An Optimized Classification Model for Time-Interval Sequences

Transcription

1 Proeedigs of the World Cogress o Egieerig 00 Vol I WCE 00, Jue 0 - July, 00, Lodo, U.K. A Optimized Classifiatio Model for Time-Iterval Seuees Chieh-Yua Tsai, Chu-Ju Chie Abstrat Seuee lassifiatio is a popular data miig method to explore ustomer behavior by assigig the most probable lass label to a give seuee. However, previous researhes seldom disussed seuee lassifiatio problem related to time iformatio. Without time iformatio, two seuees with the same itemsets but differet time-itervals will be lassified as the same lass. For this reaso, this researh presets a time-iterval seuee lassifiatio methodology to help busiess maagers uderstad their ustomer behaviors i depth. The proposed seuee lassifiatio method iludes two mai stages. The first stage is time-iterval seuetial patter miig, whih employs I-PrefixSpa algorithm to disover time-iterval seuetial patters i the large database. The seod stage is time-iterval seuee lassifiatio method, whih otais time-iterval seuee lassifiatio model ad partile swarm optimizatio proedure. A simple ase is employed to show the performae of the proposed lassifiatio method. The experimet result idiates the proposed time-iterval seuee lassifiatio method is feasible ad effiiet. Idex Terms Time-iterval seuetial patter miig, Seuee lassifiatio, Partile swarm optimizatio. I. INTRODUCTION I urret ompetitive ad fast-haged busiess eviromet, if a eterprise a provide right produts ad right servies at the right time to the right ustomers, the eterprise might have more hae to survive tha others. Therefore, it is importat for eterprises to kow their ustomer behaviors i depth. Seuetial patter miig, oe of the most popular data miig methods, reeives may attetios i reet years. Sie seuetial patter miig a disover freuet ourrig patters from large databases, it has beome a ritial approah to explore ustomer behaviors. For example, the seuetial patter miig a geerate a seuetial patter suh as ikjet priter ik artridge papers ik artridge refill kit. This patter shows that ustomers who buy a ikjet priter will have strog probability to buy a ik artridge, papers, ad ik artridge refill kit i order. With the help of this patter, maagers a sed a ik artridge refill kit promotio program to ustomers after ustomers bought a ikjet priter, a ik artridge, ad papers. The researhes related to seuetial patter miig maily fous o miig iterestig seuetial patters ad detetig Mausript reeived February, 009. Chieh-Yua Tsai is with the Departmet of Idustrial Egieerig ad Maagemet, Yua Ze Uiversity, Taiwa, R.O.C. (phoe: Ext. 5; fax: ; ytsai@satur.yzu.edu.tw) ISBN: ISSN: (Prit); ISSN: (Olie) similar seuetial patters [] []. There is few researhes disuss the issue of how to aurately lassify a usee seuee. The seuee lassifiatio is to assig the most probable lass label to a give seuee by a geerative model (or lassifier). Huag et al. [4] employed support vetor mahie (SVM) to develop seuee lassifiatio model. Joug et al. [5] employed hidde Markov model (HMM), a statistial model i whih the system beig modeled is assumed to be a Markov proess with uobserved state, to geerate a seuee lassifiatio model. Bouhaffra ad Ta [6] exteded the traditioal hidde Markov model amed strutural hidde Markov model by partitioig the set of observatio seuees ito lasses of euivalees to ehae the auray for the seuee lassifiatio model. Bruy et al. [7] itegrated estimatio, lusterig, ad lassifiatio ito the traditioal, three-step approah to make the result of seuee lassifiatio more reliable. The above seuee lassifiatio researhes maily disuss about the biologial protei seuee lassifiatio ad text reogitio. Seldom of them applied it to ustomer behavior preditio. I additio, the seuetial patters i these studies do ot over time-iterval iformatio. However, this drawbak is espeially serious whe dealig with ustomer behavior data. For example, otebook ( week) priter ad otebook ( year) priter are two seuetial patters with the same order but differet time-itervals. It is lear that ustomers buy the priter after they bought otebook week later ad year should ot be viewed as the same behavior. If time-iterval iformatio is ot osidered i the two seuetial patters, maagers might osider the two patters as the same patter of otebook priter. To solve the above problems, this study developed a effiiet lassifier that a aurately predit the lass label of the seuees with time-iterval iformatio. The proposed lassifier is expeted to help deisio makers ot oly a learly distiguish differet types of ustomers behavior over time but a propose more itelliget busiess strategies aordig the lassifiatio result. II. RESEARCH METHOD The framework of the proposed time-iterval seuee lassifiatio model is preseted i Fig. whih iludes two stages. I the first stage, I-PrefixSpa algorithm [8] is used to geerate time-iterval seuetial patters for every lass i the database, respetively. I the seod stage, the similarity betwee eah pair of time-iterval seuees is alulated first. Next, the geerated time-iterval seuetial patter sets WCE 00

2 Proeedigs of the World Cogress o Egieerig 00 Vol I WCE 00, Jue 0 - July, 00, Lodo, U.K. Time-iterval Seuetial Patter Miig Database of trasatio reords with timeiterval Evaluate the similarity betwee eah pair of timeiterval seuees ad patters Geerate timeiterval seuetial patters aordig to eah lass The timeiterval seuetial patter sets with lass Time-iterval Seuee Classifiatio Method Build time-iterval seuee lassifiatio model Optimize the weights i the lassifiatio model Fig. Framework of the proposed time-iterval seuee lassifiatio model are employed to build the time-iterval seuee lassifiatio model. The the optimizatio method based o partile swarm optimizatio (PSO) is employed to update the weights iluded i the time-iterval seuee lassifiatio model to maximize the auray of the lassifiatio result. Fially, whe a ew time-iterval seuee iputted, the proposed lassifiatio model a aurately predit the lass label of the time-iterval seuee. A. Time-Iterval Seuetial Patter Miig The trasatio database is divided to sub-databases aordig to the lass that eah seuee belogs to. Let the th sub-database be preseted as PH, where =,,,. After odutig time-iterval seuetial patter miig (I-PrefixSpa algorithm) to PH, the freuet time-iterval seuetial patter sets for lass, deoted as are foud.the I-PrefixSpa algorithm, whih is proposed by [8] is used to geerate the time-iterval seuetial patters from seuee data. It is exteded from the well-kow PrefixSpa algorithm. I-PrefixSpa is a projeted-based algorithm whose steps for geeratig time-iterval seuetial patters are show i Fig.. B. Similarity Measure betwee Seuees ad Patters To failitate the followig lassifiatio model buildig proess, the dissimilarity betwee a seuee i PH ad a time-iterval seuetial patter i, should be defied first. Two dissimilarity premises betwee a time-iterval seuee ad a time-iterval seuetial patter are larified. First, eah time-iterval ours after a item was take plae but before the followig item appeared. Therefore, the time-iterval ad the item ourred before it is treated as a uit whe odutig the edit distae evaluatio i the dyami programmig. Seod, item ompariso is oduted first whe alulatig the dissimilarity betwee a seuee ad a patter. Wheever items are the same i the seuee ad the patter, dissimilarity betwee the followig time-itervals is the evaluated. If items i the seuee are ot the same with the item i the patter, the dissimilarity betwee the time-itervals appeared after the two items are ot worth to disuss. Base o the above oept, the ost of takig reuired edit operatios is summarized as (): Algorithm I-PrefixSpa(α, l, PH α ) Parameter: α : a time-iterval seuetial patter; l : the legth of α; : the lass label where =,,, ; Method: () Sa PH α oe time. () If l = 0, the fid all freuet items i PH α. () For every freuet item f, apped f to α as α. (4) Output all α. (5) If l > 0, the ostrut TI_Table by saig all the trasatios i PH α. (6) For every freuet ell TI_Table(I i, f), apped (I i, f) to α as α. (7) Output all α. (8) For eah α ostrut α -projeted database PH α, ad all I-PrefixSpa (α, l+, PH α ) Fig. The pseudo-ode of the I-PrefixSpa algorithm Cost p, =, if Isertio or Deletio, if Substitutio (with differet items) f( Ip) f( I) 0 + r, f( Im) f( I0) + if Substitutio (with the same items) 0, if No Chage where p meas the pth uit i the time-iterval seuetial patter, meas the th uit i the seuee. The ratio r, defied by users, is the maximum degree that time-iterval dissimilarity a affet the ost. f(i b ) is the rak of the time-iterval I b ad is defied as f(i b ) = b where b = 0,,, m. The ost for edit distae is the degree of dissimilarity betwee a time-iterval seuee ad a time-iterval seuetial patter. Therefore, the similarity betwee eah edit operatio is defied as mius the ost of eah edit operatio, whih is defied as: Sim = Cost () p, p, Based o (), the total similarity betwee the whole time-iterval seuee ad the whole time-iterval seuetial patter is the sum of all Sim p, ad divides by the value of the logest legth betwee the seuee ad the seuetial patter. The similarity of the ith time-iterval seuetial patter ad the jth seuee is summarized i () where p =,,, l s ad =,,..., l p, l s deotes the legth of the time-iterval seuee ad l p deotes the legth of the time-iterval seuetial patter. This ormalizatio operatio is set to avoid the oditio the loger seuees obtai higher similarity value with a speifi patter whih might affets the fairess of similarity measure. Sim = ls p lp Sim p, max( l, l ) s p where p =,,, l s ad =,,..., l p. C. Framework of the Classifiatio Method Similar to the framework of the lassifiatio model proposed by Exarhos et al. [9], whih was origially applied to evaluate the biologial seuee dataset, the proposed framework is desiged to lassify time-iterval seuees. I the proposed lassifiatio method, all seuees () () ISBN: ISSN: (Prit); ISSN: (Olie) WCE 00

3 Proeedigs of the World Cogress o Egieerig 00 Vol I WCE 00, Jue 0 - July, 00, Lodo, U.K. { PH =,,..., } { =,,..., } S ad all the freuet seuetial patters F are used as iput to the lassifiatio model, ad the output is a ofusio matrix (CM) deotig the lassifiatio auray iformatio. Let seuees i database PH be marked with lass labels deoted as database PH = {S j, }, where S j represets the jth seuee ad represets the lass seuee belogs, with is the umber of lasses ad s is the overall umber of seuees i database PH, where =,,,. I additio, the umber of time-iterval seuetial patters i F is preseted as where =,,,. The lassifiatio method is divided ito four steps, ad they are desribed as follows: Step : Calulatio of the patter sore matries. After the extratio of the time-iterval seuetial patters, we use the seuees ad the time-iterval seuetial patter sets to ostrut the patter sore matrix for eah lass. The patter sore matries are deoted as PSM = [y kj ] where =,,,, k =,,,. Symbol deotes the th PSM, k deotes the kth row of PSM, j meas the seuee S j. Every elemet i PSM, deoted as y kj, stads for a sore whih defies the similarity of the kth time-iterval seuetial patter withi lass betwee the seuees S j. Thus, the size of a PSM is s. Step : Update of the patter sore matries. Eah row of the patter sore matrix is multiplied by a parameter whih represets the weight of a speifi time-iterval seuetial patter i the lass. That is, y kj i the same row are multiplied by same weight. Therefore, eah PSM is updated as: k k k row = w _ patter row (4) k where row deotes the kth row i the th PSM, ad the k w _ patter is the weight of the kth time-iterval seuetial patter i the th patter set. The weights are geerated from a effiiet partile swarm algorithm, whih will be itrodued i ext setio. Step. Calulatio of the lass sore matrix. The lass sore matrix, deoted as CSM, is derived from the updated PSM. Assume CSM = [x j ] where eah x j is the elemet of CSM represets the sore of similarity of the seuees S j belogig to the th lass. As metioed above, the row size of PSM depeds o the umber of time-iterval seuetial patters the th lass otais. Therefore, the more time-iterval seuetial patters i the lass, the higher sore the th row of CSM. I order to prevet suh ufair situatio, every ell of the CSM has to be ormalized. The sore of similarity of seuees S j i the th lass i CSM is defied as: x j = k = y kj where =,,,, k =,,,, ad j=,,, s. (5) is the sum of the sore of all the patters i th lass for the seuees S j divided by the umber of patters the th lass otaied. Therefore, the size of the lass sored matrix CSM ISBN: ISSN: (Prit); ISSN: (Olie) (5) is s. Step 4. Update of the lass sore matrix. Eah row of the lass sore matrix is multiplied by a parameter whih represets the weight of a speifi lass. That is, x j i the same row is multiplied by the same weight. Thus, eah row of the lass sore matrix is updated as: row = w _ lass row (6) where deotes the th row of CSM ad the w _ lass is the weight of the th lass. The weights are also geerated from partile swarm algorithm itrodued i the ext setio. For eah seuee S j, a lass is predited base o the updated CSM. The predited lass (p j ) is determied after estimatig the lass whih got the highest sore for the seuee S j : p j = max =,,..., (CSM(, j)). Based o the real lass r j ad the predited lass p j of eah seuee, the ofusio matrix (CM) for all seuees i database is the alulated. The rows of the ofusio matrix (CM) represet the predited lass while the olums of the CM represet the atual lass. The diagoal of the ofusio matrix deotes the umber of the orretly lassified seuees for eah lass. Therefore, or_la(cm) is the futio that summarizes the diagoal elemets of the ofusio matrix CM. The larger the value of or_la(cm) is, the more aurate the lassifiatio result. D. The Optimizatio Proess for Classifiatio Model Two sets of weights, w_lass for eah row of the lass sore matrix (CSM) ad w_patter for eah row of patter sore matries (PSM) have bee defied above. However, the values of the two sets of weights (w_patter ad w_lass) might dramatially affet the auray of the proposed lassifiatio model. Therefore, the optimal values of the two sets of weights should be derived so that the best lassifiatio result a be obtaied. This researh employs partile swarm optimizatio (PSO) algorithm, a global optimizatio searh approah, to fid the best w_lass ad w_patter. PSO algorithm ot oly is easy to ode but also the ru time is short. The objetive futio of this optimizatio problem is the defied as: mi f(cm) = s or_la(cm) (7) where s is the umber of all seuees i database PH, ad or_la(cm) is the umber of orretly lassified seuees i CM desribed i last setio. Notes that f(cm) is the fitess futio i the PSO algorithm. The miimal value of the objetive futio is 0 whe all seuees are orretly lassified (s = or_la(cm) ). I additio, i this researh, a partile is represeted as: x i = [,...,,, w _ lass, w _ lass,, w _ lass ]. where the total dimesio of the partile is ( ) +. = WCE 00

4 Proeedigs of the World Cogress o Egieerig 00 Vol I WCE 00, Jue 0 - July, 00, Lodo, U.K. PH PH TABLE THE DATASET PH sid Si PH PH <(A, ) (B, 5) (C, 5) (C, 5) (D, 7)> <(A, 5) (B, 7) (E, 4) (C, 70)> <(B, 4) (C, 6) (A, 7) (A, 65)> <(A, 0) (C, 49) (D, 5) (C, 06)> <(B, ) (A, 7) (B, 5)> <(A, ) (C, 6) (D, 6) (D, 70)> <(A, ) (B, 7) (C,0) (D, 5)> <(A, ) (B, 5) (D, 7)> <(B, 7) (D, ) (D, 44) (B, 5)> <(A, 6) (A, ) (D, 5) (D, 46)> <(B, 8) (B, ) (D, 4) (C, 79) (D, 85)> <(B, ) (D, 8) (A, ) (D,58)> <(C, ) (B, 7) (D, 9) (C, 4)> <(C, ) (B, 8) (D, )> <(B, ) (A, ) (D, ) (B 6) (D, 0)> <(B, ) (B, 7) (C, ) (D, 8)> <(C, ) (B, 5) (E, )> <(C, 9) (B, 7) (A, 0) (E, 9)> <(A, ) (B, 0) (C, ) (E, 7)> <(C, 6) (A, 8) (E, ) (A, 45)> <(B, 4) (C, ) (B, 8) (E, 50) (A, 8)> <(B, 4) (C, ) (E, 9) (A, 6 )> <(A, ) (C, 5) (E, 8) (A, 6)> <(C, 9) (B, ) (E, 6) (A, )> TABLE TIME-INTERVAL SEQUENTIAL PATTERNS IN EACH CLASS Time-iterval seuetial patters A I B A I D A I E A I4 C A I5 D B I C C I D C I4 D A I B I C A I4 C I 4 D A I D A I4 D B I C B I D B I D B I4 D B I5 C B I5 D C I D D I B D I D A I D I D B I C I D B I5 C I D B I E B I A B I E B I5 A C I B C I E C I A C I5 A E I A E I4 A C I B I A C I E I 4 A III. EXPERIMENT RESULTS A. Itrodutio to Dataset Let the merhadise itemset be I = {A, B, C, D, E} where eah alphabet represets a item. The sytheti dataset iludes twety-four trasatio reords whih imitates ustomer purhasig behaviors. Customers are divided ito three lasses ( = ). That is, eight seuees belog to the same lass. Table show the dataset. Note the uit of time i datasets is a day. For example, ustomer sid buys item A i day, buys item B i day 5, the buys C i day 5 ad so o. I eah lass, six seuees are used as traiig data to reate the seuee lassifiatio model ad the remaiig two seuees are used for testig. Hee, the traiig dataset PH trai osists of 8 seuees ( PH trai = 8) ad the test dataset PH test osists of 6 seuees ( PH = 6 ). B. Geeratio of the Time-Iterval Cassifiatio Model Ay seuee i the sytheti dataset PH belogs to oe of the three lasses. Therefore, PH = {S i, i } with S i beig the seuee ad i beig the orrespodig lass. The sytheti test i TABLE THE SET OF WEIGHTS OF PSM FOR. w _ patter A I B.94 A I 4 C.0806 A I 5 D 0.97 B I C.000 C I D.0 C I 4 D.747 A I B I C.946 A I 4 C I 4 D.0987 TABLE 4 THE SET OF WEIGHTS OF PSM FOR. w _ patter A I D 0.76 A I D.9 A I 4 D B I C.090 B I D.00 B I D B I 4 D.005 B I 5 C.0857 B I 5 D C I D D I B. D I D A I D I D.098 B I C I D B I 5 C I D TABLE 5 THE SET OF WEIGHTS OF PSM FOR 5. w _ patter A I E B I E.08 B I A.09 B I E B I 5 A C I B.0598 C I E.0049 C I A.49 C I 5 A.007 E I A E I 4 A 0.98 C I B I A.078 C I E I 4 A dataset is divided to three sub-datasets whe miig freuet time-iterval seuetial patters by I-Prefixspa algorithm. Assume that the value of support is set as, ad the set of time-itervals TI = {I 0, I, I, I, I 4, I 5 }, where I 0 : t = 0, I : 0 < t 0, I : 0 < t 0, I : 0 < t 0, I 4 : 0 < t 40, ad I 5 : 40 < t. After odutig I-Prefixspa to eah sub-dataset, the geerated time-iterval seuetial patter sets are deoted as where =,, ad are show i Table. The PSO algorithm is employed to the optimizatio proess. The parameters i the PSO suh as populatio of partiles, p; the iertial ostat, w; the ogitive parameter, ; ad the soial parameter,, ad the restritio of movig veloity of partiles (v max ) are all set by user. The iertial ostat, w, is usually set withi the rage 0.5 to. Therefore, w is set as 0.5 plus a radom value divided to i aordae with advie of the literatures [] Further, the restritio of ogitive ad soial parameter ad is + 4, for fast overgee, is set as.5, ad is set as.5, too. Ad the populatio of partiles, p, is set as 0. However, i order to remai value of w_patter ad w_lass positive ad stable, veloity v i of ISBN: ISSN: (Prit); ISSN: (Olie) WCE 00

5 Proeedigs of the World Cogress o Egieerig 00 Vol I WCE 00, Jue 0 - July, 00, Lodo, U.K. partile p i where i =,,, 0, is restrited i the rage TABLE 6 THE SET OF WEIGHTS OF CSM. row i of CSM w_lass row ( ).048 row ( ).897 row ( ) TABLE 7 THE OPTIMIZED CLASSIFICATION RESULT. Si Preditio Preditio Origial Witout With Class Optim. Optim. ( i ) (p i ) (p i ) <(A, ) (B, 5) (C, 5) (C, 5) (D, 7)> <(B, 4) (C, 6) (A, 7) (A, 65)> <(A, 0) (C, 49) (D, 5) (C, 06)> <(A, ) (C, 6) (D, 6) (D, 70)> <(A, ) (B, 7) (C,0) (D, 5)> <(A, ) (B, 5) (D, 7)> <(B, 7) (D, ) (D, 44) (B, 5)> <(A, 6) (A, ) (D, 5) (D, 46)> <(B, 8) (B, ) (D, 4) (C, 79) (D, 85)> <(C, ) (B, 8) (D, )> <(B, ) (A, ) (D, ) (B 6) (D, 0)> <(B, ) (B, 7) (C, ) (D, 8)> <(C, ) (B, 5) (E, )> <(C, 9) (B, ) (E, 6) (A, )> <(C, 6) (A, 8) (E, ) (A, 45)> <(B, 4) (C, ) (B, 8) (E, 50) (A, 8)> <(B, 4) (C, ) (E, 9) (A, 6 )> <(C, 9) (B, 7) (A, 0) (E, 9)> [-.5,.5], ad is realulated util the updated value of partile p i is positive. Last, to avoid too extremely large value of variables of dimesio of the partiles, the dyami rage of variables of dimesios i eah partile is restrited smaller tha 5. Table to Table 6 display the output of PSO optimizatio proess. Based o the updated PSM(s) ad CSM, the preditios for eah seuee a be derived, as it is show i Table 7. Aordig to Table 7, the seuee <(B, 4) (C, 6) (A, 7) (A, 65)>, <(A, ) (C, 6) (D, 6) (D, 70)>, ad <(B, 7) (D, ) (D, 44) (B, 5)> were iorretly lassified without usig optimizatio proess are ow orretly lassified as their origial lass with usig the PSO optimizatio proess. Thus, the auray of the lassifiatio method is ireased by.7 % (from 77.7 % without usig optimizatio proess to % with usig the PSO optimizatio proess). To ofirm the fairess ad reliability of lassifiatio result, 4-fold ross-validatio is employed. The sytheti dataset is divided ito four groups as sample sets, ad eah group otais six seuees whih ilude two seuees from eah lass ( =,, ). Oe of sample sets of the sytheti dataset is seleted as testig data, the rest three sample sets are used as traiig data whih are employed to build the lassifiatio model. The experimet is repeated for four times so that every group of sample sets is employed as testig data for the lassifiatio model. The lassifiatio result of the first fold is displayed as above. After the experimet, four lassifiatio results are obtaied ad show i Table 8 ad Table 9. IV. CONCLUSION Nowadays, how to seizig ustomer behavior ad makig proper busiess strategies to differet types of ustomers are TABLE 8 CLASSIFICATION ACCURACY OF TRAINING DATA. Experimet Without After Number optimizatio optimizatio Improvemet fold- 7.% 88.89% 6.67% fold- 6.% 66.67% 5.56% fold % 8.% 7.77% fold-4 6.% 77.78% 6.67% Average 6.50% 79.7% 6.67% TABLE 9 CLASSIFICATION ACCURACY OF TESTING DATA. Experimet Without After Number optimizatio optimizatio Improvemet fold- 8.% 8.% 0.00% fold-.% 50.00% 6.67% fold % 50.00% 0.00% fold % 8.% 6.66% average 58.% 66.67% 8.% importat issues for eterprises. This researh proposes a time-iterval seuee lassifiatio method osiderig the time-iterval iformatio betwee items. With the proposed lassifiatio method, a ew ustomer a be easily lassified as oe of previous kow ustomer lasses aordig to his/her time-iterval seuee. Oe the lass of a ustomer is kow, deisio makers a develop differet busiess strategies to differet ustomers at the right time. The lassifiatio auray is greatly improved after applyig the partile swarm optimizatio proess. There are two major otributios of this researh. First, a ew similarity measure ad evaluatio approah for time-iterval seuees have bee proposed. Seod, this researh proposes a effetive lassifiatio method ivolvig partile swarm optimizatio proess for time-iterval seuees. REFERENCES [] C. Y. Tsai, C. Y. Tsai, ad P. W. Huag, A assoiatio lusterig algorithm for a-order poliies i the joit repleishmet problem, Iteratioal Joural of Produtio Eoomis, vol. 7, 009, pp.0-4. [] C. Y. Tsai ad Y. C. Shieh, A hage detetio method for seuetial patters, Deisio Support Systems, vol. 46, 009, pp [] C. S. Wag ad A. J. T. Lee, Miig iter-seuee patters, Expert Systems with Appliatios, vol. 6, 009, pp [4] D. S. Huag, X. M. Zhao, G. B. Huag, ad Y. M. Cheug, Classifyig protei seuees usig hydropathy bloks, Patter Reogitio, vol. 9, 006, pp [5] J. G. O. S. J. Joug ad B. T. Zhag, Protei seuee-based risk lassifiatio for huma papillomaviruses, Computers i Biology ad Mediie, vol. 6, 006, pp [6] D. Bouhaffra ad J. Ta, Strutural hidde Markov models usig a relatio of euivalee: appliatio to automotive desigs, Data Miig ad Kowledge Disovery, vol., 006, pp [7] A. D. Bruy, J. C.Liehty, E. K. R. E.Huizigh, ad G. L Lilie. Offerig olie reommedatios with miimum ustomer iput through ojoit-based deisio aids, Marketig Siee, 008, pp. 8. [8] Y. L. Che, M. C. Chiag, ad M. T.Ko, Disoverig time-iterval seuetial patters i seuee database, Expert Systems with Appliatios, vol. 5, 00, pp [9] T. P. Exarhos, M. G. Tsipouras, C. Papaloukas, ad D. I. Fotiadis, A two-stage methodology for seuee lassifiatio based o seuetial patter miig ad optimizatio, Data Miig ad Egieerig, vol. 66, 008, pp [0] O. Arbell, G. M. Ladau, ad J. S. B. Mithell, Edit distae of ru-legth eoded strigs, Iformatio Proessig Letters, vol. 8, 00, pp ISBN: ISSN: (Prit); ISSN: (Olie) WCE 00

6 Proeedigs of the World Cogress o Egieerig 00 Vol I WCE 00, Jue 0 - July, 00, Lodo, U.K. [] S. W. Li ad S. C. Che, PSOLDA: A partile swarm optimizatio approah for ehaig lassifiatio auray rate of liear disrimiat aalysis, Applied Soft Computig, vol. 9, 009, pp ISBN: ISSN: (Prit); ISSN: (Olie) WCE 00