Bayesian Learning of Hierarchical Multinomial Mixture Models of Concepts for Automatic Image Annotation

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1 Bayesan earnng of Herarchca Mutnoma Mxture Modes of Concepts for Automatc Image Annotaton Ru Sh Tat-Seng Chua Chn-Hu ee 2 and Sheng Gao 3 Schoo of Computng Natona Unversty of Sngapore Sngapore Schoo of ECE Georga Insttute of Technoogy Atanta GA 3332 USA 3 Insttute for Infocomm Research Sngapore 963 {shru chuats}@comp.nus.edu.sg ch@ece.gatech.edu gaosheng@2r.a-star.edu.sg Abstract. We propose a nove Bayesan earnng framework of herarchca mxture mode by ncorporatng pror herarchca knowedge nto concept representatons of mut-eve concept structures n mages. Characterzng mage concepts by mxture modes s one of the most effectve technques n automatc mage annotaton (AIA) for concept-based mage retreva. However t aso poses probems when arge-scae modes are needed to cover the wde varatons n mage sampes. To aevate the potenta dffcutes arsng n estmatng too many parameters wth nsuffcent tranng mages we treat the mxture mode parameters as random varabes characterzed by a ont conugate pror densty of the mxture mode parameters. Ths factates a statstca combnaton of the kehood functon of the avaabe tranng data and the pror densty of the concept parameters nto a we-defned posteror densty whose parameters can now be estmated va a maxmum a posteror crteron. Expermenta resuts on the Core mage dataset wth a set of 37 concepts ndcate that the proposed Bayesan approach acheved a maxmum F measure of.69 whch outperforms many state-of-the-art AIA agorthms. Introducton It s sad that a pcture s worth a thousand words. Foowng the advances n computng and Internet technooges the voume of dgta mage and vdeo s ncreasng rapdy. The chaenge s how to use these arge and dstrbuted mage coectons to ncrease human productvty n the reuse of vauabe assets and the retreva of nformaton n domans such as crme preventon medcne and pubshng. Thus effectve toos to automatcay ndex mages are essenta n order to support appcatons n mage retreva. In partcuar automatc mage annotaton has become a hot topc to factate content-based ndexng of mages. Automatc mage annotaton (AIA) refers to the process of automatcay abeng the mage contents wth a predefned set of keywords or concepts representng mage semantcs. It s used prmary for mage database management. Annotated mages can be retreved usng keyword-based search whe non-annotated mages can ony be found usng content-based mage retreva (CBIR) technques whose performance eves are st not good enough for practca mage retreva appcatons. Thus AIA ams to annotate the mages as accuratey as possbe to support keyword-based mage H. Sundaram et a. (Eds.): CIVR 26 NCS 47 pp Sprnger-Verag Bern Hedeberg 26

2 Bayesan earnng of Herarchca Mutnoma Mxture Modes of Concepts 3 search. In ths paper we oosey use the term word and concept nterchangeaby to denote text annotatons of mages. Most approaches to AIA can be dvded nto two categores. The AIA modes n the frst category focus on fndng ont probabtes of mages and concepts. Cooccurrence mode (CO) [2] transaton mode (TR) [3] and cross-meda reevance mode (CMRM) [7] are a few exampes n ths category. To represent an mage those modes frst segment the mage nto a coecton of regons and quantze the vsua features from mage regons nto a set of regon custers (so-caed bobs). Gven a tranng mage corpus represented by a coecton of bobs many earnng agorthms have been deveoped to estmate the ont probabty of the concepts and bobs. In the annotaton phase the top concepts that maxmze such a ont probabty are assgned as concept assocated wth the test mage. To smpfy the ont densty characterzaton the concepts and bobs for an mage are often assumed to be mutuay ndependent [7]. As ponted out n [2] there s some contradcton wth ths naïve assumpton because the annotaton process s based on the Bayes decson rue whch rees on the dependency between concepts and bobs. In the second category of approaches each concept corresponds to a cass typcay characterzed by a mxture mode. AIA s formuated as a mut-cass cassfcaton probem. In [2] the probabty densty functon for each cass was estmated by a tree structure whch s a coecton of mxtures organzed herarchcay. Gven a predefned concept herarchy the approach n [4] focused on fndng an optma number of mxture components for each concept cass. Dfferent from approaches n [2] and [4] ontooges are used n [4] to bud a herarchca cassfcaton mode (HC) wth a concept herarchy derved from WordNet [] to mode concept dependences. Ony one mxture component was used to mode each concept cass. An mproved estmate for each eaf concept node was obtaned by shrnkng ts M (maxmum kehood) estmate towards the M estmates of a ts ancestors tracng back from that eaf to the root. A mut-topc text categorzaton (TC) approach to AIA was proposed n [5] by representng an mage as a hgh-dmenson document vector wth assocatons to a set of mutpe concepts. When more mxture components are needed to cover arger varatons n mage sampes t often eads to poor AIA performance due to the nsuffcent amount of tranng sampes and naccurate estmaton of a arge number of mode parameters. To tacke ths probem we ncorporate pror knowedge nto the herarchca concept representaton and propose a new Bayesan earnng framework caed BHMMM (Bayesan Herarchca Mutnoma Mxture Mode) to estmate the parameters of these concept mxture modes. Ths factates a statstca combnaton of the kehood functon of the avaabe tranng data and the pror densty of the concept parameters nto a we-defned posteror densty whose parameters can now be estmated va a maxmum a posteror (MAP) crteron. Expermenta resuts on the Core mage dataset wth 37 concepts ndcate that our proposed framework acheved an average per-concept F measure of.69 whch outperforms many state-of-the-art AIA technques. The rest of the paper s organzed as foows. In Secton 2 we address the key ssues n genera mxture modes and formuate the AIA probem usng herarchca Bayesan mutnoma mxture modes. In Secton 3 we dscuss budng concept herarches from WordNet. Two concept modes namey two-eve and mut-eve herarchca modes or T-HM and M-HM for short are proposed to specfy the

3 4 R. Sh et a. hyperparameters needed to defne the pror densty and perform the MAP estmaton of the concept parameters. Expermenta resuts for a 37-concept AIA task on the Core dataset and performance comparsons are presented n Secton 4. Fnay we concude our fndngs n Secton 5. 2 Probem Formuaton Snce mxture modes are used extensvey n our study we frst descrbe them n deta. In [3 7] any mage can be represented by an mage vector I = (n n 2 n ) where s the tota number of bobs and n ( ) denotes the observed count of the th bob n mage I. Gven a tota of J mxture components and the th concept c the observed vector I from the concept cass c s assumed to have the foowng probabty: J pi ( ) w pi ( θ ) Λ = = where Λ = {W Θ } s the parameter set for the above mxture mode ncudng mxture weght set W { } J J = w ( = w = ) and mxture parameter set Θ= { θ } J. = = pi ( θ ) s the th mxture component to characterze the cass dstrbuton. In ths paper we use θ to denote the mxture parameters of concept cass c and θ to denote the parameters of the th mxture component of the concept cass c. In ths study we assume that each mxture component s modeed by mutnoma dstrbuton as foows: n θ = () pi ( θ ) (2) where θ = ( θ θ 2... θ ) θ > θ = and each eement θ ( ) = represents the probabty of the th bob occurrng n the th mxture component of the th concept cass. Now for a tota of N concepts we are gven a coecton of ndependent tranng mages D (I t D ) for each concept cass c the parameters n set Λ can be estmated wth a maxmum kehood (M) crteron as foows: D pd pi t Λ Λ t= Λ = arg max og ( Λ ) = arg max og ( Λ ) (3) We foowed the EM agorthm [3] to estmate the mode parameter Λ wth M crteron. In ths foowng we w use ths mode as our basene. Athough the mxture mode s a smpe way to combne mutpe smper dstrbutons to form more compex ones the maor shortcomng of mxture mode s that there are usuay too many parameters to be estmated but not enough tranng mages for each concept. In cases when there are arger varatons among the mage exampes more mxture components are needed to cover such dverstes. Ths probem s partcuary severe for natura mages that tend to have arge varatons among them. Furthermore for more

4 Bayesan earnng of Herarchca Mutnoma Mxture Modes of Concepts 5 genera concepts there are key to be arger varatons among the mages too. Fgure shows some mages from the genera hawa concept cass. It s cear a arge-scae mxture mode s needed to mode ths partcuar concept. Fg.. Image exampes from hawa One way to enhance the M estmates s to ncorporate pror knowedge nto modeng by assumng the mxture parameters n θ as random varabes wth a ont pror densty p ( θ ϕ ) wth a set of parameters ϕ (often referred to as hyperparameters). The posteror probabty of observng the tranng set can now be evauated as: D J t θ t= = p( Λ D) = a { [ w p( I )]} p ( Θ ϕ ) (4) where a s a scang factor that depends on D. In contrast to conventona M estmaton shown n Eq. (3) we can mpose a maxmum a posteror (MAP) crteron to estmate the parameters as foows: D J map p D w p I t θ p Λ Λ t= = Λ = arg max og ( Λ ) = arg max og{ [ ( )]} ( Θ ϕ ) (5) Generay speakng the defnton of the pror densty p may come from subect matter consderatons and/or from prevous experences. Due to the compexty of the data set for new appcatons we often do not have enough experences to specfy the hyperparameters. However n most practca settngs we do have pror doman knowedge whch descrbes the dependences among concepts often n terms of a herarchca structure. Thus based on the posteror densty n Eq. (4) we propose a new Bayesan herarchca mutnoma mxture mode (BHMMM) to characterze the herarchca concept structure. The basc dea behnd the proposed BHMMM s that the mxtures from the most dependent concepts share the same set of hyperparameters and these concept mxture modes are constraned by a common pror densty parameterzed by ths set. Ths s reasonabe snce gven a concept (say eopard ) the mages from ts most dependent concepts (say tger ) are often reated and can be used as pror knowedge. Obvousy how to defne most dependent depends on our pror doman knowedge. For exampe Fg.2a shows the smpest two-eve concept herarchy n whch a the concepts (c c 2 c N) are derved from the root node abeed entty. The structure of ths two-eve herarchca mode (T-HM) s shown n Fg.2b n whch a the mxture parameters share ony one common pror densty wth the same hyperparameter setϕ. The advantage of usng such a two-eve concept herarchy s that we don t need any pror doman knowedge. However the two-eve concept herarchy can not capture a the concept dependences accuratey. For nstance there s not much

5 6 R. Sh et a. entty θ θ 2 ϕ... θ J θ N θ N2... θ NJ c c 2 c N D D N (a) Two-eve concept herarchy c c c 2 c M (b) Two-eve Herarchca Mode (T-HM) ϕ θ 2 θ... θ D J (c) Sub-tree of mut-eve concept herarchy (d) Mut-eve HM (M-HM) Fg. 2. An ustraton of the proposed BHMMM dependency between the concepts of budngs street and the concept of tger. To better mode the concept dependences we frst derve a concept herarchy through WordNet n Secton 3.. Fg. 2c shows a sub-tree of mut-eve concept herarchy n whch the concepts (c c 2 c M) are derved from ther parent node abeed c. We then extend the two-eve to mut-eve herarchca mode (M-HM) by characterzng the pror densty parameters for the th concept mxture mode wth a separate set of hyperparametersϕ as shown n Fg 2d. Then the mxtures from concepts c c 2 c M share the same set of hyperparametersϕ. Ceary more hyperparameters are needed n M-HM than n T-HM. We w compare the two modes n Secton 3. 3 Herarchca Modes 3. Budng Concept Herarchy As dscussed n Secton 2 we are nterested n accuratey mode the concept dependences whch requres fndng reatonshps between concepts. Ontooges such as the WordNet [] are convenent specfcatons of such reatonshps. WordNet s an eectronc thesaurus to organze the meanng of Engsh nouns verbs adectves and adverbs nto synonym sets and are used extensvey n exca semantcs acquston [9]. Every word n WordNet has one or more senses each of whch has a dstnct set of reated words through other reatons such as hypernyms hyponyms or hoonyms. For exampe the word path s a concept n our corpus. Path has four senses n WordNet and each sense s characterzed by a sequence of words (hypernyms): (a) path course acton actvty abstract entty; (b) path way artfact obect entty; (c) path route ne ocaton obect entty and (d) path track ne ocaton obect entty. Thus the key for budng a concept herarchy s to dsambguate the senses of words. Snce the words used as annotatons n our data set (Core CD) are nouns we ony use the hypernym reaton whch ponts to a word that s more generc than a gven

6 Bayesan earnng of Herarchca Mutnoma Mxture Modes of Concepts 7 word n order to dsambguate the sense of words. We further assume that one word corresponds to ony one sense n the whoe corpus. Ths s reasonabe as a word naturay has ony one meanng wthn a context. Wth ths assumpton we adopt the basc dea that the sense of a word s chosen f the hypernyms that characterze ths sense are shared by ts co-occurred words n our data set. For exampe the co-occurred words of path are tree mountan wa fower and so on. Thus path way artfact obect entty s chosen snce ths sense s mosty shared by these co-occurred words of path. Our approach for dsambguatng the senses of words s sar to that used n []. After ths step of word sense dsambguaton every word s assgned a unque sense characterzed by ts hypernyms. Thus we can easy bud a mut-eve concept herarchy wth entty as the root node of the overa concept herarchy. 3.2 Defnton of Pror Densty Based on the MAP formuaton n Eq. (5) three key ssues need to be addressed: () choosng the form of the pror densty () specfcaton of the hyperparameters and () MAP estmaton. It s we-known that a Drchet densty s the conugate pror for estmatng the parameters of mutnoma dstrbutons so that the posteror dstrbuton has a sar form to the Drchet densty whch makes t easy to estmate ts parameters. Such methods have been used successfuy n automatc speech recognton for adaptve estmaton of hstograms mxture gans and Markov chans [6 9]. We adopt Drchet dstrbuton as the pror dstrbuton p wth hyperparameterϕ (as n Fgures 2b and 2d) as foows: Γ( ϕ ) = ( ϕ ) p ( θ ϕ ) = θ Γ( ϕ ) = = where ϕ = ( ϕ ϕ2... ϕ ) or Γ( ϕ ) = ϕ p ( θ ϕ) = θ Γ( ϕ ) = = ( ) ϕ > and the hyperparameter ϕ can be nterpreted as pror observaton counts for the th bob occurrng n the th concept cass and Γ( x) s the Gamma functon. As dscussed n Secton 2 the performances of the proposed BHMMM framework depend on the structure of the concept herarchy. Ths s reated to how we ntend to specfy the hyperparameters. The remanng ssue s the estmaton of hyperparameters whch w be addressed next. 3.3 Specfyng Hyperparameters Based on Concept Herarchy We frst dscuss how to specfy hyperparameters based on two-eve concept herarchy as shown n Fgures 2a and 2b. If we assume that a mxture parameters θ share the same set of hyperparameters ϕ we can then adopt an emprca Bayes approach [6] to estmate these hyperparameters. et Θ = { θ θ 2... θ N } denote the mxture parameter set estmated wth M crteron as n Eq. (3). We then pretend to vew Θ as a set of random sampes from the Drchet pror p( ϕ ) n Eq. (6). Thus the M estmate of ϕ maxmzes the ogarthm of the kehood functon og p( Θ ϕ). As (6)

7 8 R. Sh et a. ponted out n [] there exsts no cosed-form souton to ths M estmate and the fxed-pont teratve approach [] can be adopted to sove for the M estmate based on a premnary estmate of ϕ that satsfes the foowng: Ψ ( ϕ ) =Ψ ( ϕ ) + og θ N J new = N J = = (7) where dγ( x) Ψ ( x) = s known as the dgamma functon. More detas can be found dx n []. For characterzng mut-eve concept herarchy we assume that a mxture parameters θ n the th concept share the same set of hyperparameters ϕ then we can use the data n D to obtan a premnary M estmate θ and pretend to vew θ as a set of random sampes from the Drchet pror p ( ) ϕ n Eq. (6). Then the M estmate of ϕ can be soved by maxmzng the og-kehood og p( θ ϕ ). The above fxed-pont teratve approach [] can agan be adopted to sove for the M estmate based on a premnary estmate of ϕ that satsfes the foowng: Ψ ( ϕ ) =Ψ ( ϕ ) + ogθ J new = J = (8) It s cear that the concept-specfc hyperparameter estmate ϕ uses ess data n Eq. (8) than those n Eq. (7) for genera hyperparameter estmateϕ. 3.4 MAP Estmaton of Mxture Mode Parameters Wth the pror densty gven n Eq. (6) and the hyperparameters specfed n Eq. (7) or (8) we are now ready to sove MAP estmaton n Eq. (5) as foows: By traversng the nodes one by one from eft to rght n the same eve and from root eve down to the eaf eve for each node c n the concept herarchy: et c p denote the parent node of c and p ( ϕ p ) denote the pror densty functon for the mxture mode parameters of c p we have: D J map p D w p I t θ p ϕp Λ Λ t= = where ϕp = ( ϕp ϕp2... ϕp ) ϕ p >. Λ = argmax og ( Λ ) = argmaxog{ [ [ ( )]} ( Θ ) (9) If c has the chd node then the pror densty functon p ( ) ϕ for mxture parameters of c can be cacuated by the approach descrbed n Secton 4. ϕ = arg max og ( θ ϕ ) ϕ We smpy extend the EM agorthm n [3] to sove Eq. (9). Gven a premnary estmate of Λ the EM agorthm can be descrbed as foows: new p

8 Bayesan earnng of Herarchca Mutnoma Mxture Modes of Concepts 9 new new E-step: w = w θ = θ Λ {{ } J { } J = w = θ = } M-step: nt + ϕp w ( θ ) pi ( t θ ) p ( θ ϕp) w = t Λ = = J J nt + ϕp pi ( t θ ) p ( θ ϕp) w w ( θ ) = = = D D p( It Λ ) t= p( It Λ ) ( nt+ ϕp ) new t=. D θ = D p( It Λ ) ( nt + ϕp ) t= = p( I ) w new = Here D denotes the sze of tranng set D for c n t ( ) denotes the observed count of the th bob n the mage I t D and p( It Λ ) s the probabty that the th mxture component fts the mage I t gven the parameter Λ. 4 Testng Setup and Expermenta Resuts Foowng [3 7] we conduct our experments on the same Core CD data set consstng of 45 mages for tranng and 5 mages for testng. The tota number of regon custers (bobs) s =5. In ths corpus there are 37 concepts n the tranng set but ony 263 such concepts appear n the testng set wth each mage assgned -5 concepts. After the dervaton of concept herarchy as dscussed n Secton 3. we obtaned a concept herarchy contanng a tota of 53 concepts ncudng 322 eaf concepts and 9 non-eaf concepts. The average number of chdren of non-eaf concepts s about 3. If a non-eaf concept node n the concept herarchy doesn t beong to the concept set n Core CD corpus then ts tranng set w consst of a the mages from ts chd nodes. As wth the prevous studes on ths AIA task the AIA performance s evauated by comparng the generated annotatons wth the actua mage annotatons n the test set. We assgn a set of fve top concepts to each test mage based on ther kehoods.. Tabe. Performances of our approaches Modes (mxture number) Basene (J=5) Basene T-HM (J=5) T-HM M-HM (J=5) M-HM # of concepts (reca>) Mean Per-concept metrcs on a 263 concepts on the Core dataset Mean Precson Mean Reca Mean F We frst compare the performances of T-HM and M-HM wth the basene mxture mode. In order to hghght the abty to cover arge varatons n the mage set we seect two dfferent numbers of mxtures (5 and 25) to emuate mage varatons.

9 R. Sh et a. These two numbers are obtaned by our emprca experences. The resuts n terms of averagng precson reca and F are tabuated n Tabe. From Tabe we can draw the foowng observatons: (a) The performance of basene s worse than that of basene (J=5). Ths s because the number of tranng mage exampes are same n both cases and we are abe to estmate the sma number of parameters for basene (J=5) more accuratey. Ths resut hghghts the mtaton of mxture mode when there are arge varatons n mage sampes. (b) The F performances of T-HM and M-HM are better than that of the basene (J=5). Ths ndcates that the proper use of pror nformaton s mportant to our AIA mxture mode. (c) Compared wth T-HM (J=5 25) M-HM (J=5 25) acheves about 2% and 2% mprovements on F measure. Ths shows that the use of concept herarchy n M-HM resuts n more accurate estmate of pror densty snce M-HM permts a concept node to ony nhert the pror nformaton from ts parent node. Overa M-HM acheves the best performance of.69 n terms of F measure. Tabe 2. Performances of state-of-the-art AIA modes Modes CO [82] TR [38] CMRM [78] HC [4] #concepts wth reca> Mean per-concept resuts on a 263 concepts on the Core dataset Mean Per-concept Precson Mean Per-concept Reca For further comparson we tabuate the performances of a few representatve stateof-the-art AIA modes n Tabe 2. These are a dscrete modes whch used the same expermenta settngs as n Tabe. From Tabe 2 we can draw the foowng observatons: (a) Among these modes HC acheved the best performance n terms of precson and reca measures snce HC aso ncorporated the concept herarchy derved from the WordNet nto the cassfcaton. Ths further renforces the mportance of utzng the herarchca knowedge for AIA task. (b) Compared wth HC whch used ony one mxture for each concept cass and adopted M crteron to estmate the parameters HM-M acheved about 4% and 28% mprovements on the measure of mean per-concept precson and mean per-concept reca respectvey. Ths demonstrates agan that HM-M s an effectve strategy to AIA task. To anayze the benefts of our strateges we perform a second test by dvdng the testng concepts nto two sets desgnated as prmtve concept (PC) and Tabe 3. Performances of our approaches n PC and NPC Modes (mxture components) Basene (J=5) T-HM M-HM Basene (J=5) T-HM M-HM Concept Spt Resuts wth 37 concepts n PC Resuts wth 26 concepts n NPC #concepts (reca>) Mean Per-concept F

10 Bayesan earnng of Herarchca Mutnoma Mxture Modes of Concepts non-prmtve concept (NPC) sets. The PC concepts such as tger graffe and pyramd have reatvey concrete vsua forms. On the other hand the NPC concepts such as andscape ceremony and cty do not exhbt concrete vsua descrptons. The tota number of concepts s 37 and 26 for NPC and PC sets respectvey. We expect the use of M-HM that utzes the concept herarchy to be more benefca to the concepts n the NPC set than those n the PC set. In ths test we seect the best performng system n each category namey Basene (J=5) T-HM and M-HM. The resuts on the PC and NPC sets are presented n Tabe 3 for the F measure. It s cear that M-HM acheves the best performance on the NPC set among the three cases. M-HM can detect 3 more concepts on the NPC set as compared to the basene but ony 5 more concepts on the PC set. In terms of the F measure M-HM acheves about 47% and 42% mprovement over the basene on the NPC and PC sets respectvey. Overa both M-HM and T-HM outperform the Basene on both the PC and NPC sets. The M-HM mode beng abe to take fu advantage of the mut-eve concept structure to mode the concepts n the NPC set performs better than T-HM mode. Tabe 4. Mean number of tranng exampes Concept Spt Number of concept casses n each group Mean number of tranng exampes for each concept cass () NPC #concepts (reca>) (2) NPC #concepts (reca=) (3) PC #concepts (reca>) (4) PC #concepts (reca=) To anayze the effect of the number of tranng exampes on the performances we further anayze the resuts by spttng the testng concepts nto four groups two concept groups for NPC wth reca> and reca= and two concept groups for PC wth reca> and reca=. In arrvng at the number of concept casses of 77 (or 54) for NPC (or PC) we smpy combne a the casses wth reca> obtaned from the three methods (Basene T-HM and M-HM). From the resuts presented n Tabe 4 the mean number of tranng exampes from () and (3) s sgnfcanty more than that n (2) and (4). Athough we ddn t nvestgate the quatatve reatonshps between the number of tranng exampes and the performances ths resut ceary states that f the number of tranng exampes s too sma our proposed BHMMM coud not acheve good performances. So from ths perspectve how to acqure more tranng exampes for concept casses s an mportant probem whch we w tacke n our future work. 5 Concuson In ths paper we ncorporated pror knowedge nto herarchca representaton of concepts to factate modeng of mut-eve concept structures. To aevate the potenta dffcutes arsng n estmatng too many parameters wth nsuffcent tranng mages we proposed a Bayesan herarchca mxture mode framework. By

11 2 R. Sh et a. treatng the mxture mode parameters as random varabes characterzed by a ont conugate pror densty t factates a statstca combnaton of the kehood functon of the avaabe tranng data and the pror densty of the concept parameters nto a we-defned posteror densty whose parameters can now be estmated va a maxmum a posteror crteron. On the one hand when no tranng data are used MAP estmate s the mode of the pror densty. On the other hand when a arge of amount of tranng data s avaabe the MAP estmate can be shown to asymptotcay converge to the conventona maxmum kehood estmate. Ths desrabe property makes the MAP estmate an dea canddate for estmatng a arge number of unknown parameters n arge-scae mxture modes. Expermenta resuts on the Core mage dataset show that the proposed BHMMM approach usng a mut-eve structure of 37 concept wth a maxmum of 25 mxture components per concept acheves a mean F measure of.69 whch outperforms many state-of-the-art technques for automatc mage annotaton. References [] K. Barnard P. Duyguu and D. Forsyth Custerng Art In Proceedngs of CVPR 2. [2] G. Carnero and N. Vasconceos Formuatng Semantc Image Annotaton as a Supervsed earnng Probem In Proceedngs of CVPR 25. [3] P. Duyuu K. Barnard N. de Fretas and D. Forsyth Obect Recognton as Machne Transaton: earnng a excon for a Fxed Image Vocabuary In Proc. of ECCV 22. [4] J. P. Fan H. Z. uo and Y.. Gao earnng the Semantcs of Images by Usng Unabeed Sampes In Proceedngs of CVPR 25. [5] S. Gao D.-H. Wang and C.-H. ee Automatc Image Annotaton through Mut-Topc Text Categorzaton In Proceedngs of. ICASSP Tououse France May 26. [6] Q. Huo C. Chan and C.-H. ee Bayesan Adaptve earnng of the Parameters of Hdden Markov Mode for Speech Recognton IEEE Trans. Speech Audo Processng vo. 3 pp Sept [7] J. Jeon V. avrenko and R. Manmatha Automatc Image Annotaton and Retreva Usng Cross-Meda Reevance Modes In Proceedngs of the 26 th ACM SIGIR 23. [8] V. avrenko R. Manmatha and J. Jeon A Mode for earnng the Semantcs of Pctures In Proceedngs of the 6 th Conference on NIPS 23. [9] C.-H. ee and Q. Huo On Adaptve Decson Rues and Decson Parameter Adaptaton for Automatc Speech Recognton In Proceedngs of the IEEE vo. 88 no. 8 Aug 2. [] T. Mnka Estmatng a Drchet Dstrbuton 23. [] G. A. Mer R. Beckwth C. Febaum D. Gross and K. J. Mer Introducton to WordNet: an on-ne exca database Int. Jour. of excography vo. 3 pp [2] Y. Mor H. Takahash and R. Oka Image-to-Word Transformaton Based on Dvdng and Vector Quantzng Images wth Words In Proceedngs of MISRM 999. [3] J. Novovcova and A. Mak Appcaton of Mutnoma Mxture Mode to Text Cassfcaton Pattern Recognton and Image Anayss NCS 2652 pp [4] M. Srkanth J. Varner M. Bowden and D. Movan Expotng Ontooges for Automatc Image Annotaton In Proceedngs of the 28 th ACM SIGIR 25.