OSSM Ordered Sequence Set Mining for Maximal Length Frequent Sequences A Hybrid Bottom-Up-Down Approach

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1 Global Journal of Computer Sene and Tehnology Volume 12 Issue 7 Verson 1.0 Aprl 2012 Type: Double Blnd Peer Revewed Internatonal Researh Journal Publsher: Global Journals In. (USA) Onlne ISSN: & Prnt ISSN: OSSM: Ordered Sequene Set Mnng for Maxmal Length Frequent Sequenes A Hybrd Bottom-Up-Down By Anurag Choubey, Dr. Ravndra Patel & Dr. J.L. Rana Rajv Gandh Tehnologal Unversty, Bhopal, Inda Abstrat - The proess of fndng sequental rule s ndspensable n frequent sequene mnng. Generally, n sequene mnng algorthms, sutable methodologes lke a bottom up approah s used for reatng large sequenes from tny patterns. Ths paper proposed on an algorthm that uses a hybrd two-way (bottom-up and top-down) approah for mnng maxmal length sequenes. The model proposed s optng to bottom-up approah alled Conurrent Edge Prevson and Rear Edge Prunng (CEG&REP) for temset mnng and top-down approah for maxmal length sequene mnng. It also explans optmalty of top-to-bottom approah n dervng maxmal length sequenes frst and lessens the sannng of the dataset. GJCST Classfaton: F.3.m OSSM Ordered Sequene Set Mnng for Maxmal Length Frequent Sequenes A Hybrd Bottom-Up-Down Strtly as per the omplane and regulatons of: Anurag Choubey, Dr. Ravndra Patel & Dr. J.L. Rana. Ths s a researh/revew paper, dstrbuted under the terms of the Creatve Commons Attrbuton-Nonommeral 3.0 Unported Lense permttng all non-ommeral use, dstrbuton, and reproduton nany medum, provded the orgnal work s properly ted.

2 OSSM: Ordered Sequene Set Mnng for Maxmal Length Frequent Sequenes A Hybrd Bottom-Up-Down Anurag Choubey α, Dr. Ravndra Patel σ & Dr. J.L. Rana ρ Abstrat - The proess of fndng sequental rule s ndspensable n frequent sequene mnng. Generally, n sequene mnng algorthms, sutable methodologes lke a bottom up approah s used for reatng large sequenes from tny patterns. Ths paper proposed on an algorthm that uses a hybrd two-way (bottom-up and top-down) approah for mnng maxmal length sequenes. The model proposed s optng to bottom-up approah alled Conurrent Edge Prevson and Rear Edge Prunng (CEG&REP) for temset mnng and top-down approah for maxmal length sequene mnng. It also explans optmalty of top-to-bottom approah n dervng maxmal length sequenes frst and lessens the sannng of the dataset. I. Introduton R esearhers feel enthusast on the sequental pattern mnng problems and wde range of possbltes of applatons regardng the envsagng of the ustomer buyng patterns and sentf dsoveres [1, 2, 3, 4, 5] dsussed by Agrawal and Srkant [1]. Let us explan wth an example lke fndng the gven tme stamped sequenes of purhase made by a ustomer. In ths example the man objetve s to fnd sequene of same tme stamped lst of tems purhased by the ustomer. So the algorthm of sequene pattern mnng should onentrate on fndng the repeated sequenes whh are alled as frequent sequene. Suh sequenes lst out the frequeny of ommon ourrenes. several heursts lke GSP [1], SPADE [3], Prefx Span [2] and the SPIRIT [4] attempt to fnd the frequent patterns n produtve method by strvng to ut short a seres, hene derease searh spae. The GSP algorthm [1] utlzes the ant-monotone property (all subsequenes of a frequent sequene are also frequent). The SPADE fnds frequent sequenes usng the latte searh [3] and nterseton based approah. In ths partular method the sequene database s onverted nto a vertal format. The anddate sequenes wll be made nto dfferent groups. These Author α : Dean Aadem, Tehnorats Insttute of Tehnology, Bhopal M.P., Inda. E-mal: anuragphd11@gmal.om Author σ : Assoate Professor and Head, Department of Computer Applatons at Rajv Gandh Tehnologal Unversty, Bhopal, Inda. Emal: ravndra@rgtu.net Author ρ : Group Dretor, Radha Raman Group of Insttute, Bhopal. Emal: jl_rana@yahoo.om frequent sequenes wll be lsted n SPADE utlzng two methods namely breadth frst method and depth frst method. The base s alulated for the produed sequenes. The approah of mentoned three algorthms an be grouped as the anddate-produton wth a base evaluaton. The PrefxSpan [2] algorthm adopts growth method pattern. It utlzes reorded database to aomplsh.. Prefx s Projeted Sequental Pattern mnng whh heks prefx subsequenes and nludes the postfx sub sequenes nto the databases. II. Related work The sequental tem set mnng problem was ntated by Agrawal and Srkant, and the same developed a fltered algorthm, GSP [1], based on the Apror property [1]. Sne then, lots of sequental tem set mnng algorthms are beng developed to nrease the effeny. Some are SPADE [3], PrefxSpan[2], and SPAM [11]. SPADE[3] s on prnple of vertal d-lst format and t uses a latte-theoret method to deompose the searh spae nto many tny spaes, on the other hand PrefxSpan[2] mplements a horzontal format dataset representaton and mnes the sequental tem sets wth the pattern-growth paradgm: grow a prefx tem set to attan longer sequental tem sets on buldng and sannng ts database. The SPADE[3] and the PrefxSPan[2] hghly perform GSP[1]. SPAM[11] s a reent algorthm used for mnng lengthy sequental tem sets and mplements a vertal btmap representaton. Its observatons reveal, SPAM[11] s more effent n mnng long tem sets ompared to SPADE[3] and PrefxSpan[2] but, t stll takes more spae than SPADE[3] and PrefxSpan[2]. Sne the frequent losed tem set mnng [12], many apable frequent losed tem set mnng algorthms are ntrodued, lke A-Close [12], CLOSET [13], CHARM [14], and CLOSET+ [15]. Many suh algorthms are to mantan the ready mned frequent losed tem sets to attan tem set losure hekng. To derease the memory usage and searh spae for tem set losure hekng, two algorthms, TFP [17] and CLOSET+2, mplement a ompat 2-level hash ndexed result-tree struture to keep the readly mned frequent losed tem set anddates. Some prunng methods and tem set losure verfyng methods, ntated that an be extended for optmzng the mnng 2012 Aprl Global Journals In. (US)

3 Aprl of losed sequental tem sets also. CloSpan s a new algorthm used for mnng frequent losed sequenes [16]. It goes by the anddate mantenane-and-test method: ntally reate a set of losed sequene anddates stored n a hash ndexed result-tree struture and do post-prunng on t. It requres some prunng tehnques suh as Common Prefx and Bakward Sub- Itemset prunng to prune the searh spae as CloSpan[16] requres mantanng the set of losed sequene anddates, t onsumes muh memory leadng to heavy searh spae for tem set losure hekng when there are more frequent losed sequenes. Beause of whh, t does not sale well the number of frequent losed sequenes. III. Sequene, sub sequene and frequent sequenes We an say a sequene means an ordered set of events [1], set of events S= { s, s, s,... s, s,... s! s= {1,2,3, j, j+ 1,... n}} j j+ 1 n And every event s s onsdered as an tem set, whh s a non-empty, unordered, fnte set of tems, whh an be represented as s= {,,,...,! e= {1, 2,3,4,..., m}}, here m e e for e = 1.. m s tem. The length of a sequene s the number of tems present n the sequene. A sequene an be referred wth ts length, as an example a sequene of length k s alled a k-sequene. A sequene S 1 s sad to be a subsequene of another sequene S2 f and only f s1 s2 e = {1, 2,3,.m e < e < e... < e... < } and for e s event of S 2.The 2 S1 and 1 S s sad to super sequene of S s sad to subsequene of S 2. The sequene database S s a set of the form (td, s) where td s the transaton-d and s s the sequene generated from transaton. Let the mnmum support as a threshold defned by user whh ndates the desred mnmum ourrenes of the sequene to be lamed as frequent. A sequene s j s lengthest fs j! {s S ={1..m}}. We explan the maxmal support of an event e whh onssts of tems (,,..., ) as 1 2 MS = max{sup( ), sup( ), sup( ),..., sup( )! t = e m t Here sup( n ) frequeny of tem n ourrene. And, the maxmal support fator MSF of a sequene s represented by sum of maxmal support of all events belongs to that sequene. Let s be a sequene of events { e1, e2,..., em! e = {1,2,3,..., m}} and then maxmal support fator an be measured as MSF() s = MS( e ) m = 1 The Maxmal Support Fator s the threshold used n our proposal to mnmze the subsequene searh n top to bottom approah. We apply an ordered searh on sequene database, hene the sequene database wll be ordered n desendng manner by MSF of sequenes. Then the searh for super sequene of a gven sequene s lmted to the sequenes wth greater or equal MSF of the gven sequene. The preproessed dataset wth the sorted transaton lst has several propertes that an be used to ut short the searh spae whh are hypotheszed below: Hypothess 1: A super sequene searh of gven sequene s an stop at a sequene st f MSF( s ) < MSF( s ). Puttng dfferently a t k {1,2,3,..., m}} anddate sub sequene s wll not be a subsequene of s f MSF( s) > MSF( s). Hypothess 2: A sequene s s frequent f ount of super sequenes for s s equal or greater than the gven mnmum support threshold by user. mnsupport(s ) an be referred as maxourrene(s ) and t an be measured as SM max Ourrene( s) = { f ( s s) = 1 or = 0} = 1 Here SM s set of order sequenes n desendng manner for eah sequene MSF s greater or equal to MSF( s ). Hypothess 3: Let sm be maxmal sequene and maxourrene( sm) ms then avod all subsequenes of s m from onsderng to evaluate maxmal sequenes Hypothess 4: Let s be sequene suh that maxourrene( s ) < ms then dsard all supersets of s.sne s s nfrequent then ts super sequenes also nfrequent. n 2012 Global Journals In. (US)

4 IV. Ossm overvew Intally we apply (CEG & REP)[7] to fnd losed frequent temsets, whh s bottom-up approah alled Conurrent Edge Prevson and Rear Edge Prunng (CEG & REP)[7]. Elmnate the tems from transatons that are not part of any event e suh that e I and referred as outlers. An tem s an outler f o Ttd and { Is for s = {1... I } o Here Ttd s a transaton represented by transaton d td and Is s an temset that belongs to set I of frequent temsets. Buld sequenes by groupng tems as events n a gven transaton. Here we follow the top-to-bottom approah to buld events. Frst we buld events based on maxmal length temsets and ontnue the proess n desendng order of the temset lengths. Measure the Maxmal support of eah event e of the gven transaton T td (refer seton 3 for measurng maxmal support MS for an event e of transatont td ). Measure the Maxmal Support Fator MSF of eah sequene S td (Refer seton 3 for measurng Maxmal Support Fator MSF of sequene S td ) Order the sequenes n sequene dataset S n desendng manner of ther MSF. Buld weghted ayl dreted graph from frequent temsets of length two. o Elements of the temset onsdered as vertes o Support of that temset onsdered as edge weght Apply WFI algorthm to fnd rtal path between any two tems whh represents the maxmal sequene between two elements opted. Apply all four propertes that are hypotheszed n seton 3 to dsard, prune sequenes or selet maxmal length sequenes. V. OSSM: Top-Down Ordered Sequene Set Mnng for maxmal length sequenes a) Conurrent Edge Prevson and Rear Edge Prunng (CEG&REP)[7] n OSSM. Preproess Dataset preproessng and temsets Database ntalzaton s performed by us as the frst stage of proposal. As we fnd temsets wth sngle element, we n parallel prune t wth the temsets of sngle elements f the support of the seleted temsets s less than the requred support.. Conurrent Edge Prevson In ths phase, we selet all temsets from gven temset database as nput n parallel. Then we start projetng edges from eah seleted temset to all possble elements. The frst teraton nludes the prunng proess n parallel, from the seond teraton onwards ths prunng s not requred, whh we lamed as an effent proess ompared to other smlar tehnques lke BIDE [8]. In frst teraton, we projet an temset sp that spawned from seleted temset s from DBS and an element e onsdered from I. If the fts ( s p ) s greater or equal to rs, then an edge wll be defned between s and e. If fts ( s ) fts ( sp ) then we prune s from DB S. Ths prunng proess s requred and lmted to frst teraton only. From the seond teraton onwards projet the temset S that spawned from S p' defned between to eah element e of I. An edge an be S p' and e f fts ( s p ) s greater or S p' s a projeted temset equal to rs. In ths desrpton n prevous teraton and elgble as a sequene. Then apply the followng valdaton to fnd the losed sequene.. Rear Edge Prunng If any of f ( s ) f ( s ) that edge wll be ts p' ts p pruned and all dsjont graphs exept sp wll be onsdered as losed sequene and moves t nto DBS and remove all dsjont graphs from memory. The termnaton of above proess do not take plae tll the graph beomes empty,.e. tll the elements whh are onneted through transtve edges and projetng temsets are avalable n the memory. b) Buldng Sequene Set from Transaton Dataset Here n ths seton we explore the proess of buldng sequene dataset. TD s the gven transaton dataset I s the set of losed frequent temsets of length 1 to m. Here m s the maxmal length of the temset. Intally set of losed frequent temsets s ordered n desendng manner by temset length. For eah transaton T td n the gven transaton dataset TD o Buld events based on the losed frequent temsets of the set I suh that the event lengths wll be deded n the desendng order of the frequent temset length. o Intally events wth length of m determned that s maxmal length of the frequent temsets. Then p Aprl Global Journals In. (US)

5 Aprl events wth length of m 1wll be determned. Ths proess ontnues to determne events wth length{ m = {2,3,... m 1}}. o Then elmnates the tems that are not part of the any event n the transatont td, whh also referred as outlers. ) Measurng MSF and Orderng the Sequene Dataset As a part of the OSSM, we order the sequene dataset n the desendng manner of the Maxmal support Fator (refer seton 3 for detals). Let S be the determned sequene dataset from the gven transaton dataset TD and set of frequent temsets I. For eah sequene s of the gven sequene set S o Fnd Maxmal support MS() e of the eah event e of the sequene s (refer seton 3 for proess of measurng MS() e ) o Fnd Maxmal Support Fator MSF() s (refer seton 3 for proess of measurng MSF() s ) Order the sequene set n desendng order of the MSF d) Buldng Weghted Ayl Dreted Graph In ths phase of OSSM, we explore the buldng of a weghted ayl dreted graph. Let I2 be the set of frequent temsets of length 2. Let G be the graph ntally wth vertex ount of zero V = 0and edge ount of zero E = 0. Here V s vertex set and E s edge set. For eah temset s d of I2 buld an edge ed n graph G o Let onsder tem s s d as soure vertex, and add tem s to vertex set V. Inrement V by 1. o Let onsder tem d s d as destnaton vertex, and add tem d to vertex setv. Inrement V by 1. o Buld a dreted edge ed between s and d, add dreted edge ed to edge set E. Inrement E by 1. o Add support of s d as weght to edge ed. e) Fndng Crtal Paths between two Items as Maxmal Length Sequenes In ths phase we apply WFI algorthm [9, 10]. In the frst pass of algorthm we try to dentfy and evaluate potental long and rh anddates. The rh sequenes are the one whose onsttuent 2-sequenes have hgh support. In the dreted graph, the 2-sequenee frequenes are represented by the edge weghts; we an easly ompute the path wth the hghest weghts between all pars of nodes. Here we use WFI algorthm [9,10] for the purpose fndng rtal path(a path wth maxmal vertex ount) wth maxmal weghts. f) Sequene Evoluton Eah rtal path generated from the graph G wll be onsdered as anddate sequene and stored n anddate sequene set ss g) Verfyng Frequeny of Canddate Sequene For eah anddate sequene s of anddate sequene set ss o Fnd MSF( s ) o For eah sequene s suh that { s S MSF( s) MSF( s)} (refer hypothess 1n seton 3) If s s then nrement sup( s ) by 1 o If sup( s) st (refer the hypothess 2 n seton 3) then Move s to frequent sequene set fss For eah anddate sequene s ' of anddate sequene set ss suh that s ' s If s ' s then onsder s ' as frequent (refer hypothess 3 n seton 3) and move s ' from ss to fss o Else For eah anddate sequene s ' of anddate sequene set ss suh that s ' s If s s ' then onsder s ' as not frequent and prune t from ss (refer hypothess 4 n seton 3) h) Fndng Maxmal Length Sequenes Let fss be the frequent sequene set generated n prevous phase Order the fss n desendng manner by Maxmal support Fator MSF of the frequent sequenes of fss. Let a Boolean fator sts as true. For eah frequent sequene fs of the fss and sts s true o For eah frequent sequene fs ' suh that { fs ' fss MSF( fs ') MSF( fs)} and fs fs ' and sts s true If fs fs ' then set sts as false o If sts s true then move frequent sequene fs to maxmal length frequent sequene set mlfss Fnally, maxmal length frequent sequene set mlfss ontans sequenes that are not subsequene of any other frequent sequenes Global Journals In. (US)

6 VI. Conluson The proposed ordered sequene set mnng (OSSM) approah s a salable and optmal beause of ts hybrd bottom-up-down approah. OSSM s supported by our earler Conurrent Edge Prevson and Rear Edge Prunng (CEG&REP)[7] for frequent losed temset mnng, whh was proven as effent n memory usage and salable on dense datasets. A novel mehansm of sequene dataset generaton from transaton dataset s ntrodued n ths paper. The proposed OSSM s apable to generate the longest anddate sequene by weghted ayl dreted graph onstruton and also effent and salable to fnd frequent sequene set and maxmal length frequent sequene set due to top-down approah. To ompute the support for a anddate sequene, t uses the maxmal support fator of sequenes. And the order approah that orderng the sequene dataset n desendng order of MSF ensures that whole data set s not sanned. Also, f the data set ontans long regular sequenes, t s dentfed early enough and thus all the subsequenes of ths s also marked regular and need not be evaluated. The longest possble sequene s buld up by bottom up algorthms startng from 2- sequene. Referenes référenes referenas 1. Agrawal, R., and Srkant, R., Mnng Sequental Patterns: Generalzatons and Performane Improvements Proeedngs of the 5th Internatonal Conferene on Extendng Database Tehnology: Advanes n Database Tehnology p. 3 17, (1996). 2. Pe J, Han J. et al: PrefxSpan: Mnng Sequental Patterns Effently by Prefx- Projeted Pattern Growth n Int'l Conf Data Engneerng,p (2001) 3. Zak, M. J., SPADE: An Effent Algorthm for Mnng Frequent Sequenes, Mahne Learnng, v.42 n.1-2, p.31-60, January-February Garofalaks M, Rastog R and Shm, K, Mnng Sequental Patterns wth Regular Expresson Constrants, n IEEE Transatons on Knowledge and Data Engneerng, vol. 14, nr. 3, pp , (2002). 5. Antunes, C and Olvera, A.L: "Generalzaton of Pattern-Growth Methods for Sequental Pattern Mnng wth Gap Constrants" n Int'l Conf Mahne Learnng and Data Mnng, (2003) Ln, D I, and Kedem, Z M, Pner Searh: A new algorthm for dsoverng the maxmum frequent set, n Internatonal onferene on Extendng database tehnology, Anurag Choubey, Dr. Ravndra Patel and Dr. J.L. Rana, "Conurrent Edge Prevson and Rear Edge Prunng for Frequent Closed Itemset Mnng"; (IJACSA) Internatonal Journal of Advaned Computer Sene and Applatons, Vol. 2, No. 11, Janyong Wang, Jawe Han: BIDE: Effent Mnng of Frequent Closed Sequenes. ICDE 2004: Floyd, R.: Algorthm 97: Shortest path. Communatons of the ACM 5 (1962) 10. Warshall, S.: A theorem on boolean matres. Journal of the ACM 9 (1962) 11. M. Zak, SPADE: An Effent Algorthm for Mnng Frequent Sequenes. Mahne Learnng, 42:31-60, Kluwer Aadem Pulshers, N. Pasquer, Y. Bastde, R. Taoul and L. Lakhal, Dsovng frequent losed temsets for assoaton rules. In ICDT 99, Jerusalem, Israel, Jan M. Zak, and C. Hsao, CHARM: An effent algorthm for losed temset mnng. In SDM 02, Arlngton, VA, Aprl R. Kohav, C. Brodley, B. Frasa, L.Mason, and Z. Zheng, KDD-up 2000 organzers report: Peelng the Onon. SIGKDD Exploratons, 2, J. Han, J. Wang, Y. Lu, and P. Tzvetkov, Mnng Top- K Frequent Closed Patterns wthout Mnmum Support. In ICDM 02, Maebash, Japan, De P. Aloy, E. Querol, F.X. Avles and M.J.E. Sternberg, Automated Struture-based Predton of Funtonal Stes n Protens: Applatons to Assessng the Valdty of Inhertng Proten Funton From Homology n Genome Annotaton and to Proten Dokng. Journal of Moleular Bology, 311, J. Pe, J. Han, and W. Wang, Constrant-based sequental pattern mnng n large databases. In CIKM 02, MLean, VA, Nov Aprl Global Journals In. (US)

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