreasonablefor comparingindividual concepts,but not forcomparingconceptmaps. In future researchwe intendtoperforma formal analysisandto developefficient approxi-mationsof thisapproach.

Relevanceof suggestions: We performeda pilot experi-ment to evaluatewhetherour metricscan be exploited toprovide better recommendationsthan the simple baselinemethodof countingsharedkeywords. In the experiment,subjectswerepresentedwith a conceptmap,with onecon-ceptdesignatedastheconceptto beextended,anda list of50 suggestionschosenrandomlyfrom thesetof extensionscontainingat leastonekeyword in commonwith the con-ceptto beextended.Tensubjects,all graduatestudentsnotinvolved in the project,assessedthe relevanceof retrievedinformationona scaleof 0 to 10. Their rankingswerecom-paredto therelevancescoresassignedbyourtechniques.WethenusedSpearmanrankcorrelationto comparetherankingproducedby thehumansubjectsto therankingproducedbyouralgorithms.

In our study, bestresultsareobtainedwhenusefulness-based« comparisonmeasures(Method 4) are usedto pre-selecttarget conceptmapsandthe combinationof weight-basedcomparisonmetric (Method 1) and distance-basedcomparisonmetric (Method2) is usedto ranksuggestions.In thisapproach,theweight-basedmetricmeasuresthesimi-larity betweenthesourcebaseconcept,i.e.,theconcepttobeextended,andthe targetbaseconcept,i.e., theconceptthatis connectedto potentiallyrelevantextensions;thedistance-basedmetriccomparesthebasesourceconceptto thepoten-tially relevant extension. Intuitively, weight-basedmetricsbetweenconceptstell ushow similartwo givenconceptsare,while thedistance-basedmetrichelpstopredicthow suitableis for aconceptto haveanothernew conceptasaneighbor.

Our resultsshow a correlationfactorof 0.77, with a 2-tailed significancelevel ¬®­°¯ ( ¯F¯F¯ ¤ , betweenthe valuesobtainedby the combinedmethodand the aggregationoftheevaluationsmadeby humansubjects.Our resultsshowa correlationfactorof 0.63,with ¬R­2¯ ( ¯F¯F¯ ¤ , betweenval-uesfrom thebaseline“countingcommonkeywords”andtheaggregateof the resultsreturnedby humansubjects.Thissuggeststhatour methodsarecapturingregularitiesbeyondthosecapturedby thebaselinemethod.

Comparisonto RelatedWorkTheprojectdescribedhererelatesto numerousresearchar-eassuchasknowledgemodelingandsharing,conceptrep-resentation,information retrieval, and case-basedreason-ing. As a knowledgemodelingproject, it contrastswithknowledgeengineeringapproachesthat dependon hand-craftingknowledgerepresentations,aimingto empowerdo-mainexpertsto directlyconstruct,navigate,share,andcriti-cizeknowledgemodels.This requiresthat theconceptrep-resentationsbenaturalfor themto construct,andsufficientlyexpressivefor othersto understandtheir conceptualizations.Therepresentationthatwe have chosen,conceptmapsaug-mentedwith supplementaryresources,appearsto providetheneededinformationin aneasy-to-useform, anda recentstudysubstantiatestheusefulnessof conceptmapnavigationfor guidingknowledgeaccess(Carnotetal. 2001).

Keyword-basedretrieval techniquesare commonin theinformationretrieval literature(Baeza-Yates& Ribeiro-Neto1999). Becauseconceptmapsprovide additionalstructure,our methodsaugmentkeyword-basedmethodswith consid-erationof thetopologicalrole of a keyword, inheritedfromthetopologicalrole of theconceptin which it appears.TheIR communityhasalsodoneconsiderableresearchonmeth-odsinvolving metricclusters, in which keywordsarecom-paredin termsof theirdistance(usuallydefinedby thenum-berof wordsbetweenthemin a document,with infinite dis-tancebetweenkeywordsin differentdocuments).Our no-tion of distance-basedglobal correlationsis an adaptationof theseideas.

Thecomparisonof structuredinformationhasbeenexten-sively studiedin researchon case-basedreasoningandana-logical reasoning.Ourmethodsrely on topologicalanalysistechniquesratherthanonexplicit structuremapping,asdoneby (Falkenhainer, Forbus,& Gentner1989).Structuralanal-ysisrequiresastandardizedrepresentationlanguage,andas-

sumesthat the most importantmatchesinvolve the links,ratherthan the entitiesthat theselinks relate. In conceptmaps, the representationalvocabulary is nonstandardizedandlink namestendto be generic,so the mostsignificantinformationsourceis usuallyon theconceptsratherthanonthelinks.

ConclusionConceptmappingprovidesa meansto captureand exam-ine humanconcepts,aswell asa tool for aidingexpertsandnovicesatconstructingandrefiningtheirown understandingof adomain.Augmentingconceptmappingtoolswith intel-ligent methodsfor suggestingrelevantconceptsto compareandconsideris promisingfor aidingtheseprocessesandfa-cilitating knowledgesharing.Developingthesemethodsde-pendson beingableto efficiently andeffectively assesstherelevanceof conceptsin prior mapsto selectedconceptsintheconceptmapscurrentlybeingconstructed.

Thepaperhasidentifiedkey issuesfor this taskandpre-senteda setof approachesfor assessingconceptualsimilar-ity andrelevancefor conceptmapping. Theseapproacheshave beenimplementedin a suggestersystemcombinedwith the electronicconceptmappingtools of the Institutefor HumanandMachineCognition,with encouraginginitialresultsthat we arepreparingto test moreextensively in alarger-scalestudy. Basedon theresultsof thatstudy, we in-tendto refinetheseindividualmethodsandinvestigatepossi-bilities for combinationsto exploit theirindividualstrengths,as well as to addressadditionalissuessuchas selectivelyadjustingconceptweightsto reflectadditionalinformationabouttaskcontexts.

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