Simultaneous Ranking and Clustering of Sentences: A Reinforcement Approach to Multi-Document Summarization

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1 Sulaneous Ranng and Cluserng of Senences: A Renforceen Approach o Mul-Docuen Suarzaon Xaoyan Ca, Wenje L, You Ouyang, 2 Hong Yan Deparen of Copung, The Hong ong Polyechnc Unvery {csxca,cswjl,csyouyang}@cop.polyu.edu.h 2 Deparen of Logscs and Mare Sudes, The Hong ong Polyechnc Unvery lghyan@polyu.edu.h Absrac Mul-docuen suarzaon as o produce a concse suary ha conans salen nforaon fro a se of source docuens. In hs feld, senence ranng has hhero been he ssue of os concern. Snce docuens ofen cover a nuber of opc hees wh each hee represened by a cluser of hghly relaed senences, senence cluserng was recenly explored n he leraure n order o provde ore nforave suares. Exsng cluserbased ranng approaches appled cluserng and ranng n solaon. As a resul, he ranng perforance wll be nevably nfluenced by he cluserng resul. In hs paper, we propose a renforceen approach ha ghly negraes ranng and cluserng by uually and ulaneously updang each oher so ha he perforance of boh can be proved. Experenal resuls on he DUC daases deonsrae s effecveness and robusness. Inroducon Auoac ul-docuen suarzaon has drawn ncreang aenon n he pas wh he rapd growh of he Inerne and nforaon exploon. I as o condense he orgnal ex no s essenal conen and o ass n flerng and selecon of necessary nforaon. So far exracve suarzaon ha drecly exracs senences fro docuens o copose suares s sll he ansrea n hs feld. Under hs fraewor, senence ranng s he ssue of os concern. Though radonal feaure-based ranng approaches and graph-based approaches eployed que dfferen echnques o ran senences, hey have a leas one pon n coon,.e., all of he focused on senences only, bu gnored he nforaon beyond he senence level (referrng o Fgure (a. Acually, n a gven docuen se, here usually exs a nuber of hees (or opcs wh each hee represened by a cluser of hghly relaed senences (Harabagu and Lacausu, 25; Hardy e al., 22. These hee clusers are of dfferen ze and especally dfferen porance o ass users n undersandng he conen n he whole docuen se. The cluser level nforaon s supposed o have foreseeable nfluence on senence ranng. Ranng Ranng Cluserng Ranng Cluserng (a (b (c Fgure. Ranng vs. Cluserng In order o enhance he perforance of suarzaon, recenly cluser-based ranng approaches were explored n he leraure (Wan and Yang, 26; Sun e al, 27; Wang e al, 28a,b; Qazvnan and Radev, 28. Norally hese approaches appled a cluserng algorh o oban he hee clusers frs and hen raned he senences whn each cluser or by explorng he neracon beween senences and obaned clusers (referrng o Fgure (b. In oher words, cluserng and ranng are regarded as wo ndependen processes n hese approaches alhough he cluser-level nforaon has been ncorporaed no he senence ranng process. As a resul, 34 Proceedngs of he 23rd Inernaonal Conference on Copuaonal Lnguscs (Colng 2, pages 34 42, Bejng, Augus 2

2 he ranng perforance s nevably nfluenced by he cluserng resul. To help allevae hs proble, we argue n hs paper ha he qualy of ranng and cluserng can be boh proved when he wo processes are uually enhanced (referrng o Fgure (c. Based on, we propose a renforceen approach ha updaes ranng and cluserng neracvely and eravely o ul-docuen suarzaon. The an conrbuons of he paper are hree-fold: ( Three dfferen ranng funcons are defned n a b-ype docuen graph consruced fro he gven docuen se, naely global, whncluser and condonal ranngs, respecvely. (2 A renforceen approach s proposed o ghly negrae ranng and cluserng of senences by explorng er ran dsrbuons over he clusers. (3 Thorough experenal sudes are conduced o verfy he effecveness and robusness of he proposed approach. The res of hs paper s organzed as follows. Secon 2 revews relaed wor n cluser-based ranng. Secon 3 defnes ranng funcons and explans renforced ranng and cluserng process and s applcaon ul-docuen suarzaon. Secon 4 presens experens and evaluaons. Secon 5 concludes he paper. 2 Relaed Wor Cluserng has becoe an ncreangly poran opc wh he exploon of nforaon avalable va he Inerne. I s an poran ool n ex nng and nowledge dscovery. Is ably o auoacally group lar exual objecs ogeher enables one o dscover hddelary and ey conceps, as well as o suarze a large aoun of ex no a sall nuber of groups (aryps e al., 2. To suarze a scenfc paper, Qazvnan and Radev (28 presened wo senence selecon sraeges based on he clusers whch were generaed by a herarchcal aggloeraon algorh appled n he caon suary newor. One was called C-RR, whch sared wh he larges cluser and exraced he frs senence fro each cluser n he order hey appeared unl he suary lengh l was reached. The oher was called C-LexRan, whch was lar o C-RR bu adoped LexRan o ran he senences whn each cluser and chose he os salen one. Meanwhle, Wan and Yang (28 proposed wo odels o ncorporae he cluser-level nforaon no he process of senence ranng for generc suarzaon. Whle he Cluser-based Condonal Marov Rando Wal odel (CluserCMRW ncorporaed he cluser-level nforaon no he ex graph and anpulaed clusers and senences equally, he Cluser-based HITS odel (CluserHIT reaed clusers and senences as hubs and auhores n he HITS algorh. Bedes, Wang e al. (28 proposed a language odel o ulaneously cluser and suarze docuens. Nonnegave facorzaon was perfored on he erdocuen arx ung he er-senence arx as he base so ha he docuen-opc and senence-opc arces could be consruced, fro whch he docuen clusers and he correspondng suary senences were generaed ulaneously. 3 A Renforceen Approach o Mul-docuen Suarzaon 3. Docuen B-ype Graph Frs of all, le s nroduce he senence-er b-ype graph odel for a se of gven docuens D, based on whch he algorh of renforced ranng and cluserng s developed. Le G =< V, E, W >, where V s he se of verces ha conss of he senence se S = { s, s2,, sn} and he er se T = {, 2,, },.e., V = S T, E s he se of edges ha connec he verces,.e., E = { < v, v j > v, v j V}. W s he adjacency arx n whch he eleen w j represens he wegh of he edge connecng v and v j. Forally, W can be decoposed no four blocs,.e., W SS, W ST, W TS and W TT, each represenng a sub-graph of he exual objecs ndcaed by he subscrps. W can be wren as WSS W =, WTS WTT where W ST s he nuber of es he er j appears n he senence s. W SS (, s 35

3 he nuber of coon ers n he senences s and s j. W TS s equal o W ST T as he relaonshps beween ers and senences are syerc. For plfcaon, n hs sudy we assue here s no drec relaonshps beween ers,.e., W TT =. In he fuure, we wll explore effecve ways o negrae er seanc relaonshps no he odel. 3.2 Bac Ranng Funcons Recall ha our ulae goal s senence ranng. As an ndspensable par of he approach, he bac ranng funcons need o be defned frs Global Ranng (whou Cluserng Le r ( s (=, 2,, n and r ( j (j=, 2,, denoe he ranng scores of he senence s and he er j n he whole docuen se, respecvely. Based on he assupons ha Hghly raned ers appear n hghly raned senences, whle hghly raned senences conan hghly raned ers. Moreover, a senence s raned hgher f conans any ers ha appear any oher hghly raned senences. we defne n = λ j + ( λ WSS r ( s j ( j= j= and n j = WTS ( j, r (. (2 = For calculaon purpose, r ( s and r ( j are noralzed by and j n j. ' j' ' = j' = Equaons ( and (2 can be rewren ung he arx for,.e., T WSS = λ + ( λ T WSS. (3 WTS T = WTS We call r ( and r (T he global ranng funcons, because a hs oen senence cluserng s no ye nvolved and all he senences/ers n he whole docuen se are raned ogeher. Theore: The soluon o r ( and r (T gven by Equaon (3 s he prary egenvecor of λ W W + ( λ W and ST λ W ( I ( λ W W, respecvely. TS SS ST Proof: Cobne Equaons ( and (2, we ge WTS WTS WSS = λ + ( λ WTS W W SS ST WTS WTS WSS = λ + ( λ WTS WSS As he erave process s a power ehod, s guaraneed ha r ( converges o he prary egenvecor of λ W ST WTS + ( λ W SS. Slarly, r (T s guaraneed o converge o he prary egenvecor of λ W ( I ( λ W W. TS SS Local Ranng (whn Clusers Assue now hee clusers have been generaed by ceran cluserng algorh, denoed as C = { C, C2,, C } where C (=, 2,, represens a cluser of hghly relaed senences S C whch conan he ers C ( TC ( C. The senences and ers whn he cluser C for a cluser b-ype graph wh he adjacency arx W C. Le r C ( S C and r C ( T C denoe he ranng scores of S C and T C whn C. They are calculaed by an equaolar o Equaon (3 by replacng he docuen level adjacency arx W wh he cluser level adjacency arx W C. We call r C ( S C and r C ( T C he whncluser ranng funcons wh respec o he cluser C. They are he local ranng funcons, n conras o r ( and r (T ha ran all he senences and ers n he whole docuen se D. We beleve ha wll benef senence overall ranng when nowng ore deals abou he ranng resuls a he fner granulary of hee clusers, nsead of a he coarse granulary of he whole docuen se. TS ST SS 36

4 3.2.3 Condonal Ranng (across Clusers To faclae he dscovery of ran dsrbuons of ers and senences over all he hee clusers, we furher defne wo condonal ranng funcons r ( S C and r ( T C. These ran dsrbuons are necessary for he paraeer esaon durng he renforceen process nroduced laer. The condonal ranng score of he er j on he cluser C,.e., r T C s drecly derved fro ( T C,.e., r ( j C = r C ( j f j C, and r ( j C = oherwse. I s furher noralzed as j C j C =. (4 j = j C Then he condonal ranng score of he senence s on he cluser C s deduced fro he ers ha are ncluded n s,.e., j = n j C C =. (5 W = j= ST j C Equaon (5 can be nerpreed as ha he condonal ran of s on C s hgher f any ers n s are raned hgher n C. Now we have senence and er condonal rans over all he hee clusers and are ready o nroduce he renforceen process. 3.3 Renforceen beween Whn- Cluser Ranng and Cluserng The condonal rans of he er j across he hee clusers can be vewed as a ran dsrbuon. Then he ran dsrbuon of he senence s can be condered as a xure odel over condonal ran dsrbuons of he ers conaned n he senence s. And he senence s can be represened as a - denonal vecor n he new easure space, n whch he vecors can be used o gude he senence cluserng updae. Nex, we wll explan he xure odel of senence and use EM algorh (Bles, 997 o ge he coponen coeffcens of he odel. Then, we wll presen he lary easure beween senence and cluser, whch s used o adjus he clusers ha he senences belong o and n urodfy whn-cluser ranng for he senences n he updaed clusers Senence Mxure Model For each senence s, we assue ha follows he dsrbuon r ( T o generae he relaonshp beween he senence s and he er se T. Ths dsrbuon can be condered as a xure odel over coponen dsrbuons,.e. he er condonal ran dsrbuons across hee clusers. We use γ, o denoe he probably ha s belongs o C, hen r ( T can be odeled as: T = γ, T C and γ, =. (6 = = γ, can be explaned as p ( C and calculaed by he Bayean equaon p ( C C p ( C, where p ( s C s assued o be r ( s C obaned fro he condonal ran of s on C as nroduced before and p ( C s he pror probably Paraeer Esaon We use EM algorh o esae he coponen coeffcens γ, along wh { p ( C }. A hdden varable C z, z {,2,, } s used o denoe he cluser label ha a senence er par ( s, j are fro. In addon, we ae he ndependen assupon ha he probably of s belongng o C and he probably of j belongng o C are ndependen,.e., p s, C = s C ( j p ( j C, where, j C s he probably of s and j boh belongng o C. Slarly, p ( j C s assued o be r ( j C. Le Θ be he paraeer arx, whch s a n arx Θ n = { γ, } ( =,, n; =,,. The bes Θ s esaed fro he relaonshps observed n he docuen b-ype graph,.e., W ST and W SS. The lelhood of generang all he relaonshps under he paraeer Θ can be calculaed as: ' L ( Θ, WSS = Θ WSS Θ n n W j W j = p j Θ ST (, p s j Θ SS (, (, (, = j= = j= 37

5 where p ( s, j Θ s he probably ha s and j boh belong o he sae cluser, gven he curren paraeer. As p ( s, s j Θ does no conan varables fro Θ, we only need o conder axzng he frs par of he lelhood n order o ge he bes esaon of Θ. Le L( Θ be he frs par of lelhood. Tang no accoun he hdden varable C z, he coplee log-lelhood can be wren as log L( Θ, CZ = log = j= = log (, j, Θ (, j, Θ Θ = j= = log = j= ( p (, j Θ Z W ST. In he E-sep, gven he nal paraeer Θ, whch s se o γ, = for all and, he expecaon of log-lelhood under he curren dsrbuon of C s: Z Q( Θ, Θ = E (log L( Θ W Θ ST, CZ f ( CZ, = log( p (, j = C, j, Θ + = = j= n log( = C Θ = C, j, Θ = = j= The condonal dsrbuon n he above equaon,.e., p ( = C, j, Θ, can be calculaed ung he Bayean rule as follows: = C, j, Θ, j = C, Θ = C Θ. (7 p ( C p ( j C p ( = C In he M-Sep, we frs ge he esaon of p ( C z = C by axzng he expecaon Q ( Θ, Θ. By nroducng a Lagrange ulpler λ, we ge he equaon below. [ Q( Θ, Θ + λ( = C ] = = C = = C, j, Θ + λ = C = = j= z C Thus, he esaon of p ( C z = C gven prevous Θ s = C, j, Θ = j= p = C = = j= (. (8 Then, he paraeers γ, can be calculaed wh he Bayean rule as C = C γ =. (9, s C C = C l By seng = Θ, he whole process can be repeaed. The updang rules provded n Equaons (7-(9 are appled a each eraon. Fnally Θ wll converge o a local axu. A lar esaon process has been adoped n (Sun e al., 29, whch was used o esae he coponen coeffcens for auhorconference newors. Θ Slary Measure Afer we ge he esaons of he coponen coeffcens γ, for s, s wll be represened as a denonal vecor = ( γ,, γ, 2,, γ,. The cener of each cluser can hus be calculaed accordngly, whch s he ean of s for all s n he sae cluser,.e., C Cener C =, C where C s he ze of C. Then he lary beween each senence and each cluser can be calculaed as he cone lary beween he,.e.,, C = 2 s ( l z s C ( l Cener ( l (. ( l 2 CenerC ( l Fnally, each senence s re-asgned o a cluser ha s he os lar o he senence. Based on he updaed clusers, whn-cluser ranng s updaed accordngly, whch rggers he nex round of cluserng refneen. I s expeced ha he qualy of clusers should be proved durng hs erave updae process nce he lar senences under new arbues wll be grouped ogeher, and eanwhle he qualy of ranng wll be proved along wh he beer clusers and 38

6 hus offers beer arbues for furher cluserng. 3.4 Enseble Ranng The overall senence ranng funcon f s defned as he enseble of all he senence condonal ranng scores on he clusers. f ( = α C, ( = where α s a coeffcen evaluang he porance of C. I can be forulaed as he noralzed cone lary beween a hee cluser and he whole docuen se for generc suarzaon, or beween a hee cluser and a gven query for query-based suarzaon. α [,] and α =. = Fgure 2 below suarzes he whole process ha deernes he overall senence enseble ranng scores. Inpu: The b-ype docuen graph G =< S T, E, W >, ranng funcons, he cluser nuber, ε =, Tre =., IerNu =. Oupu: senence fnal enseble ranng vecor f (.. ; 2. Ge he nal paron for S,.e. C, =,2,, calculae cluser ceners Cener C accordngly. 3. For (=; <IerNu && ε > Tre ; Calculae he whn-cluser ranng r C ( T, C r C ( S C and he condonal ranng r ( s C ; 5. Ge new arbue s for each senence s, and new arbue Cener C for each cluser C ; 6. For each senence n S 7. For = o 8. Calculae lary value ( s, C 9. End For +. Asgn o C, arg ax (, = C. End For 2. ε = Cener C + Cener C ax End For 5. For each senence s n S 6. For = o 7. f ( = α C = 8. End For 9. End For Fgure 2. The Overall Senence Ranng Algorh 3.5 Suary Generaon Iul-docuen suarzaon, he nuber of docuens o be suarzed can be very large. Ths aes nforaon redundancy appears o be ore serous ul-docuen suarzaon han n ngle-docuen suarzaon. Redundancy conrol s necessary. We apply a ple ye effecve way o choose suary senences. Each e, we copare he curren canddae senence o he senences already ncluded n he suary. Only he senence ha s no oo lar o any senence n he suary (.e., he cone lary beween he s lower han a hreshold s seleced no he suary. The eraon s repeaed unl he lengh of he senences n he suary reaches he lengh laon. In hs paper, he hreshold s se o.7 as always n our pas wor. 4 Experens and Evaluaons We conduc he experens on he DUC 24 generc ul-docuen suarzaon daase and he DUC 26 query-based uldocuen suarzaon daase. Accordng o as defnons, syses are requred o produce a concse suary for each docuen se (whou or wh a gven query descrpon and he lengh of suares s led o 665 byes n DUC 24 and 25 words n DUC 26. A well-recognzed auoac evaluaon ool ROUGE (Ln and Hovy, 23 s used n evaluaon. I easures suary qualy by counng overlappng uns beween sysegeneraed suares and huan-wren reference suares. We repor wo coon ROUGE scores n hs paper, naely ROUGE- and ROUGE-2, whch base on Un-gra ach and B-gra ach, respecvely. Docuens and queres are pre-processed by segenng senences and splng words. Sop words are reoved and he reanng words are seed ung Porer seer. 4. Evaluaon of Perforance In order o evaluae he perforance of renforced cluserng and ranng approach, we copare wh he oher hree ranng approaches: ( Global-Ran, whch does no apply cluserng and ply reles on he 39

7 senence global ranng scores o selec suary senences; (2 Local-Ran, whch clusers senences frs and hen ran senences whn each cluser. A suary s generaed n he sae way as presened n (Qazvnan and Radev, 28. The clusers are ordered by decreang ze; (3 Cluser-HITS, whch also clusers senences frs, bu hen regards clusers as hubs and senences as auhores n he HITS algorh and uses he obaned auhory scores o ran and selec senences. The clascal cluserng algorh -eans s used where necessary. For query-based suarzaon, he addonal query-relevance (.e. he cone lary beween senences and query s nvolved o re-ran he canddae senences chosen by he ranng approaches for generc suarzaon. Noe ha -eans requres a predefned cluser nuber. To avod exhausve search for a proper cluser nuber for each docuen se, we eploy he specra approach nroduced n (L e al., 27 o predc he nuber of he expeced clusers. Based on he senence lary arx ung he noralzed -nor, for s egenvalues λ (=,2,, n, he rao α = λ + / λ ( λ s 2 defned. If α α + >. 5 and α s sll close o, hen se =+. Tables and 2 below copare he perforance of he four approaches on DUC 24 and 26 accordng o he calculaed. DUC 24 ROUGE- ROUGE-2 Renforced Cluser-HITS Local-Ran Global-Ran Table. Resuls on he DUC 24 daase DUC 26 ROUGE- ROUGE-2 Renforced Cluser-HITS Local-Ran Global-Ran Table 2. Resuls on he DUC 26 daase I s no surprsed o fnd ha Global-Ran shows he poores perforance, when ulzes he senence level nforaon only whereas he oher hree approaches all negrae he addonal cluser level nforaon n varous ways. In addon, as resuls llusrae, he perforance of Cluser- HITS s beer han he perforance of Local-Ran. Ths can be anly creded o he ably of Cluser-HITS o conder no only he cluser-level nforaon, bu also he senence-o-cluser relaonshps, whch are gnored n Local-Ran. I s happy o see ha he proposed renforceen approach, whch ulaneously updaes cluserng and ranng of senences, consenly ouperfors he oher hree approaches. 4.2 Analys of Cluser Qualy Our orgnal nenon o propose he renforceen approach s o hope o generae ore accurae clusers and ranng resuls by uually refnng whn-cluser ranng and cluserng. In order o chec and onor he varaon rend of he cluser qualy durng he eraons, we defne he followng easure (, C C quan = (, (2 = ( s, s s C s C l,, j l where ( s, C C denoes he dsance beween he cluser cener and he border senence n a cluser ha s he farhes away fro he cener. The larger s, he ore copac he cluser s. ( s, s, on j s C, s C he oher hand, denoes he dsance beween he os dsan par of senences, one fro each cluser. The saller s, he ore separaed he wo clusers are. The dsance s easured by cone lary. As a whole, he larger quaeans he beer cluser qualy. Fgure 3 below plos he values of quan n each eraon on he DUC 24 and 26 daases. Noe ha he algorh converges n less han 6 rounds and 5 rounds on he DUC 24 and 26 daases, respecvely. The curves clearly show he ncreasen of quan and hus he proved cluser qualy. Quan DUC IerNu j l DUC26 Fgure 3. Cluser Qualy on DUC 24 and 26 j 4

8 Whle quan drecly evaluae he qualy of he generaed clusers, we are also que neresed n wheher he proved clusers qualy can furher enhance he qualy of senence ranng and hus consequenly rase he perforance of suarzaon. Therefore, we evaluae he ROUGEs n each eraon as well. Fgure 4 below llusraes he changes of ROUGE- and ROUGE-2 resul on he DUC 24 and 26 daases, respecvely. Now, we have coe o he pove concluon. ROUGE- ROUGE-2 DUC24 DUC IerNu IerNu Fgure 4. ROUGEs on DUC 24 and Ipac of Cluser Nubers In prevous experens, he cluser nuber s predced hrough he egenvalues of -nor noralzed senence lary arx. Ths nuber s jus he esaed nuber. The acual nuber s hard o predc accuraely. To furher exane how he cluser nuber nfluences suarzaon, we conduc he followng addonal experens by varyng he cluser nuber. Gven a docuen se, we le S denoe he senence se n he docuen se, and se n he followng way: = ε S, (3 where ε (, s a rao conrollng he expeced cluser nuber. The larger ε s, he ore clusers wll be produced. ε ranges fro. o.9 n he experens. Due o page laon, we only provde he ROUGE- and ROUGE-2 resuls of he proposed approach, Cluser-HITS and Local-Ran on he DUC 24 daase n Fgure 5. The lar curves are also observed on he 26 daase. ROUGE-2 ROUGE Cluser-HITS Local Ran Renforced ε ε Fgure 5. ROUGEs vs. ε on DUC 24 I s shown ha ( he proposed approach ouperfors Cluser-HITS and Local- Ran n alos all he cases no aer how he cluser nuber s se; (2 he perforances of Cluser-HITS and Local-Ran are ore senve o he cluser nuber and a large nuber of clusers appears o deerorae he perforances of boh. Ths s reasonable. Acually when ε geng close o, Local- Ran approaches o Global-Ran. These resuls deonsrae he robusness of he proposed approach. 5 Concluon In hs paper, we presen a renforceen approach ha ghly negraes ranng and cluserng ogeher by uually and ulaneously updang each oher. Experenal resuls deonsrae he effecveness and he robusness of he proposed approach. In he fuure, we wll explore how o negrae er seanc relaonshps o furher prove he perforance of suarzaon. Acnowledgeen The wor descrbed n hs paper was suppored by an nernal gran fro he Hong ong Polyechnc Unvery (G-YG8. 4

9 References J. Bles A Genle Tuoral on he e Algorh and Is Applcaon o Paraeer Wsaon for Gausan Mxure and Hdden Marov Models. Techncal Repor ICSI-TR-97-2, Unvery of Bereley. Brn, S., and Page, L The Anaoy of a Large-scale Hyperexual Web Search Engne. In Proceedngs of WWW998.. Harabagu S. and Lacausu F. 25. Topc Thees for Mul-Docuen Suarzaon. In Proceedngs of SIGIR25. Hardy H., Shzu N., Srzalow T., Tng L., Wse G. B., and Zhang X. 22. Cross- Docuen Suarzaon by Concep Clasfcaon. In Proceedngs of SIGIR22. Jon M. lenberg Auhorave Sources n a Hyperlned Envronen. In Proceedngs of he 9 h ACM-SIAM Sypou on Dscree Algorhs. aryps, George, Vpn uar and Mchael Senbach. 2. A Coparson of Docuen Cluserng Technques. DD worshop on Tex Mnng. Ln, C. Y. and Hovy, E. 2. The Auoaed Acquon of Topc Sgnaure for Tex Suarzaon. In Proceedngs of COLING2. L W.Y., Ng W.., Lu Y. and Ong.L. 27. Enhancng he Effecveness of Cluserng wh Specra Analys. IEEE Transacons on nowledge and Daa Engneerng (TDE. 9(7: L, F., Tang, Y., Huang, M., Zhu, X. 29. Answerng Opnon Quesons wh Rando Wals on Graphs. In Proceedngs of ACL29. Oerbacher J., Eran G. and Radev D. 25. Ung RandoWals for Queson-focused Senence Rereval. In Proceedngs of HLT/EMNLP 25. Qazvnan V. and Radev D. R. 28. Scenfc paper suarzaon ung caon suary newors. In Proceedngs of COLING28. Sun P., Lee J.H., D.H., and Ahn C.M. 27. Mul-Docuen Ung Weghed Slary Beween Topc and Cluserng-Based Nonnegave Seanc Feaure. APWeb/WAIM 27. Sun Y., Han J., Zhao P., Yn Z., Cheng H., and Wu T. 29. Ranclus: Inegrang Cluserng wh Ranng for Heerogenous Inforaon Newor Analys. In Proceedngs of EDBT 29. Wang D.D., L T., Zhu S.H., Dng Chrs. 28a Mul-Docuen Suarzaon va Senence- Level Seanc Analys and Syerc Marx Facorzaon. In Proceedngs of SIGIR28. Wang D.D., Zhu S.H., L T., Ch Y., and Gong Y.H. 28b. Inegrang Cluserng and Mul- Docuen Suarzaon o Iprove Docuen Undersandng. In Proceedngs of CIM 28. Wan X. and Yang J. 26. Iproved Affny Graph based Mul-Docuen Suarzaon. In Proceedngs of HLT-NAACL26. Zha H. 22. Generc Suarzaon and ey Phrase Exracon ung Muual Renforceen Prncple and Senence Cluserng. In Proceedngs of SIGIR22. 42

Learning Objectives. Self Organization Map. Hamming Distance(1/5) Introduction. Hamming Distance(3/5) Hamming Distance(2/5) 15/04/2015

Learning Objectives. Self Organization Map. Hamming Distance(1/5) Introduction. Hamming Distance(3/5) Hamming Distance(2/5) 15/04/2015 /4/ Learnng Objecves Self Organzaon Map Learnng whou Exaples. Inroducon. MAXNET 3. Cluserng 4. Feaure Map. Self-organzng Feaure Map 6. Concluson 38 Inroducon. Learnng whou exaples. Daa are npu o he syse