Fuzzy Decision Tree for Data Mining of Time Series Stock Market Databases

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1 Fuzzy Deso Tree for Data Mg of Tme Seres Sto Maret Databases Mod Noor Md Sa, Rasd Hafeez Koar Fauty of Comuter See ad Iformato System Uversty Teoogy of Maaysa, 83 Suda, Joor, Maaysa Te: 67)-55349, Fa: 67) BSTRCT If te gve fat for a ateedet a fuzzy roduto rue FPR) does ot mat eaty t te ateedet of te rue, te osequet a st be dra by teque su as fuzzy reasog. May estg fuzzy reasog metods are based o Zade s Comostoa rue of Iferee CRI) requres settg u a fuzzy reato betee te ateedet ad te osequet art. Tere are some oter fuzzy reasog metods do ot use Zade s CRI. mog tem, te smartybased fuzzy reasog metods, mae use of te degree of smarty betee a gve fat ad te ateedet of te rue to dra ouso are e o. I ts aer, e Fuzzy Deso Tree FDT) as bee ostruted by usg egted fuzzy roduto rues WFPR). I WFPR, assg a egt arameter to ea roosto te ateedet of a fuzzy roduto rue FPR) ad assg ertaty fator CF) to ea rue. Certaty fators ave bee auated by usg some mortat varabes e.g. effet of oter omaes, effet of oter sto eages, effet of overa ord stuato, effet of ota stuato et) dyam sto maret. Fay, our roosed aroa be abe to redt sto sare des, ad mrove omutatoa effey of data mg aroaes. Keyords Data Mg, Fuzzy Logs, Deso Tree, Neura Netors.. INTRODUCTION Tme seres data are of grog mortae may e database aatos, su as data mg. tme seres s a sequee of rea umbers, ea umber reresetg a vaue at a tme ot. For eame, te sequee oud rereset sto or ommodty res, saes, eage rates, eater data bomeda measuremets, et. Dfferet smarty queres o tme-seres ave bee trodues [, ]. For eame, e may at to fd stos tat beave aromatey te same ay or aromatey te ooste ay) for edgg; or roduts tat ad smar seg atters durg te ast year; or years e te temerature atters to regos of te ord ere smar. I queres of ts tye, aromate, rater ta eat, matg s requred. Hoever mg dfferet queres from uge tme-seres data s oe of te mortat ssues for researers. I usefu data mg teques e assfato ad usterg, to ade tme-seres data s oe of te stmuatg resear ssue. Frst e overt dyam tme seres data segmet to equa set of atter same), are arorate for geera data mg metod, ad use te attrbutes of tese stat sames as te bass for eoratory fuzzy rue duto. a stat same ossts of a set of fuzzy attrbutes ad ea fuzzy attrbute osst of a set of gust terms. By usg tese gust terms, e auate assfato attrbute. From te sto vestor ersetve, te sme age te geera tred.e., from reasg to dereasg) s very mortat, se t may trgger a buyg or a seg ato. Terefore to aayze every sme age, e ave used oerfu fuzzy reasog metod our agortm. Te geera data-mg metod su as FDT) a te be used drety o te formato database to uover te rues for redtg te egt of same.e., te turg ot of a sto maret quotato). FDT s are eras suessfu metods for aurate deso mag. It a rovde a g eve of redtve auray, rarey do tey fatate uma seto or uderstadg. FDT a be bud by usg our agortm to trag tese stat sames. Our roosed FDT a be used to geerate ad me WFPR s. Te reresetato oer of WFPR s a be eaed by udg severa oedge arameters su as egt ad ertaty fator. May fators are affetg sto maret drety or drety, ts aer e ave aayzed some fators be reseted et seto. We use tese fators to evauate ertaty fator WFPR s. Te remder of ts aer s arraged as: seto ostruto of FDT, seto 3 eermeta resuts etrat WFPR s from FDT), ad fay ouso seto 4.. PROCSSING FDT CONSTRUCTION) FDT duto a be used to geerate ad me WFPR s ad te reresetato oer of WFPR s a be eaed by udg severa oedge arameters su as egt ad ertaty fators [3]. I ts seto, e reset a e FDT by eag tese arameters. We use some ve arameters a affet sto maret drety or drety. Our roosed FDT [4, 5] as based o mmum assfato formato etroy to seeted eaded attrbutes. Ts oet roosed by Qua 986 [6]. I ts aer, e etrat WFPR s from FDT by usg arameters, egt ad ertaty fators. FDT as four omoets: set atters, Fuzzfato of umera umbers, smarty-based fuzzy reasog metod, but fuzzy deso tree to trag fuzzy sets eames. Te foog setos reset te omreesve study of tese omoets of FDT.

2 Set Patters I frst ste of FDT e detfy atters, ad te fuzzy sets are used to otmze te roftabty of te detfed atters. Hstora data s very mortat for sto redto. Usg formato o sto erformed te ast, e a redt sto des te best ourse of ato to tae o. I seod omoet of FDT to defe fuzzy sets seeto. For fuzzy sets defg, e use traguar fuzzy members futo orresods to ea atters. I et fuzzy reasog, e e tat gve fat for a ateedet a fuzzy roduto rue does ot mat eaty t te ateedet of te rue, ad te osequet a be dra by usg our roosed smarty-based fuzzy reasog metod. fter fuzzy reasog e ostrut fuzzy deso tree for trag data. I te foog setos tese omoets are outed deta.. Set Patters for FDT I frst ste of FDT to detfy atters, te fuzzy sets are used to otmze te roftabty of te detfed atters. We overt dyam tme seres sto maret data segmet to equa set of atter, are arorate for geera data mg metod, ad use te attrbutes of stat sames as te bass for eoratory fuzzy rue duto. Tese sames osder as a stat sames.. Fuzzfato of Numera Numbers Fuzzfato s a roess of fuzzfyg umera umbers to gust terms, s ofte used to redue formato overoad uma deso mag roess. Te umera saary, for eame, may be ereved gust terms su as g, average ad o. Lgust terms are sme forms of fuzzy vaues but geeray ter members futos are uo ad eed to be determed. Oe ay of determg members futos of tese gust terms s by eert oo or by eoe s ereto. Yet aoter ay s by statsta metods [7]. agortm for geeratg erta tye of members futos, s based o sef-orgazed earg [8], a be foud [9]. Let X s a gve data set be same to gust terms T,,,...,. Te traguar members futo s deoted as ) ad s defed as: µ ) Fuzzy Sets Defg oterse Smarty- Based Metod Fuzzy Reasog Fgure : Te Comoets of Fuzzy Deso Tree...) Fuzzy Deso Tree traguar members futo a be rereseted by a tre umbers, m, ), ere s oer umber, m s md ot ad s ger umber te traguar members futo. Cosder Oe attrbute from tabe I as tree gust terms 3 ), e a fd members futo for tese gust terms as: + ) T o oterse T med T g It s obvous tat te tree gust terms a be desrbed as Lo, Medum ad Hg. Te seod oum of Tabe II sos te members degree of te attrbute Oe beogg to te tree members futos. Smary e a fd members futo for oters attrbutes ad resut sos tabe II..3 Smarty-based Fuzzy Reasog Metod Te smarty measure betee gust terms a be defed ter members futos. I ts seto e roose aoter smarty-based fuzzy reasog metod, auates te smarty betee ad usg equaty ad ardaty as Yeug et a []. I our agortm ertaty fator CF) s te ey ot. I revous smarty-based metod ertaty fator s ust assg for stregt of every rue but ere e frst auate ertaty fator by ayg some varabes sto maret. Let us frst auate smarty measure, s deoted by a, a ) ad defed as: + ) r ) oterse.3) r oterse..4) TBL I: Oe same from sto eage databases

3 TBL II: Trag Set t Fuzzy Reresetato " " " " " Fgure : Fuzzy Deso Tree by usg our roosed agortm to tra tabe II a, a ) F )... F ) Were s te symmetra dfferee of ad 5 ), vz. X, µ µ ) µ ). Tus te equato a be eressed as µ a ) µ a ) X a, a )... 6 ) µ ) X It s observed tat, ), s te degree of equaty of a a, dffers from a, a ) ad, for stae, f a a a, a ) a, te a, a ). ga f a, a ) λa for a te rue a be fred ad te aggregated egted average, G s defed as W W a, a ) *...7) a, fter te aggregated egted average as bee auated, to modfato futos are roosed to modfy te osequet C. C m {, C / * µ ) }... 8) W γ + δ ere µ s defed as: µ ρ ο ere γ, δ, ρ, ο are atve varabes tat a affet sto maret. Te foog sos at C a be dra for ea of te tree ases: Case : Te ateedet as oy oe roosto W a, a ), ).. 9) Se te / t If C m{, C / W * µ ). 5 a, a ) λa }...) Deedg o eter e at to restrt or date te members vaue ofc. Case: Te ateedet as to or more roosto oeted by ND

4 If S DS W, ) * C a a a a, a ) λ for a ), C m{, C / W * µ ) te...) }...) Case3: Te ateedet as to or more roostos oeted by OR Ts rue a be st to sme rues as so Case,.e., a, a ) W Beause for ea C,...,, s redued to a sge term beomes / If s.t. C a, a ) λ, for a ), m{, C/ma W, OR, If a a, W,... W a, a ) λ for a ), C m{, C/ ma W, W,... W, ad te )* µ ) te )* µ ) }... 3) }... 4) I ts aer, e are terested to redt dyam sto eage databases. Terefore, e are osderg four ossbe ases for every osequet orto. Cosequet aes ouso) ave bee osderg every ossbe futuato dyam sto maret. Here s te sme eame tat e ave used our agortm: IF a s fa ND a s fa THN C s f, CF µ ), T λ, λ }, W, } { a a { ND Cose s o THN Sga s o.4 FDT gortm e.g., IF Oe s o We frst formuate a robem of earg from eames t fuzzy reresetatos. Cosder a set of eames {,,... N } s defed as te uverse of dsourse X, ere X s deoted as {,,..., N }. Let ) ) ),,..., ad +) be a set of fuzzy attrbutes +) ere deotes a assfato attrbute. a fuzzy ) attrbute osst of a set of gust term L T ) { L, L,..., L m },,..., + ). gust terms are defed o te t same uverse of dsourse X. Te vaue of te eame t t reset to te attrbute, deoted by µ, s a fuzzy set defed o L T ),..., N,,,... + ). I oter ords, fuzzy set µ as a form of ) ) µ / L + µ / L µ m ) / L ere µ deotes te orresodg members degree m,..., m. To ustrate tese otatos, e osder a eame so tabe I desrbes a sma trag set of earg from fuzzy. ssume tat tese gust terms s osder as a set of data D, ere ea data as umera vaues for ) ) ) attrbutes,,...,. We tae te reasoabe same sze from ) ) ) attrbutes,,...,.. Geerate te root ode tat as a set of a data,.e., a fuzzy set of a data t te members vaue.. If a ode O t a fuzzy set of data D satsfes te foog odtos:. te roorto of a data set of a ass C s greater ta or equa to a tresod θ r, tat s C D K θ r,... 5 ) D. tere are o attrbute for more assfatos, te t s a ead ode ad assged by te ass ame. 3. If t does ot satsfy te above odtos, t s ot a eaf ad te test ode s geerated as foos: Cosder a test ode S avg attrbutes to be seeted. For ea ), te attrbute T taes m fuzzy m subsets gust terms), L, L,..., L. +) deotes te assfato attrbute, tag vaues + ) + ) + ) L, L,..., Lm. For ea attrbute vaue fuzzy subset), L, m ), ts reatve t frequees oerg te fuzzy ass ) L + defed as M L m) at te osdered oeaf ode S s L + ) S ) / M L S )... 6 ) t te osdered oeaf ode S, te fuzzy assfato etroy of L, m ) s defed as tr m og Te averaged fuzzy assfato etroy of te defed as m tr deotes te egt of te defed as m... 8 ) t vaue M S L ) / M S L t...7 ) L attrbute s )... 9 ) ad s Te above FDT ams to sear for a attrbute su tat ts average fuzzy assfato etroy attas mmum,.e., seetg su a teger o te o t attrbute) tat o M.

5 3. XPRIMNTL RSULTS We demostrate our aroa o te sto maret database. Dyam tme seres sto maret udes date, oe, o, g, ose ad voume attrbutes. I ts aer e ave tae oe, ose, ad voume attrbute beause by tese attrbutes vestors ay more atteto o movemets of sto sares to every sge ut of tme. I ts seto e etrat WFPR s from FDT. 3. WFPR s trato from FDT We a etrat WFPR s from FDT so fgure 3: Rue: IF OeLo) ND CoseLo) ND VoumeLo) THN Otma SgaLo), CF.95, 5.65, , 7 ) Rue: IF OeLo) ND CoseMed) ND VoumeHg) THN Otma SgaMed), CF.85,.65, , 9.45) Rue3: IF OeHg) ND CoseLo) ND VoumeMed) THN Otma SgaLo), CF.75, , 4 3.5, ) Rue4: IF OeMed) ND CoseHg) ND VoumeLo) THN Otma SgaHg), CF.65, 4 5.5, , 7.3) Rue5: IF OeLo) ND CoseHg) ND VoumeLo) THN Otma SgaHg), CF.6, , 6.5, ) Rue6: IF OeHg) ND CoseHg) ND VoumeHg) THN Otma SgaHg), CF 5, , 6.53, 9.35,) 4. CONCLUSION Ts aer resets a e FDT for uredtabe dyam sto eage databases. Most of te estg data mg teques are ot so effet to dyam tme seres databases. FDT as bee ostruted t oer of WFPR s. It s based o mmum assfato formato etroy to seet eaded attrbutes. I smarty-based fuzzy reasog metod e aayze WFPR s are etrated from FDT. Te aayss s based o te resut of osequet dra for dfferet gve fats e.g. varabes tat a affet sto maret) of te ateedet. Proosed metod as some advatages su as aurate sto redto, effey ad omreesbty of te geerated WFPR s rues, are mortat to data mg. Tese WFPR s ao us effetvey assfy atters of o-asarae deso boudares usg members futos roery, s dffut to do usg attrbute-based assfato metods. We are o ayg our agortm for geeratg WFPR s from oe sto maret data. For eermetato, e are usg stora data. By usg formato o sto erformed te ast, you a use our system to redt te best ourse of ato to tae o. 5. RFRNC [] R. graa, K.-I. L, H.S. Saey, ad K. Sm, ªFast Smarty Sear te Presee of Nose, Sag, ad Trasato Tme-Seres Databases,º Pro. st It Cof. Very Large Data Bases VLDB 95),. 49±5, Set [] R. graa, G. Psaa,.L. Wmmers, ad M. Zat, ªQueryg Saes of Hstores,º Pro. st It Cof. Very Large Data Bases VLDB 95),. 5±54, Set [3] Yeug, D.S.; Tsag,.C.C.; Xzao Wag; Fuzzy rue mg by fuzzy deso tree duto based o fuzzy feature subset Systems, Ma ad Cyberets, I Iteratoa Coferee o, Voume: 4, 6-9 Ot. Pages:6. vo.4 [4] R. H. Koar, Mod Noor Md Sa. Desg ad Deveomet of Neura Bayesa roa for Uredtabe Sto age Databases CW 3, Mara Madar Sgaore, 3-5 De 3 Pages: I. [5] R. H. Koar, Mod Noor Md Sa. Neuro-Prug Metod for Prug Deso Tree Large Databases, CIRS 3, Pa Paf Hote, Sgaore, 5-8 De 3. [6] J.R. Qua 986) : Iduto of Deso Tree Mae Learg, Vo,.8-6. [7] M. R. Cvaar ad H. J. Trusse, Costrutg members futos usg statsta data, Fuzzy Sets ad Systems, vo. 8, 986,. -4. [8] T. Kooe, Sef-Orgazato ad ssoato Memory Srger, Ber, 988 [9] Y. Yua ad M. J. Sa, Iduto of fuzzy deso trees, Fuzzy Sets ad Systems vo. 69, 995, [] D. S. Yeug ad. C. C. Tsag, Comaratve Study o Smarty-Based Fuzzy reasog Metods I Tras. Syst., Ma ad Cyberets-art : System ad Huma, vo., 7, No., r 997.