Table Of ContentHierarchical Re-estimation of Topic Models for
Measuring Topical Diversity
HoseinAzarbonyad,MostafaDehghani,TomKenter,MaartenMarx,JaapKamps,and
MaartendeRijke
UniversityofAmsterdam,Amsterdam,TheNetherlands
{h.azarbonyad,dehghani,tom.kenter,maartenmarx,kamps,derijke}@uva.nl
Abstract. Ahighdegreeoftopicaldiversityisoftenconsideredtobeanimpor-
tantcharacteristicofinterestingtextdocuments.Arecentproposalformeasuring
7
topicaldiversityidentifiesthreeelementsforassessingdiversity:words,topics,
1
anddocumentsascollectionsofwords.Topicmodelsplayacentralroleinthis
0
approach.Usingstandardtopicmodelsformeasuringdiversityofdocumentsis
2
suboptimalduetogeneralityandimpurity.Generaltopicsonlyincludecommon
n informationfromabackgroundcorpusandareassignedtomostofthedocuments
a inthecollection.Impuretopicscontainwordsthatarenotrelatedtothetopic;
J
impuritylowerstheinterpretabilityoftopicmodelsandimpuretopicsarelikelyto
6
getassignedtodocumentserroneously.Weproposeahierarchicalre-estimation
1
approachfortopicmodelstocombatgeneralityandimpurity;theproposedap-
proachoperatesatthreelevels:words,topics,anddocuments.Ourre-estimation
]
R approachformeasuringdocuments’topicaldiversityoutperformsthestateofthe
I artonPubMeddatasetwhichiscommonlyusedfordiversityexperiments.
.
s
c
[ 1 Introduction
Quantitativenotionsoftopicaldiversityintextdocumentsareusefulinseveralcontexts,
1
v e.g., to assess the interdisciplinarity of a research proposal [3] or to determine the
3 interestingness of a document [2]. An influential formalization of diversity has been
7 introducedinbiology[17].Itdecomposesdiversityintermsofelementsthatbelongto
2
categorieswithinapopulation[20]andformalizesthediversityofapopulationdasthe
4
expecteddistancebetweentworandomlyselectedelementsofthepopulation:
0
.
1 T T
(cid:88)(cid:88)
0 div(d)= p p δ(i,j), (1)
i j
7
i=1j=1
1
: wherep andp aretheproportionsofcategoriesiandj inthepopulationandδ(i,j)
v i j
i isthedistancebetweeniandj.Bacheetal.[3]haveadaptedthisnotionofdiversity
X
to quantify the topical diversity of a text document. Words are considered elements,
r topicsarecategories,andadocumentisapopulation.Whenusingtopicmodelingfor
a
measuringtopicaldiversityoftextdocumentd,Bacheetal.[3]modelelementsbased
ontheprobabilityofawordwgivend,P(w|d),categoriesbasedontheprobabilityof
wgiventopict,P(w|t),andpopulationsbasedontheprobabilityoftgivend,P(t|d).
Inprobabilistictopicmodeling,atestimationtime,thesedistributionsareusually
assumedtobesparse.First,thecontentofadocumentisassumedtobegeneratedby
a small subset of words from the vocabulary (i.e., P(w|d) is sparse). Second, each
topic is assumed to contain only some topic-specific related words (i.e., P(w|t) is
sparse).Finally,eachdocumentisassumedtodealwithafewtopicsonly(i.e.,(P(t|d)
issparse).Whenapproximatedusingcurrentlyavailablemethods,P(w|t)andP(t|d)
areoftendenseratherthansparse[13,19,21].Densedistributionscausetwoproblems
forthequalityoftopicmodelswhenusedformeasuringtopicaldiversity:generality
andimpurity.Generaltopicsmostlycontaingeneralwordsandaretypicallyassigned
tomostdocumentsinacorpus.Impuretopicscontainwordsthatarenotrelatedtothe
topic.GeneralityandimpurityoftopicsbothresultinlowqualityP(t|d)distributions.
Weproposeahierarchicalre-estimationprocessformakingthedistributionsP(w|d),
P(w|t)andP(t|d)moresparse.Were-estimatetheparametersofthesedistributionsso
thatgeneral,collection-wideitemsareremovedandonlysalientitemsarekept.Forthe
re-estimationweusetheconceptofparsimony[9]toextractonlyessentialparameters
ofeachdistribution.
Our main contributions are: (1) We propose a hierarchical re-estimation process
fortopicmodelstoaddresstwomainproblemsinestimatingtopicaldiversityoftext
documents,usingabiologicallyinspireddefinitionofdiversity.(2)Westudytheefficacy
ofeachlevelofre-estimation,andimprovetheaccuracyofestimatingtopicaldiversity,
outperformingthecurrentstate-of-the-art[3]onapubliclyavailabledatasetcommonly
usedforevaluatingdocumentdiversity[1].
2 Relatedwork
Ourhierarchicalre-estimationmethodformeasuringtopicaldiversityrelatestomeasur-
ingtextdiversity,improvingthequalityoftopicmodels,modelparsimonization,and
evaluatingtopicmodels.
Text diversity and interestingness. Recent studies measure topical diversity of
document[2,3,8]bymeansofLatentDirichletAllocation(LDA)[4].Themaindiversity
measureinthisworkisRao’smeasure[17](Equation1),inwhichthediversityofatext
documentisproportionaltothenumberofdissimilartopicsitcovers.Whilewealsouse
Rao’smeasure,wehypothesizethatpureLDAisnotgoodenoughformodelingtext
diversityandproposeare-estimationprocessforadaptingtopicmodelsformeasuring
topicaldiversity.
Improvingthequalityoftopicmodels.Thetwomostimportantissueswithtopic
models are the generality problem and the impurity problem [5, 13, 19, 21]. Many
approacheshavebeenproposedtoaddressthegeneralityproblem[21–23].Themain
differencewithourworkisthatpreviousworkdoesnotyieldsparsetopicrepresentations
or topic word distributions. Soleimani and Miller [19] propose parsimonious topic
models(PTM)toaddressthegeneralityandimpurityproblems.PTMachievesstate-of-
the-artresultscomparedtoexistingtopicmodels.Unlike[19],wedonotmodifythe
trainingprocedureofLDAbutproposeamethodtorefinethetopicmodels.
Modelparsimonization. Inlanguagemodelparsimonization,thelanguagemodel
of a document is considered to be a mixture of a general background model and a
document-specificlanguagemodel[6,7,9,26].Thegoalistoextractthedocument-
specificpartandremovethegeneralwords.Weemployparsimonizationforre-estimating
topicmodels.Themainassumptionin[9]isthatthelanguagemodelofadocumentisa
mixtureofitsspecificlanguagemodelandagenerallanguagemodel:
P(w|d)=λP(w|θ˜ )+(1−λ)P(w|θ ), (2)
d C
wherew isaterm,dadocument,θ˜ thedocumentspecificlanguagemodelofd,θ
d C
thelanguagemodelofthecollectionC,andλisamixingparameter.Themaingoalis
toestimateP(w|θ˜ )foreachdocument.ThisisdoneinaniterativemannerusingEM
d
algorithm.Theinitialparametersofthelanguagemodelaretheparametersofstandard
languagemodel,estimatedusingmaximumlikelihood:P(w|θ˜ )= tfw,d ,where
d (cid:80)w(cid:48)tfw(cid:48),d
tf isthefrequencyofwind.Thefollowingstepsarecomputediteratively:
w,d
E-step:
λP(w|θ˜ )
e =tf · d , (3)
w w,d λP(w|θ˜ )+(1−λ)P(w|θ ))
d C
M-step:
e
P(w|θ˜ )= w , (4)
d (cid:80) e
w(cid:48) w(cid:48)
where θ˜ is the parsimonized language model of document d, C is the background
d
collection, P(w|θ ) is estimated using maximum likelihood estimation, and λ is a
C
parameterthatcontrolsthelevelofparsimonization.Alowvalueofλwillresultina
moreparsimonizedmodelwhileλ=1yieldsamodelwithoutparsimonization.TheEM
processstopsafterafixednumberofiterationsorafterconvergence.
Evaluatingtopicmodels.Weevaluatetheeffectivenessofourre-estimatedmodels
bymeasuringthetopicaldiversityoftextdocuments.Inaddition,in§6,weanalyzethe
effectivenessofourre-estimationapproachintermsofpurityindocumentclustering
anddocumentclassificationtasks.Forclassification,following[10,16,19],wemodel
topicsasdocumentfeatureswithvaluesP(t|d).Forclustering,eachtopicisconsidered
aclusterandeachdocumentisassignedtoitsmostprobabletopic[16,24,25].
3 Measuringtopicaldiversityofdocuments
Tomeasuretopicaldiversityoftextdocuments,weproposeHiTR(hierarchicaltopic
modelre-estimation).HiTRcanbeappliedtoanytopicmodelingapproachthatmodels
documentsasdistributionsovertopicsandtopicsasdistributionsoverwords.
TheinputtoHiTRisacorpusoftextdocuments.Theoutputisaprobabilitydis-
tribution over topics for each document in the corpus. HiTR has three levels of re-
estimation: (1) document re-estimation (DR) re-estimates the language model per
documentP(w|d);(2)topicre-estimation(TR)re-estimatesthelanguagemodelper
topicP(w|t);and(3)topicassignmentre-estimation(TAR)re-estimatesthedistribu-
tionovertopicsperdocumentP(t|d).Basedonapplyingornotapplyingre-estimation
atdifferentlevels,therearesevenpossiblere-estimationapproaches;seeFig.1.HiTR
referstothemodelthatusesallthreere-estimationtechniques,i.e.,TM+DR+TR+TAR.
Next,wedescribeeachofthere-estimationstepsinmoredetail.
Document re-estimation (DR) re-estimates P(w|d). Here, we remove unneces-
sary information from documents before training topic models. This is comparable
to pre-processing steps, such as removing stopwords and high- and low-frequency
words, that are typically carried out prior to applying topic models [4, 11, 15, 16].
level 1 level 2 level 3
TM
TAR TM + TAR
TM TR TM + TR
Corpus TAR TM + TR + TAR
TM + DR
DR TAR TM + DR + TAR
TM TR TM + DR + TR
TAR HiTR Hierarchical Topic model Re-estimation
Fig.1:Differenttopicre-estimationapproaches.TMisatopicmodelingapproach
like,e.g.,LDA.DRisdocumentre-estimation,TRistopicre-estimation,andTAR
istopicassignmentre-estimation.
Properpre-processingofdocuments,however,takeslotsofeffortandinvolvestuning
manyparameters.Documentre-estimation,however,removesimpureelements(general
words)fromdocumentsautomatically.Ifgeneralwordsareabsentfromdocuments,we
expect that the trained topic models will not contain general topics. After document
re-estimation,wecantrainanystandardtopicmodelonthere-estimateddocuments.
Documentre-estimationusestheparsimonizationmethoddescribedin§2.There-
estimatedmodelP(w|θ˜ )in(4)isusedasthelanguagemodelofdocumentd,andafter
d
removingunnecessarywordsfromd,thefrequenciesoftheremainingwords(words
withP(w|θ˜ )>0)arere-estimatedfordusingthefollowingequation:
d
(cid:106) (cid:107)
tf(w,d)= P(w|θ˜ )·|d| ,
d
where |d| is the document length in words. Topic modeling is then applied on the
re-estimateddocument-wordfrequencymatrix.
Topic re-estimation (TR) re-estimates P(w|t) by removing general words. The
re-estimateddistributionsareusedtoassigntopicstodocuments.Thegoalofthisstep
is to increase the purity of topics by removing general words that have not yet been
removedbyDR.Thetwomainadvantagesoftheincreasedpurityoftopicsare(1)it
improveshumaninterpretationoftopics,and(2)itleadstomoredocument-specifictopic
assignments,whichisessentialformeasuringtopicaldiversityofdocuments.
Ourmainassumptionisthateachtopic’slanguagemodelisamixtureofitstopic-
specific language model and the language model of the background collection. TR
extractsatopic-specificlanguagemodelforeachtopicandremovesthepartthatcanbe
explainedbythebackgroundmodel.Weinitializeθ˜ andθ asfollows:
t T
(cid:80) P(w|θTM)
P(w|θ˜)=P(w|θTM) P(w|θ )= t∈T t
t t T (cid:80) (cid:80) P(w(cid:48)|θTM)
w(cid:48)∈V t(cid:48)∈T t(cid:48)
wheretisatopic,θ˜ istopic-specificlanguagemodeloft,andθ isthebackground
t T
languagemodelofT (thecollectionofalltopics),P(w|θTM)istheprobabilityofw
t
belongingtotopictestimatedbyatopicmodelTM.Havingtheseestimations,thesteps
ofTRaresimilartothestepsofparsimonization,exceptthatintheE-stepweestimate
tf ,thefrequencyofwint,byP(w|θTM).
w,t t
Topic assignment re-estimation (TAR) re-estimates P(t|d). In topic modeling,
mosttopicsareusuallyassignedwithanon-zeroprobabilitytomostofdocuments.For
documentswhichareinrealityaboutafewtopics,thistopicassignmentisincorrect
andoverestimatesitsdiversity.TARaddressesthegeneraltopicsproblemandachieves
moredocumentspecifictopicassignments.Tore-estimatetopicassignments,atopic
modelisfirsttrainedonthedocumentcollection.Thismodelisusedtoassigntopics
todocumentsbasedontheproportionofwordstheyhaveincommon.Wethenmodel
thedistributionovertopicsperdocumentasamixtureofitsdocument-specifictopic
distributionandthetopicdistributionoftheentirecollection.
WeinitializeP(t|θ˜ )andP(t|θ )asfollows:
d C
(cid:80) P(t|θTM)
P(t|θ˜ )=P(t|θTM) P(t|θ )= d∈C d .
d d C (cid:80) (cid:80) P(t(cid:48)|θTM)
t(cid:48)∈T d(cid:48)∈C d(cid:48)
Here, t is a topic, d a document, P(t|θ˜ ) the document-specific topic distribution,
d
andP(t|θ )thedistributionoftopicsintheentirecollectionC,andP(t|θTM)the
C d
probabilityofassigningtopicttodocumentdestimatedbyatopicmodelTM.The
remainingstepsofTARfollowtheonesofparsimonization,thedifferencebeingthatin
theE-step,weestimatef usingP(t|θTM).
t,d d
4 Experimentalsetup
Our main research question is: (RQ1) How effective is HiTR in measuring topical
diversityofdocuments?Howdoesitcomparetothestate-of-the-artinaddressingthe
generalandimpuretopicsproblem?
To address RQ1 we run our models on a binary classification task. We generate
a synthetic dataset of documents with high and low topical diversity (the process is
detailedbelow),andthetaskforeverymodelistopredictwhetheradocumentbelongs
tothehighorlowdiversityclass.WeemployHiTRtore-estimatetopicmodelsanduse
there-estimatedmodelsformeasuringtopicaldiversityofdocuments.Togaindeeper
insightsintohowHiTRperforms,weconductaseparateanalysisofthelasttwolevels
ofre-estimation,TRandTAR:1 (RQ2.1)DoesTRincreasethepurityoftopics?Ifso,
howdoesusingthemorepuretopicsinfluencetheperformanceintopicaldiversitytask?
(RQ2.2)HowdoesTARaffectthesparsityofdocument-topicassignments?Andwhat
istheeffectofre-estimateddocument-topicassignmentsonthetopicaldiversitytask?
ToanswerRQ2.1,wefirstevaluatetheperformanceofTRonthetopicaldiversitytask
andcompareitsperformancetoDRandTAR.ToanswerRQ2.2,wefirstevaluateTAR
togetherwithLDAinatopicaldiversitytaskandanalyzeitseffectontheperformance
ofLDAtostudyhowsuccessfulTARisinremovinggeneraltopicsfromdocuments.
Dataset,pre-processing,evaluationmetrics,andparameters:Following[3],we
generate500documentswithahighvalueofdiversityand500documentswithalow
valueofdiversity.Weselectover300,000documentsarticlespublishedbetween2012to
2015fromPubMed[1].Forgeneratingdocumentswithahighvalueofdiversity,wefirst
select20journalsandcreate10pairsofjournals.Eachpaircontainstwojournalsthatare
relativelyunrelatedtoeachother(weusethepairsofjournalsselectedin[3]).Foreach
pairofjournalsAandBweselect50articlestocreate50probabilitydistributionsover
1AstheDRlevelofre-estimationdirectlyemploystheparsimoniouslanguagemodelingtech-
niquesin[9],weomititfromourin-depthanalysis.
topics:werandomlyselectonearticlefromAandonefromBandgenerateadocument
byaveragingtheselectedarticle’sbagoftopiccounts.Thus,foreachpairofjournals
wegenerate50documentswithahighdiversityvalue.Also,foreachofthechosen20
journals,werepeattheprocedurebutinsteadofchoosingarticlesfromdifferentjournals,
weselectthemfromthesamejournaltogenerate25non-diversedocuments.
Forpre-processingdocuments,weremovestopwordsincludedinthestandardstop
wordlistfromPython’sNLTKpackage.Inaddition,weremovethe100mostfrequent
wordsinthecollectionandwordswithfewerthan5occurrences.
Measuringtopicaldiversity:Afterre-estimatingworddistributionsindocuments,
topics,anddocumenttopicdistributionsusingHiTR,weusethefinaldistributionsover
topicsperdocumentformeasuringtopicaldiversity.Diversityoftextsiscomputedusing
Rao’scoefficient[3]usingEquation1.Weusethenormalizedangulardistanceδ for
measuringthedistancebetweentopics,sinceitisaproperdistancefunction[2].
Tomeasuretheperformanceoftopicmodelsonthetopicaldiversitytask,weuseROC
curvesandreporttheAUCvalues[3].Wealsomeasurethecoherenceoftheextracted
topics;thismeasureindicatesthepurityofP(w|t)distributions,whereahighvalueof
coherenceimplieshighpuritywithintopics.Weestimatecoherenceusingnormalized
pointwisemutualinformationbetweenthetopN wordswithinatopic[11,16].Asthe
referencecorpusforcomputingwordoccurrences,weusetheEnglishWikipedia.2
ThetopicmodelingapproachusedinourexperimentswithHiTRisLDA.Follow-
ing[3,18,19]wesetthenumberoftopicsto100.Wesetthetwohyperparametersto
α = 1/T and β = 0.01, where T is the number of topics, following [16]. In the re-
estimationprocess,ateachstepoftheEMalgorithm,wesetthethresholdforremoving
unnecessarycomponentsfromthemodelto0.0001andremovetermswithanestimated
probabilitylessthanthisthresholdfromthelanguagemodels,asin[9].
Weperform10-foldcrossvalidation,using8foldsastrainingdata,1foldtotune
theparameters(λforDR,TR,andTAR),and1foldfortesting.Ourbaselineforthe
topicaldiversitytaskisthemethodproposedin[3],whichusesLDA.Wealsocompare
ourresultstoPTM[19],whichweuseinsteadofLDAformeasuringtopicaldiversity.
PTMisthebestavailabletopicmodelingapproach,andthecurrentstateoftheart.
Forstatisticalsignificancetesting,wecompareourmethodstoPTMusingpairedtwo-
tailedt-testswithBonferronicorrection.Toaccountformultipletesting,weconsideran
improvementsignificantif:p≤α/m,wheremisthenumberofconductedcomparisons
and α is the desired significance. We set α = 0.05. In §5, (cid:78) and (cid:72) indicate that the
correspondingmethodperformssignificantlybetterandworsethanPTM,respectively.
5 Results
In this section, we report on the performance of HiTR on the topical diversity task.
Additionallyweanalyzetheeffectivenessoftheindividualre-estimationapproaches.
5.1 Topicaldiversityresults Fig.2plotstheperformanceofourtopicmodelsacross
differentlevelsofre-estimation,andthemodelswecompareto,onthePubMeddataset.
WeplotROCcurvesandcomputeAUCvalues.ToplottheROCcurvesweusethediver-
sityscorescalculatedforthegeneratedpseudo-documentswithdiversitylabels.HiTR
improvestheperformanceofLDAby17%andPTMby5%intermsofAUC.FromFig.2
two observations can be made.
2WeuseadumpofJune2,2015,containing15.6millionarticles.
First, HiTR benefits from the
ROC Curve
threere-estimationapproachesit 1.0
encapsulatesbysuccessfullyim-
0.8
provingthequalityofestimated ate
R
diversityscores.Second,theper- e 0.6
v
formanceofLDA+TAR,which Positi0.4 Random AUC=0.5
tprrioesbletom,aidsdhreigsshetrhtehagnentheeraplietry- True 0.2 LPLLDDDTMAAA ++ AATTUUARCCR =A= AU00UC..77C=8=0.07.377
formanceofLDA+TR,whichad- LDA+DR AUC=0.75
HiTR AUC=0.82
0.0
dressesimpurity.Generaltopics 0.0 0.2 0.4 0.6 0.8 1.0
False Positive Rate
haveastrongernegativeeffecton
Fig.2:Performanceoftopicmodelsintopicaldi-
measuringtopicaldiversitythan
versitytaskonthePubMeddataset.Theimprove-
impure topics. Also, LDA+DR
mentofHiTRoverPTMisstatisticallysignificant
outperforms LDA+TR. So, re-
(p<0.05)intermsofAUC.
moving impurity from P(t|d)
distributions is the most effective approach in the topical diversity task, and remov-
ingimpurityfromP(w|d)distributionsismoreeffectivethanremovingimpurityfrom
P(w|t)distributions.Table1illustratesthedifferencebetweenLDAandHiTRwiththe
topicsassignedbythetwomethodsforanon-diversedocumentthatiscombinedfrom
twodocumentsfromthesamejournal,entitled“MolecularNeuroscience:Challenges
Ahead”and“RewardNetworksintheBrainasCapturedbyConnectivityMeasures,”
usingtheproceduredescribedin§4.Asonlyaverybasicstopwordlistbeingapplied,
words like also and one still appear. We expect to have a low diversity value for the
combineddocument.However,usingRao’sdiversitymeasure,thetopicaldiversityof
thisdocumentbasedontheLDAtopicsis0.97.Thisisduetothefactthattherearethree
document-specifictopics—topics1,2and4—andfourgeneraltopics.Topics1and2are
verysimilarandtheirδis0.13.Theother,moregeneraltopicshavehighδvalues;the
averageδvaluebetweenpairsoftopicsisashighas0.38.Forthesamedocument,HiTR
onlyassignsthreedocument-specifictopicsandtheyaremorepureandcoherent.The
averageδvaluebetweenpairsoftopicsassignedbyHiTRis0.19.Thediversityvalueof
thisdocumentusingHiTRis0.16,whichindicatesthatthisdocumentisnon-diverse.
Hence,HiTRismoreeffectivethanotherapproachesinmeasuringtopicaldiversityof
documents;itsuccessfullyremovesgeneralityfromP(t|d).
5.2 Topicre-estimationresults ToanswerRQ2.1,wefocusontopicre-estimation
(TR). Since TR tries to remove impurity from topics, we expect it to increase the
coherenceofthetopicsbyremovingunnecessarywordsfromtopics.Wemeasurethe
Table 1: Topic assignments for a non-diverse document using LDA and HiTR.
OnlytopicswithP(t|d)>0.05areshown.
LDA HiTR
TopicP(t|d)Top5words P(t|d)Top5words
1 0.21 brain,anterior,neurons,cortex,neuronal 0.68 brain,neuronal,neurons,neurological,nerve
2 0.14 channel,neuron,membrane,receptor,current 0.23 channel,synaptic,neuron,receptor,membrane
3 0.10 use,information,also,new,one 0.09 network,nodes,cluster,community,interaction
4 0.08 network,nodes,cluster,functional,node
5 0.08 using,method,used,image,algorithm
6 0.08 time,study,days,period,baseline
7 0.07 data,values,number,average,used
Table 2: Topic model coherence in terms of average normalized mutual informa-
tionbetweentop10wordsinthetopicsonthePubMeddataset.
LDA PTM LDA+TR LDA+DR+TR
8.17 9.89 9.46 10.29(cid:78)
purityoftopicsbasedonthecoherenceofwordsinP(w|t)distributions.Table2shows
the coherence of topics according to different topic modeling approaches, in terms
ofaveragemutualinformation.TRsignificantlyincreasesthecoherenceoftopicsby
removingtheimpurepartsfromtopics.ThecoherenceofPTMishigherthanofTR.
However,whenwefirstapplyDR,trainLDA,andfinallyapplyTR,thecoherenceofthe
extractedtopicsissignificantlyhigherthanthecoherenceoftopicsextractedbyPTM.
WeconcludethatTRiseffectiveinremovingimpurityfromtopics.Moreover,DRalso
contributesinmakingtopicsmorepure.
5.3 Topic assignment re-estimation results To answer RQ2.2, we focus on TAR
(topicassignmentre-estimation).WeareinterestedinseeinghowHiTRdealswithgen-
eraltopics.Wesumtheprobabilityofassigningatopictoadocument,overalldocuments:
for each topic t, we com-
(cid:80)
pute P(t|d),whereC is
d∈C LDA
the document collection. Fig. 3 LDA+TAR
showsthedistributionofproba- Non-general topics
bility mass before and after ap-
plying TAR; topics are sorted
based on the topic assignment
probability of LDA. LDA as-
signs a vast proportion of the
probability mass to a relatively
small number of topics, mostly
generaltopicsthatareassigned
to most documents. We expect
thatmanytopicsarerepresented Fig.3:Thetotalprobabilityofassigningtopicsto
in some documents, while rela- the documents in the PubMed dataset estimated
tivelyfewtopicswillberelevant using LDA and LDA+TAR. (The two areas are
to all documents. After apply- equaltothenumberofdocuments(N ≈300K)).
ingTAR,thedistributionisless
skewedandtheprobabilitymassismoreevenlydistributed.
(cid:80)
Therearetopicsthathaveahigh P(t|d)valueinLDA’stopicassignmentsanda
d
(cid:80)
high P(t|d)valueafterapplyingTARtoo;wemarkedthemas“non-generaltopics”
d
in Fig. 3. Table 3, column 2 shows the top five words for these topics. TAR is able
tofindthesethreenon-generaltopicsandtheirassignmentprobabilitiestodocuments
intheP(t|d)distributionsisnotchangedasmuchastheactualgeneraltopics.Thus,
TARremovesgeneraltopicsfromdocumentsandincreasestheprobabilityofdocument-
specifictopicsforeachdocument.TofurtherinvestigatewhetherTARreallyremoves
general topics, Table 3, column 3 shows the top five words for the first 10 topics in
Fig.3,excludingthe“non-generaltopics.”Theseseventopicshavethehighestdecrease
Table3: TopfivewordsforthetopicsdetectedbyTARasgeneraltopicsandnon-
generaltopics.
TopicNon-generaltopics Generaltopics
1 health,services,public,countries,data use,information,also,new,one
2 surgery,surgical,postoperative,patient,performedci,study,analysis,data,variables
3 cells,cell,treatment,experiments,used time,study,days,period,baseline
4 group,control,significantly,compared,groups
5 study,group,subject,groups,significant
6 may,also,effects,however,would
7 data,values,number,average,used
(cid:80)
in P(t|d) values due to TAR. Clearly, they contain general words and are not
d
(cid:80)
informative.Fig.3showsthatafterapplyingTAR,the P(t|d)valueshavedecreased
d
dramaticallyforthesetopics,withoutcreatingnewgeneraltopics.
5.4 Parameteranalysis Next,weanalyzetheeffectoftheλparameterontheper-
formance of DR, TR, and TAR. Fig. 4 displays the performance at different levels
of re-estimation. With λ = 1, no re-estimation occurs, and all methods equal LDA.
We see that DR peaks with
moderate values of λ (0.4 ≤ 0.8
0.7
λ ≤ 0.45). This reflects that
0.6
documents contain a moderate 0.5
C
amount of general information U0.4
A
0.3
and that DR is able to success- LDA
0.2 DR
fully deal with it. For λ ≥ 0.8, 0.1 TR
TAR
theperformanceofDRandLDA 0.0
0.0 0.2 0.4 0.6 0.8 1.0
isthesameandforthesevalues λ
of λ DR does not increase the Fig.4: The effect of the λ parameter on the per-
quality of LDA. Also, the best formanceoftopicsmodelsinthetopicaldiversity
performance of TR is achieved taskonthePubMeddataset.
with high values of λ (0.65 ≤
λ≤0.75).Fromthisobservationweconcludethattopicstypicallyneedonlyasmall
amountofre-estimation.Withthisslightre-estimation,TRisabletoimprovethequality
ofLDA.However,forλ≥0.75theaccuracyofTRdegrades.Lastly,TARachievesits
bestperformancewithlowvaluesofλ(0.02≤λ≤0.05).Hence,mostofthenoiseisin
theP(t|d)distributionsandaggressivere-estimationallowsTARtoremovemostofit.
6 Analysis
Inthissection,wewanttogainadditionalinsightsintoHiTRanditseffectsontopic
computation. The purity of topic assignments based on P(t|d) distributions has the
highest effect on the quality of estimated diversity scores. Thus, we investigate how
pureestimatedtopicassignmentsareusingHiTR.Tothisend,wecomparedocument
clusteringandclassificationresults,basedonthetopicsassignedbyHiTR,LDAand
PTM.Forclustering,following[16],weconsidereachtopicasacluster.Eachdocumentd
isassignedtothetopicthathasthehighestprobabilityvalueinP(t|d).Forclassification,
we use all topics assigned to the document and consider P(t|d) as features for a
supervisedclassificationalgorithm;weuseSVM.Weviewhighaccuracyinclustering
orclassificationasanindicatorofhighpurityoftopicdistributions.Ourfocusisnot
onachievingatopclusteringorclassificationperformance:thesetasksareameansto
assessthepurityoftopicdistributionsusingdifferenttopicmodels.
Datasetsandmetrics.WeuseRCV1[12],20-NewsGroups,3andOhsumed.4RCV1
contains806,791documentswithcategorylabelsfor126categories.Forclusteringand
classificationofdocuments,weuse55categoriesinthesecondlevelofthehierarchy.
20-NewsGroupscontains∼20,000documents(20categories,around1,000documents
per category). Ohsumed contains 50,216 documents grouped into 23 categories. For
measuringthepurityofclustersweusepurityandnormalizedmutualinformation(NMI)
[14].Weuse10-foldcrossvalidationandthesamepre-processingasin§4.
Purityresults.ThetoppartofTable4showsresultsonthedocumentclusteringtask.
Aswecansee,thetopicdistributionsextractedusingHiTRscorehigherthantheones
extractedusingLDAandPTMintermsofbothpurityandNMI.Thisshowstheability
ofHiTRtomakeP(t|d)morepure.Thetwo-levelre-estimatedtopicmodelsachieve
higherpurityvaluesthantheirrespectiveone-levelcounterpartsexceptthecombination
ofDRandTR,whichindicatesthatre-estimationateachlevelcontributestothepurity
of P(t|d). The combination of TR and DR is not effective in increasing purity over
itsone-levelcounterpartsonmostofthedatasets,indicatingthatTRandDRaddress
similarissues.ButwheneachofthemiscombinedwithTAR,thepurityofthetopic
distributionsincreases,implyingthatDR/TRandTARaddresscomplementaryissues.
ThebottompartofTable4showsresultsonthedocumentclassificationtask.HiTR
ismoreaccurateinestimatingP(t|d);itsaccuracyishigherthanthatofothertopic
models.Thehighervaluesinclassificationtask,comparedtoclusteringtask,indicatethat
themostprobabletopicdoesnotnecessarilycontainallinformationaboutthecontentof
adocument.Ifadocumentisaboutmorethanonetopic,theclassifierutilizesallP(t|d)
informationandperformsbetter.Therefore,thehigheraccuracyofHiTRinthistaskis
anindicatorofitsabilitytoassigndocument-specifictopicstodocuments.
7 Conclusions
We have proposed Hierarchical Topic model Re-estimation (HiTR), an approach for
measuringtopicaldiversityoftextdocuments.Itaddressestwomainissueswithtopic
models,topicgeneralityandtopicimpurity,whichnegativelyaffectmeasuringtopical
diversityscoresinthreeways.First,theexistenceofdocument-unspecificwordswithin
P(w|d)(thedistributionofwordswithindocuments)yieldsgeneraltopicsandimpure
topics.Second,theexistenceoftopic-unspecificwordswithinP(w|t)(thedistribution
ofwordswithintopics)yieldsimpuretopics.Third,theexistenceofdocument-unspecific
topicswithinP(t|d)(thedistributionoftopicswithindocuments)yieldsgeneraltop-
ics. We have proposed three approaches for removing unnecessary or even harmful
informationfromprobabilitydistributions,whichwecombineinourmethodforHiTR.
EstimateddiversityscoresfordocumentsusingHiTRaremoreaccuratethanthose
obtainedusingthecurrentstate-of-the-arttopicmodelingmethodPTM,orageneral
purpose topic model such as LDA. HiTR outperforms PTM because it adapts topic
modelsforthetopicaldiversitytask.Thequalityoftopicmodelsformeasuringtopical
3Availableathttp://www.ai.mit.edu/people/˜jrennie/20Newsgroups/
4Availableathttp://disi.unitn.it/moschitti/corpora.htm
