TOWARDS ADVANCED DATA RETRIEVAL FROM LEARNING OBJECTS REPOSITORIES

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1 The Fourth Internatonal Conference on e-learnng (elearnng-03), 6-7 September 03, Belgrade, Serba TOWARDS ADVANCED DATA RETRIEVAL FROM LEARNING OBJECTS REPOSITORIES VALENTINA PAUNOVIĆ Belgrade Metropoltan Unversty, SLOBODAN JOVANOVIĆ Belgrade Metropoltan Unversty, Abstract: In mprovng effcency of creatng learnng materals, fundamental role plays concept of reusablty. In order to allow effectve explotaton of ts content, a repostory of learnng objects have to enable search procedure whch s powerful and at the same tme ntutve and smple for use. We propose an archtectural soluton for enhanced search, such that both requrements are satsfed. A search algorthm based on fndng mn-cost Stener trees allows fndng not only learnng objects whch satsfes gven query, but at the same tme, t enables fndng mplct relatonshps among dfferent concept. To enable applcaton of such algorthm, we developed a novel algorthm for sparse weghted graph representaton of a LO repostory. In addton, user s ablty to retreve relevant nformaton can be further mproved by extenson of query language. We proposed one possble extenson based on formal logc and desgned an algorthm for parsng such language. Keywords: E-Learnng, Stener trees, Query language. INTRODUCTION Consderng the emergng popularty of personalzed dstance-based learnng n many nsttutons, there s constant growng demand for more effectve creaton of educatonal materals. A key concept n mproved effcency of ths process s reusablty of already created learnng content. Fundamental workng unt of teachng materal n e-learnng s learnng object (LO), defned by LOM standard as any entty, dgtal or non-dgtal, that may be used for learnng, educaton or tranng [][]. Created learnng objects are organzed and stored n LO repostores, from where they can be searched and retreved when necessary. The prevous defnton of LO allows ncluson of materal n varous formats (textual, mage, vdeo, etc.) whch present serous challenge n organzng and searchng tasks. In order to mprove these procedures, learnng objects are enrched by addtonal descrpton through metadata. Central role n data retreval from a LO repostory s textual search. Even f the targeted LO s not of textual type, varous metadata are gven as plan text (ttle, keywords, descrpton, etc.) and, therefore, are subject to textual search. In addton, most of teachng materal s n textual format, whch emphasze necessty for ths type of search even more. The am of ths paper s to present an archtectural soluton for effectve textual search n large LO repostores. Instead of tradtonal search encountered n web browsers and textual processng applcatons, we propose search based on fndng Stener trees. Ths approach has two man advantages: Even f there s no object whch satsfes all terms from a query, t s possble to detect set of mnmal number of closely related objects such that each term from the query s present n at least one of the objects. It s possble to detect mplct relatonshps among learnng objects. Besdes search procedure, effcency of search procedure depends on used query language. Tradtonally, query language usually does not provde any operators. Query s composed of terms and t s assumed that only one operator s between them - operator and. For example, query "mathematcal physcs" s equvalent to request "fnd all objects whch contans term mathematcal and term physcs". Such conventon does not support submttng query whch corresponds to request lke "fnd all objects whch contans terms mathematcal or chemcal physcs." A novel contrbuton of ths paper conssts of the followng: We desgn an algorthm for creatng sparse weghted graph representaton of a learnng objects repostory, whch s sutable for applcaton of algorthm for fndng Stener trees. We propose an extenson of query language based on formal logc and an algorthm for parsng such language. Archtecture of the system s presented n Fgure. LORMS (Learnng Objects Repostory Management System) creates graph representaton of LOR whch s used by search engne to obtan results. Query has to be processed by query parser before performng search procedure. Detals of ths steps are explaned n the rest of the paper. 53

2 query. Intutvely, a vald soluton to the prevous problem should satsfy the followng two condtons: Fgure. Archtecture of search system. DATA RETRIEVAL FOR LO REUSABILITY Startng pont n the most common type of textual search s formng a query (Q) composed of relevant terms. Typng functon lmt n a web browser wll result n web pages whch contan both terms functon and lmt. However, the challenge arses wth ncreasng query complexty. For example, what s a result f there s no page contanng all terms from query? The answer depends on search engne. For example, Google search engne wll try to elmnate part of the query and perform search on modfed queres, thus, retrevng pages whch partally satsfy the query. In searchng through LO repostores, ths mght not be the desred soluton. Instead of tryng to return one LO whch satsfes the complete query, whch may result n empty resultng set f there s no such query, search engne could try to return a set of learnng objects, such that the whole set satsfes query, even f a partcular element of the set does not. In the prevous example, f there s no such LO whch contans both terms (functon and lmt), the result of search procedure can be set of two LO, one of whch contans functon, and the other contans lmt. In addton, ths type of search s sutable for fndng mplct relatonshps among concepts, whch can be useful tool n creatng learnng materal. Fnally, results of ths type of search can be used as a recommender system whch provdes possble drectons how to proceed further after completng explanaton of one concept. The proposed approach rases an mportant ssue whch accompanes every search process rankng of the obtaned results. Obvously, there could be more than one LO whch contans term functon and, smlarly, more than one LO whch contans term lmt. Any combnaton from these two groups s an answer to the query, but t s not obvous n whch order these answers should be presented to the user. In addton, queres wth more than two terms could result n more complcated structures. For example, n case of a three-term query, the fnal result can consst of one, two, or three LO, wth varous combnatons whch LO contans whch term from the Ths paper provdes some results obraned by the project wth code III44006 fnanced by the Mnstry of Educaton, Scence and Technologcal Development of Rebublc of Serba 54 [C] Results whch contan smaller number of LO correspond to stronger relatonshps among terms from query and should have advantage n rankngs (the best soluton consst of only one LO); [C] Results whch contan more smlar LO (from the same area or subject) correspond to stronger relatonshps among terms from query and should have advantage n rankngs. The second condton ntroduces some ambguty and needs further clarfcaton. Let s say that there s a functon sm(lo, LO) whch return degree of smlarty between learnng objects LO and LO. Specfyng such functon wll be one of topc n the rest of the paper. Such functon enables creaton of a weghted graph whose vertces represent learnng objects from repostory and edge weghts are determned by functon sm. Each vertex s characterzed by addtonal attrbutes terms whch corresponds to words from LO s body or ts metadata. In the rest of the paper, we wll see how to specfy functon sm, create a graph representaton of the repostory and perform search on such graph n an effcent way. 3. LO REPRESENTATION AND SIMILARITY MEASURE Vector space model R = d d d be a repostory of learnng Let,,..., r} objects and W = w, w,..., w } the set of all dstnct k terms from R. The set W s obtaned by the followng procedure: foreach learnng object d n R foreach word w n d f(w not n stop_words) stem(w); add w to W; In the prevous algorthm, when searchng for words n a partcular LO, one has to search for words from the content of LO and varous metadata ttle, keywords, descrpton, etc. All parts of LO from whch words are collected wll be referred as LO slots n the rest of the paper. Non-descrptve stop words are excluded (lke artcles, prepostons, conjunctons, etc.), whle other types of words are stemmed to obtan ther base or root. For example, words fshng, fshed and fsher are all reduced to root fsh. For representng learnng objects we wll use vector space model, a common way to represent documents n varous NLP tasks. Accordng to t, each LO from the repostory R s represented as an m-dmensonal TF-IDF vector r ( d ) = ( tfdf, tfdf,..., tfdf m ). () (

3 It s determned n the followng way. Frst, for each term of a learnng object d, value tf s calculated as ts weghted frequency: tf = h jn, j) j (, () where n (, j) s number of occurrences of term w n the j j-th slot of LO d ; h s a weght assocated wth the j-th slot. Second, nverse document frequency s calculated n the followng way: Weghted sum n tf component s used n order to emphasze mpact of certan LO slots. In search process, weghts are assgned accordng to prortes: The hghest mpact (weght) should have terms from metadata ttle, keywords and descrpton. Medum mpact s reserved for terms from content (f there s textual content). Terms from the rest of searchable metadata should have low mpact. LO smlarty Text smlarty has been studed n varous contexts of NLP tasks. Probably the most popular and used s cosne dstance whch corresponds to correlaton between two vectors. For two learnng objects LO and LO, cosne smlarty s defned as cosne of angle between vectors whch represent these learnng objects n vector space model: sm( d, d ) r( d) r( d ) =, (5) r( d) * r( d) where ndcates scalar product of two vectors and r r(d ( d ) denotes the ntensty of vector ). Although cosne can have values n nterval [-, ], functon sm can have values from nterval [0, ] because all components of vectors n vector space model are postve. If smlarty s perfect, sm returns ; lower values correspond to lower smlarty degree. Smlarty measure defned by (5) returns larger values for objects whch exhbts more sgnfcant smlarty. There 55 are stuatons where the opposte s requred, n whch case dstance measure s used nstead of smlarty measure. Obvously, dstance and smlarty measure are correlated and each of them can be defned by usng the other one. For cosne smlarty, we can defne dstance measure n one of the followng ways: dst( d, d ) sm( d, d ) =, (7) dst( d, d ) log( sm( d, d )) =. (8) 4. GRAPH REPRESENTATION OF LO REPOSITORY Specfed smlarty measure between learnng objects enables creatng graph representaton of repostory. Graph R df = log d R : w d}, (3) G=V, E} s created n the followng way: The set of vertces V corresponds to the set of learnng objects. Each LO s represented n the graph where A s cardnal number of a set A. The role of df by one vertex. component s to reduce mpact of words whch are Each vertex of the graph s enrched by the set of frequent across all documents and, thus, have small attrbutes A, whch corresponds to the set of words dscrmnatng power. Fnally, -th component of the by whch LO can be searched. These words are from vector s calculated as product of term frequency and all searchable slots of the LO. nverse document frequency: Intally the set of edges E contans edges between every two vertces. The weght of each edge s tfdf = tf * df. (4) defned by the functon (4) dst and corresponds to the dstance between approprate learnng objects. The reason for usng dstance nstead of smlarty measure for edge weghts wll be explaned later n secton whch deals wth the search algorthm. Graph representaton allows us to formalze through graph-theory termnology the central problem n ths paper: Problem defnton (MCGST-k) Let G=V, E} be an undrected weghted graph wth set of vertces V and set of weghted edges E. Each vertex v from V s characterzed wth set of attrbutes A. Let Q be a query whch conssts of n terms. An answer tree to a query s any tree from G, such that each term from Q s contaned n the set of attrbutes of at least one vertex of the tree. The task s to fnd top-k answer trees. Rankng s performed such that condtons C and C from Secton are satsfed. For a three-term query whch conssts of terms w, w, w3, examples of possble results are gven n Fgure. A result can contan only one object whch satsfes all turns from query (a). Such result s the best ranked. Result whch consst of two objects (b) should be hgher ranked then result whch conssts of three objects (c). It s possble that a resultng tree contans nodes whch do not contan any term from the query (dark node n d). The man problem n performng any knd of search on a graph created as prevously explaned s performance lmted by the complexty of graph. Number of learnng objects r nduces r / edges, but sgnfcant number among them has small weghts close to zero, whch ndcates there s no relevant smlarty. Such edges should be elmnated from the graph. In other words, after

graph creaton, t s necessary to perform graph sparsfcaton. else wmax; break; edge) foreach edge e n P f (exsts relatonshp metadata between LO represented by vertces of add e to S; the Fgure.

4 graph creaton, t s necessary to perform graph sparsfcaton. else wmax; break; edge) foreach edge e n P f (exsts relatonshp metadata between LO represented by vertces of add e to S; the Fgure. Examples of Stener-trees search The followng requrements should be satsfed: No vertex should be removed from the graph. Edges whch represent low smlarty should be removed from the graph. Edge removal should not volate graph connectvty. Targeted number of edges whch should reman n the graph s specfed by threshold value T. Graph obtaned by sparsfcaton process should have less than T edges, unless t volates connectvty constrant. If an edge wth weght w s n S, then all edges wth weghts greater than or equal to w should be n S because there should be no prorty among edges of equal weghts. If two learnng objects are n relatonshp specfed by the approprate metadata relaton, t should be preserved n the graph regardless of smlarty degree between these two learnng objects. For graph sparsfcaton whch satsfes all prevous requrements, we propose the followng algorthm: Sparsfy(G, T) sort n decreasng order all edges accordng to ther weghts and put them n prorty queue P; add all vertces from G to S; whle(true) wmax <- weght of the edge wth maxmum weght from P; nmax <- number of edges from P wth weght wmax; f (S s not connected) add to S all edges from P wth weght wmax; remove all edges from P wth weght wmax; else f (number of edges n S + nmax < T) add to S all edges from P wth weght wmax; remove all edges from P wth weght 56 Fgure 3. Blok dagram of sparsfy algorthm The complexty of the proposed algorthm s domnated by the sortng procedure from the begnnng of the algorthm. The rest of the procedure s lnear n number of edges. Consderng the fact that ntally number of edges s quadratc functon of number of learnng objects, complexty of the algorthm s O ( E log E ) = O( r ). 5. SEARCH Search algorthm Search problem MCGST-k, as defned n the prevous secton, s an extenson of the problem of fndng the

5 hghest ranked tree known as mnmum cost group Stener tree problem (MCGST-). The problem belongs to class of NP-complete problems whch s proved by reducng t to mnmum set cover problem [3]. Varous approxmate solutons of MCGST- problem are proposed. Some of them [3]-[7] are not easly extended to solvng MCGST-k n an effcent manner because t would requre fndng all possble solutons [8]. Recently, several extendable solutons are proposed [8]-[0]. For our purpose, satsfyng soluton s algorthm DBPF-k proposed n [] because t satsfes the followng condtons: Although the soluton of MCGST-k s approxmate, the frst returned result s optma,.e., soluton of MCGST- s optmal. Soluton s obtaned n polynomal tme. Effcency of DBPF-k algorthm depends on graph sparseness. In the prevous secton, we showed how to perform sparsfcaton of a graph. Therefore, we can expect DBPF-k to perform well on graphs obtaned from repostores of learnng objects. Effcency of DBPF-k algorthm depends on number of terms n query ( Q <<log V ). Typcal usage scenaro n searchng for learnng objects satsfes ths condton. Therefore, we do not expect ths condton to be an obstacle n effcency. Algorthm DBPF s developed to work on databases, but t s essentally search on underlyng graph. Therefore, once the graph representaton of a repostory s created, ts applcaton to our problem s straghtforward. Consderng the fact that DBPF s mn-cost type of algorthm, t becomes obvous why dstance measure s used for graph weghts nstead of smlarty measure. More detals on desgn of DBPF, proof of ts correctness and analyss of complexty can be fnd n []. Query language In prevous dscusson, a search query Q was defned as set of terms. Submttng such query to the search engne mples fndng all trees such that all terms from the query are contaned n each of the returned answers. For example, query math functon s a smple query and requres fndng results whch contan both words math and functon. Ths type of queres s common n search engnes of web browsers and textual processors. In searchng through a LO repostory, often there s a certan level of uncertanty about termnology and relatonshps among concepts. To avod mssng exstent learnng objects, t would be convenent to expand query language to allow resolvng such dsambguates. For example, math functon s possbly n some learnng objects named as mathematcal functon. In ths smple example, t s possble for user to type two dfferent queres and obtan wanted results. However, n longer and more complex queres, t would be more convenent and effcent for user to allow submttng a query whch fnds all learnng objects (or, more precsely, trees of learnng objects) whch corresponds to demand fnd math or mathematcal functon. For ths purpose, we propose a smple extended query language based on rules of formal logc. The language s enrched by two operators: Operator and, marked by reserved word %AND. Operator or, marked by reserved word %OR. In order to smplfy use of these operators, the followng conventon s establshed: Both operators have the same precedence prorty. Expressons are evaluated from left to rght. If there s no operator between two terms, mplctly s assumed %AND operaton. For example, math functon s evaluated as math %AND functon. Assocatvty rule s preserved from formal logc. By usng these two operators, as well as parentheses, a user can form more complex queres. A query for fndng mathematcal or math functons can be specfed as (math %OR mathematcal) %AND functon. Query (operatons management) %OR (busness operatons control) wll treat operatons management and busness operatons control as two separate queres and return unon of ther results. Before explanng an algorthm for parsng queres enrched by prevously descrbed operators, frst we wll ntroduce some formal defntons. Defnton (Term) Term (denoted by lower case letter t) s a word whch s used n a query. Defnton (Smple Query) Smple query (denoted by captal letter Q) s defned as a set of terms: Q = t, t,..., t }. () Q Defnton 3 (Expresson) Expresson (denoted by captal letter E) s defned as a set of smple queres: E = Q, Q,..., Q }. () E Query (operatons management) %OR (busness operatons control) would be evaluated as an expresson whch conssts of two smple queres: Q = operatons, management}, Q = bu sn ess, operatons, control}, E = Q, Q }. Evaluaton of more complex queres requres defnng two bnary operatons on expresson, whch corresponds to prevously ntroduced operators (%AND, %OR) of query language: Operaton corresponds to operator %AND: E j j E E = Q Q Q E, Q }. () Operaton corresponds to operator %OR: E E = E E. () 57

6 We wll explan effect of these two operatons on a smple example. Let say that we have four terms a, b, c, d. Query (a %AND b) %OR (c %AND d) can be evaluated as follows: Q = a, }, Q = c, }, E = Q, Q }. b d Therefore, search algorthm has to be appled on two smple queres and the fnal result s unon of them. Alternatvely, evaluaton can be performed n the followng way: Q = }, Q = }, Q = }, Q = }, a b 3 c 4 d E = Q }, E = Q }, E 3 = Q 3 }, E 4 = Q 4 }, E = E E ) ( E ). ( 3 E4 In ether case, the fnal result of search procedure s the same. Extendng query language by two operators (%AND, %OR) requres algorthm for parsng a query before search algorthm can be appled. Complex expressons lke (a %OR b) %AND ((c %AND d) %OR e), for example, cannot be evaluated drectly. We propose the followng algorthm for performng ths task: ntalze S as empty stack of expressons; ntalze empty set of search results R; foreach token w of query swtch(w): case (, %AND, %OR : push w to S; case ) : E<-evaluateTopExpresson(S); push E to S; default: f(prevous token s term) push %AND to S; Q = w}; E = Q}; push E to S; end swtch; E<-evaluateTopExpresson(S); foreach smple query Q from E result = DBPF-k(Q); add result to R; In the prevously descrbed algorthm, help functon evaluatetopexpresson s used to evaluate value of expresson from the top of the stack. It s realzed n the followng way: 6. CONCLUSION In ths paper, we proposed an archtectural soluton for enhanced search through repostores of learnng objects. Tradtonal textual search encountered n web browsers and text processng applcatons does not satsfy needs for data retreval from learnng object repostores manly because t gnores exstent explct and mplct relatonshps among objects. In addton, a complex query wth more words can result n an empty result set. As a soluton to these problems, we proposed search based on fndng top-k mn-cost Stener trees. In partcular, we developed an algorthm for sparse weghted graph representaton of a LO repostory, whch s sutable for applcaton of algorthm for fndng Stener trees proposed n []. To further mprove searchng capabltes, we proposed extenson of query language based on formal logc and desgned an algorthm for parsng t. In order to keep smplcty, the extenson s reduced to only two addtonal operators, whch corresponds to logcal AND and logcal OR. ACKNOWLEDGMENT Ths work was supported by Mnstry of Educaton, Scence and Technology (Project III44006). valuatetopexpresson(s) ntalze SH as empty stack; whle (S not empty) wh<-pop from S; f(wh = ( ) break; push wh to SH; whle (true) frst<-pop from SH; f (SH s empty) return frst; operator<-pop from SH; second<-pop from SH; swtch(operator) case %AND : result = frst ^ second; case %OR : result = frst v second; end swtch; push result to SH; } LITERATURE [] LOM (00). Fnal Draft Standard for Learnng Object Metadata IEEE On-lne avalable: [] IEEE Learnng Technology Standards Commttee [Onlne] Avalable: [3] G. Rech and P. Wdmayer. Beyond stener s problem: A vls orented generalzaton. In Proc. of WG 89, 989. [4] E. Ihler. Bounds on the qualty of approxmate solutons to the group stener problem. In Proc. of WG 90, 990. [5] C. D. Bateman, C. S. Helvg, G. Robns, and A. Zelkovsky. Probably good routng tree constructon wth mult-port termnals. In Proc. of ISPD 97, 997. C. Helvg, B. Robns, and A. Zelkovsky. Improved approxmaton bounds for the group Stener problem. Networks,37(),00. [6] M. Charkar, C. Chekur, T.-Y. Cheung, Z. Da, A. Goel, S. Guha, and M. L. Approxmaton algorthms for drected Stener problems. Journal of Algorthms, 33(),999. [7] W.-S. L, K. S. Candan, Q. Vu, and D. Agrawal. Query relaxaton by structure and semantcs for 58

7 retreval of logcal web documents. IEEE Trans. Knowl.Data.Eng.,4(4),00. [8] G. Bhalota, A. Hulger, C. Nakhe, S. Chakrabart, and S. Sudarshan. Keyword searchng and browsng n databases usng banks. In Proc. of ICDE 0, 00. [9] K. Varun, P. Shashank, C. Soumen, S. Sudarshan, D. Rush, and K. Hrshkesh. Bdrectonal expanson for keyword search on graph databases. In Proc. of VLDB 05,005. [0] B. Dng, J.X. Yu, S. Wang, L. Qng, X. Zhang, and X. Ln. Fndng top-k mn-cost connected trees n databases.icde,007 59

For instance, ; the five basic number-sets are increasingly more n A B & B A A = B (1)

For instance, ; the five basic number-sets are increasingly more n A B & B A A = B (1) Secton 1.2 Subsets and the Boolean operatons on sets If every element of the set A s an element of the set B, we say that A s a subset of B, or that A s contaned n B, or that B contans A, and we wrte A