Contxtual Doain for Incorporation in Data Mining Systs Alx G. Büchnr *, John G. Hughs * and David A. Bll * Northrn Irland Enginring Laboratory, Univrsity of Ulstr School of Inforation and Softwar Enginring, Univrsity of Ulstr Shor Road, Nwtownabby, BT37 0QB, UK ail: {ag.buchnr, jg.hughs, da.bll}@ulst.ac.uk Fro: AAAI Tchnical Rport WS-99-14. Copilation copyright 1999, AAAI (www.aaai.org). All rights rsrvd. Abstract Th concpt of contxtual doain knowldg is proposd and incorporatd in a gnric data ining architctur. Various typs of doain knowldg (taxonois, constraints, prviously discovrd knowldg and usr prfrncs) ar allottd with contxt inforation, which is organisd in a hirarchical topology. Mdiation is dfind in ordr to chos contxt-dpndnt doain knowldg for incorporation in a data ining xrcis. All coponnts ar bddd in a contxtual knowldg discovry architctur. Introduction Data and doain knowldg ar th two ost ssntial input ingrdints for data ining applications. Th forr is ithr providd by oprational databass or by thir warhousd countrparts in for of atrialisd viws, which can b rusd for ultipl odl building xrciss (Büchnr, Hughs, and Bll, 1999). Th lattr, in whatvr for providd, has to b r-spcifid, or at last odifid, dpnding in which contxt pattrns ar to b discovrd. This liits th concpt of doain knowldg, and thus, th objctiv of this papr is to propos th notion of contxtual doain knowldg, which can b rusd across ultipl rlatd knowldg discovry xrciss. Th structur of this papr is as follows. First, a doain knowldg classification is providd, which distinguishs btwn taxonois, constraints, prviously discovrd knowldg, and usr prfrncs. Thn, contxts ar spcifid and organisd in a hirarchical topology. Th sction that follows, cobins th two coponnts to contxtual doain knowldg, which is basd on contxt diation. In ordr to bnfit fro th nwly introducd concpts, contxtual doain knowldg is incorporatd in a data ining frawork. Finally, conclusions ar drawn and furthr rsarch is outlind. Foral spcifications and dfinitions ar supportd by xapls fro an lctronic corc scnario in which arkting intllignc has bn discovrd fro Intrnt log fils (Büchnr and Mulvnna 1998). Doain Classification Doain knowldg can b utilisd in a nubr of ways. It can b usd for aking pattrns or visibl, for constraining th sarch spac, for discovring or accurat knowldg, and for filtring out unintrsting knowldg (Anand and Büchnr 1998). Thr hav bn nurous classifications of doain knowldg for data ining purposs. A coprhnsiv taxonoy has bn prsntd by Klösgn and Zytkow (1999), which is usd for this papr in ordr to discuss contxt-rlatd issus. Th st of chosn doain knowldg typs is by no nds xhaustiv. Howvr, it bodis a rprsntativ collction that has provn sufficint for ost data ining applications. Taxonois Taxonois provid classifications, which allow th grouping of any attribut valus into a sallr nubr throf. Th thr ost typical typs of taxonoical doain knowldg ar bandings, concpt hirarchis and ntworks. Dfinition 1. A banding b is dfind as b = [b in, b ax ], whr b in and b ax rprsnt th lowr and uppr liit of a rang, rspctivly. Typical xapls of bandings ar custor ag groups, login ti rangs, and arkting sasons. Th outco of a banding opration is b in b ax t, whr t rprsnts a linguistic tr. Dfinition 2. A concpt hirarchy h is a connctd, undirctd, acyclic graph, which is dfind as th tupl h = (L, E), whr L = {l 0, l 11, l 12, l 21, l 22, } and E = { 1, 2, 3, }. Each has th for = <l i, l j >; l i, l j L, l 0 has indgr 0, l 1 l n hav indgr 1. l i is subconcpt of l j iff l i l j ; l i is suprconcpt of l j iff l j l I Multi-lvl concpt hirarchis can, for instanc, rprsnt Intrnt doain nas, custor post cods, or product rangs. Concpt hirarchis also covr groupings, which
ar rprsntd as a tr with a singl root and all lavs bing connctd dirctly to th top-lvl nod. Dfinition 3. A ntwork w is a dirctd, connctd, cyclic graph, which is dfind as th tupl w = (N, E), whr N = {n 1, n 2, n 3, } and E = { 1, 2, 3, }, ach n rprsnting a nod in w. Each has th for = <n i, n j >; n i, n j N. A typical ntwork in an lctronic corc scnario is th topology of a rtail wb sit, which provids inforation about th links aong diffrnt pags and pag clustrs. Constraints Constraints rprsnt liitations to data valus, which ar doain as wll as discovry dpndnt. Constraints can ithr xclud or includ crtain data valus. Furthror, constraints ar usually spcifid in for of attributrlationship ruls, or can b transford to such ( Anand t al. 1995). Dfinition 4. A constraint l is spcifid as a rul such that l: antcdnt consqunt. Both, th antcdnt as wll as th consqunt can hav ultipl valus, which allows th flxibl dscription of constraints. An xapl rul in th lctronic corc scnario ntiond abov stats that th profssion of th usr of an URL that is not a proxy and has th top lvl doain.du is a lcturr, studnt or rsarchr. Prviously discovrd Prviously discovrd knowldg can b rusd as doain knowldg if it is in first-ordr noral for. Dpnding on th typ of pattrn discovry thod that has bn applid (rul induction, nural ntworks, Baysian blif ntworks, t ctra), th knowldg can thortically b in any for as dfind abov or in any pattrn discovry-dpndnt forat. Typical pattrns bing rusd usually hav a vry high dgr of support and / or confidnc (also known as quasi facts), which indicats thir trunss across data ining and othr rasoning xrciss. Usr Prfrncs Usr prfrncs spcify uppr or lowr liits for crtain discovry asurs in th for of thrsholds, for xapl, support, confidnc, dviation, squnc lngth, and so forth. Silbrschatz and Tuzhilin (1996) hav distinguishd btwn intrstingnss (sub-dividd into actionability and unxpctdnss) and (soft as wll as hard) blifs, which dpnd on th pattrn discovry tchniqu bing usd. Without going into grat dtail, all ths asurs can b classifid as subjctiv or objctiv. This classification is usd for invstigating doain knowldg in contxt, sinc it rprsnts adquatly th individualistic natur of huans, bing involvd in a knowldg discovry procss (s Doain in Contxt Sction). Contxt Organisation In a knowldg discovry nvironnt, a contxt rprsnts bhavioural aspcts which ar shard by attributs of th sa ontology. Assuing an undrlying lctronic corc ontology, possibl proprtis ar a top-lvl doain s location, th xchang rat of a currncy, or th login ti zon offst. Dfinition 5. A contxt c contains a st of proprtis P c = {p c1, p c2, p c3, } whr P c P and P = {p 1, p 2, p 3, }, which rprsnts an application-spcific ontology O. Th original ida of th contxt idntity concpt is that vry singl attribut instanc is bing allottd an additional attribut contxt idntifir in a (ulti-) databas scnario, whr ach attribut instanc is rprsntd by a santic valu (Büchnr, Bll, and Hughs 1998). Th sa concpt is applid to doain knowldg so that th sa contxt inforation can b usd for both, data as wll as doain knowldg (Büchnr, Hughs, and Bll 1999). To iniis th rdundancy of contxt dclarations (for instanc, rlatd sub-lvl doains, or dats in diffrnt ti zons but fro a singl calndaric syst), contxts ar organisd hirarchically. Thus, structur and bhaviour can b inhritd, and ovrloading and ovrriding chaniss can b applid to contxts. Th whol spanning contxt tr is rprsnting th undrlying ontology and is rprsntd as a contxt hirarchy O, which is an undirctd, connctd, acyclic graph (s Dfinition 2). A furthr advantag of th hirarchical arrangnt of contxts is th possibility of packaging contxt sub-trs; w rfr to ths sub-trs as rsourcs r such that r o, that is r i r {r i o} and r o. For handling contxtual databass, furthr constructs hav bn dfind, which ncopass contxtualisd quivalnc spcifications for atoic and coplx typs, distanc asurs, as wll as contxt diation. Ths notions hav bn bddd in th ODMG objct data odl and an objct dfinition languag as wll as its qury countrpart hav bn proposd (Büchnr, Bll, and Hughs 1998). Howvr, for th purpos of conncting contxt to doain knowldg ths oprations ar not rquird. Th linkag btwn contxts and th dfind typs of doain knowldg is prford through th allotnt of contxt idntifirs to ach instanc of doain knowldg.
Doain in Contxt As dscribd arlir, thr xists a ultitud of doain knowldg typs, with rspct to structur, contnt and rusability. For th purpos of this papr, ach doain knowldg typ is invstigatd fro two diffrnt dinsions. Th first is concrnd with th dgr of rality, whr rality is rprsntd in a spctru fro a physical world to a logical odl world (s Figur 1). Th scond is intrstd in th dgr of rusability of th spcifid typs of doain knowldg. Physical World Objctiv Doain Dgr of Rality Logical Modl World Subjctiv Doain Figur 1. Doain Dgrs of Rality Objctiv and Subjctiv Doain Objctiv doain knowldg consists of a st of quasi facts of th doain a data ining xrcis is prford in. Although it can hav a crtain dgr of contxtdpndncy, it is alost always kpt as holos and only xchangd in total for its contxtual countrpart. Exapls of objctiv doain knowldg ar th topology of th -rtailr s wb sit, th hirarchical organisation of Intrnt doains, or any constraints basd on lgal grounds. Howvr, ach of ths xplars can contain a dgr of subjctivnss. A arkting xprt ight only b intrstd in all paths going through a rcnt capaign pag lading to th purchas pag, whras th wb adinistrator ight b intrstd in th ost rgularly visitd pags for caching purposs; an Intrnt srvic providr ight want to clustr th sub-lvl doains.du,.ac.uk, uni-*.d and.du.* into on virtual doain; and tax dduction schs vary, dpnding fro whr an lctronic buyr is logging into an lctronic corc sit. Subjctiv doain knowldg has a highr dgr of contxt-dpndncy than its objctiv countrpart. As a consqunc, ithr ntir doain knowldg ntitis or larg parts throf (for xapl, rsourcs) hav to xist for ultipl contxts and its incorporation in data ining xrciss. valus, or ag group bandings. Siilar to objctiv doain knowldg, ach of th xapls can hav a crtain dgr of objctivnss. Discovrd ruls with a vry high support and confidnc ight b intrprtd as quasi facts; thrsholds can dpnd on businss targt goals; and ag group bandings can b lgally groundd. It is dsirabl to handl th ntir rang of doain knowldg dgrs of rality using th sa undrlying tchniqus. Thus, contxtual doain knowldg is proposd in th nxt sub-sction, indpndnt of its dgr of rality. Contxtual Doain Lt D b th st of supportd doain knowldg typs and C a st of contxts as dfind abov. Lt us furthr assu that ach lnt in D can b rprsntd as d 1, d 2, d 3,, whr ach d rprsnts a coponnt of D. Thn, ach d can b allottd at last on contxt c. Dfinition 6. Contxtual doain knowldg is spcifid C1 C2 C3 as D = { d, d, d, }, whr ach d is part of D and 1 2 3 K ach C is a st of contxts (C ). For furthr illustration, th supportd typs of doain knowldg ar kpt sparatly, supportd by illustrativ xapls fro th -corc doain. Contxtual bandings can b handld in thr diffrnt ways, viz. totally rusd, totally rplacd and partially rusd. Whr th total options ar straightforward, partial rusability can furthr b sub-dividd. A sub-banding can ithr hav th sa uppr or lowr liit, b in btwn, or ovr-lapping with othr rangs. Although it is tchnically fasibl, it has not provn practical to dal with sub-bandings. It is thrfor proposd that only total rplacnt and rusability of bandings is prford. ac (c ) i i (c ) uk www uk (c ) du www (c, c ) du (c ) uk co ( ) co ( ) nt ( )... hk ( ) d (c ) Contxt Mdiator c c www du... Typical cass of subjctiv doain knowldg ar pattrns (dcision trs, nural ntworks, Dpstr-Shafr pics of vidnc, t ctra), which hav bn discovrd in a spcialisd data ining application, chosn thrshold ac co nt d ac hk d Figur 2. Exapl Contxtual Concpt Hirarchy
Contxtual concpt hirarchis ar of or intrst to data ining xrciss. Owing to th fact that ach nod in a ulti-lvl concpt hirarchy is allottd a contxt idntifir, it is possibl to rus a collction of nods and thir sub-trs. For instanc, th arkting anagr Europ (in contxt c ) ight only b intrstd in th subhirarchy with all Europan countris, whras th prson rsponsibl for introducing a product at ducational lvl (in contxt c ) would only b concrnd about th according sub-trs (s Figur 2). Siilarly to concpt hirarchis, ntwork structurs contain contxt inforation at ach nod, which allows th rusability of a st of nods and th xisting links aong th. For xapl, th author of onlin hlp pags on a ulti-party rtail wb sit ( aka. shopping all), ight only b intrstd in th sub-ntwork that includs all nods which lad to dynaically cratd hlp pags. Lik bandings, parts of constraints as wll as prviously discovrd knowldg can thortically b contxtualisd Howvr, it has no valu in ral-world data ining applications. Sinc usr prfrncs ar atoic nuric valus, thy ar tratd only holistically and ar not furthr split apart. Contxt Mdiation Th original purpos of th contxt diator was to rsolv conflicts and guarant introprability aong data sourcs, which hav bn accssd fro diffrnt contxts (Büchnr, Bll, and Hughs 1998). In ordr to us th contxt diator for data as wll as doain knowldg it has to b polyorph in natur. Hr, only th doain knowldg-spcific functionality of th contxt diator is dscribd. Th contxt diator has to dcid what doain knowldg is to b includd and what is to b xcludd fro a data ining task. This dcision is basd on th contxt th knowldg has bn cratd in and th contxt it is to b applid to. Ths two sits ar rfrrd to as knowldg sourc s and knowldg rcivr r. As outlind in th prvious sub-sction, ach pic of knowldg has a st of contxts allottd to it. Owing to th fact that a usr can only b in on contxt at a ti, th contxt diator only rturns th pics of doain knowldg that hav bn allottd th contxt in which th usr is currntly in. Mor forally, this can b xprssd as following. Now that all coponnts hav bn dsignd, viz. contxtual doain knowldg as wll as its data sourcbasd countrpart and th contxt diation facility, th nxt stp is to incorporat th parts into a knowldg discovry architctur. Contxtual Data Mining Architctur In ordr to dploy contxtual data as wll as doain knowldg in a data ining application, a siplifid contxtual knowldg discovry architctur has bn cratd, which is dpictd in Figur 4. Data Doain Contxt Mdiator Pattrn Discovry Figur 4. Siplifid Contxtual KDD Architctur Th contxt diator contains all th inforation about participating contxts, thir hirarchical organisation as wll bhavioural aspcts. It is polyorph in natur and thus can dal with rqusts concrnd about data (Büchnr, Bll, and Hughs 1998) as wll as doain knowldg (this papr). Dpnding on th contxt fro which inforation is rqustd, data and suitabl doain knowldg is usd as input for knowldg discovry. Th discovrd pattrns ar thn contxtualisd, that is lablld with th contxt th data ining xrcis has bn prford in, and fd back to th doain knowldg rpository. In ordr to illustrat th opration of th outlind coponnts in th architctur, considr an lctronic corc xapl, in which th task is to discovr squntial pattrns fro intrnt log fils, which ar thn b intrprtd as bhavioural pattrns. Both, th typs of stord data as wll as incorporatd arkting-rlatd doain knowldg dpnds of th typ of -tailr that is oprating th sit. Having sit-spcific log fils in an intrnt bookstor nvironnt which contains inforation about URI, login ti, logoff ti, HTTP rfrrr, status, cooki ID, t ctra, th arkting anagr is looking for intrsting pattrns, and so is th wb adinistrator 1. Th arkting xprt has spcifid his/hr doain knowldg in for of rgion-basd concpt hirarchis as wll as targt-rlatd ag bandings. Th wb adinistrator howvr, has cratd a ntwork of th topology of th contxt diator c r D r := Ud s d s Ds cs( d s) = cr contxt diator D r Figur 3. Contxt Mdiator Structur 1 In this scnario, only on log fil in considrd for siplicity. Mor coplx constllations occur rgularly in lctronic shopping alls with ultipl sourcs and rcivrs. Also, th xapl can asily b xtndd to two arkting xprts with diffrnt rsponsibilitis.
rtailr s wb sit. Th thrshold paratrs providd by th xprts ar budgt- and cach siz-drivn, rspctivly. Th typs of squncs (associations across ti) which ar discovrd ar ost likly to b diffrnt, sinc thy ar goal- as wll as contxt-drivn. Thy can vn b contradictionary, which happns or rgularly whn classifications or associations ar to b discovrd. Finally, ach pic of knowldg that is found and chosn by th doain xprt to b kpt is taggd with th currnt contxt and orisd in th doain knowldg rpository for futur usag. Conclusions and Furthr Work Th considration of contxt inforation has bn proposd in rlatd disciplins, ainly in cas-basd rasoning (Öztürk and Aaodt 1997; Jurišica and Glasgow 1997; Dubitzky t al. 1999), but has, to th bst of our knowldg, not yt bn applid in data ining scnarios. W hav closd that link in proposing an architctur that considrs contxtual data and doain knowldg, as wll as a contxt diation facility, which rconcils discrpancis aong th participatd ntitis. Ongoing rsarch is orintatd towards thr ain dirctions. First is daling with a highr dgr of uncrtainty, which allows th allotnt of contxtual wights (Turnr, 1997) and rquirs a or sophisticatd contxt diator. On th sa trs, th allocation of a data lnt or a pic of doain knowldg to or than on contxt has potntial applications, but rquirs vn or coplicatd diation facilitis. Scond is invstigating th ipact of allotting contxt inforation not only to nods but also to dgs in graph-basd doain knowldg (for xapl, th link fro a ho pag to a sarch pag on an onlin bookstor ight b lss intrsting fro a arkting prspctiv than a link fro th ho pag to a spcial offr). Finally, contxtual inforation as such is usd by data ining algoriths thslvs in ordr to discovr or prsonalisd pattrns. Büchnr, A.G. and Mulvnna, M.D. 1998. Discovring Intrnt Markting Intllignc through Onlin Analytical Wb Usag Mining, ACM SIGMOD Rcord, 27(4) 54-61. Büchnr, A.G., Hughs, J.G and Bll, D.A. 1999. Contxtual Data and Doain for Incorporation in Discovry Systs, subittd to CONTEXT 99. Dubitzky, W., Büchnr, A.G., Hughs, J.G. and Bll, D.A. 1999. Towards Concpt-Orintd Databass, Journal on Data and Enginring, forthcoing. Jurišica, I. and Glasgow, J. 1997, Iproving Prforanc of Cas-Basd Classification using Contxt-basd Rlvanc, Int l Journal of Artificial Intllignc Tools, 6(3&4): 511-536. Klösgn, W. and Zytkow, J. ds. 1999. Handbook of Data Mining, Oxford Univrsity Prss, forthcoing. Öztürk, P. and Aaodt, A. 1997. Towards a odl of contxt for cas-basd diagnostic probl solving, Proc. 1 st Int l and Intrdisciplinary Conf. on Modling and Using Contxt, pp. 198-208. Silbrschatz, A. and Tuzhilin, A. 1996. What Maks Pattrns Intrsting in Discovry Systs. IEEE Trans. on and Data Enginring 8(6):970-974. Turnr, R.M. 1997. Dtrining th contxt-dpndnt aning of fuzzy substs, in Proc. 1 st Int l and Intrdisciplinary Conf. on Modling and Using Contxt, pp. 233-242. Rfrncs Anand, S.S., Bll, D.A. and Hughs, J.G. 1995. Th Rol of Doain in Data Mining, in Proc. 4 th Int l ACM Conf. on Inforation and Managnt, pp. 37-43. Anand, S.S. and Büchnr, A.G. 1998. Dcision Support using Data Mining, FT Pitan Publishrs. Büchnr, A.G., Bll, D.A. and Hughs, J.G. 1998. A Contxtualisd Objct Data Modl basd on Santic Valus, in Proc. 11 th Int l. Conf. on Paralll and Distributd Coputing Systs, pp. 171-176.