Composite Pattern Matching in Time Series

 Wilfred Cross
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1 Composite Pttern Mthing in Time Series Asif Slekin, 1 M. Mustfizur Rhmn, 1 n Rihnul Islm 1 1 Deprtment of Computer Siene n Engineering, Bnglesh University of Engineering n Tehnology Dhk1000, Bnglesh Astrt For lst few yers mny reserh hve een tken ple to reognize vrious meningful ptterns from time series t. These reserhes re se on reognizing si time series ptterns. Most of these works use templte se, rule se n neurl network se tehniques to reognize si ptterns. But in time series there exist mny omposite ptterns omprise of simple si ptterns. In this pper we propose two novel pprohes of reognizing omposite ptterns from time series t. In our propose pproh we use omintion of templte se n rule se pprohes n neurl network n rule se pprohes to reognize these omposite ptterns. Inex Terms Pttern reognition, Rule se pproh, Neurl network, Templte se pproh,composite pttern I. INTRODUCTION There is wie rnge of pplitions in lmost every omin where time series t is eing generte. For exmple, ily?ututions of the stok mrket, tres proue y omputer luster, meil n iologil experimentl oservtions, reings otine from sensor networks, position uptes of moving ojets in lotionse servies, et, re ll represente in time series. Consequently, there is n enormous interest in nlysing (inluing query proessing n mining) time series t, whih hs resulte in lrge numer of works on new methoologies for inexing, lssifying, lustering, n summrizing time series t. Stok mrket prie flutution lso genertes time series t. Tehnil nlysts n trers lim ertin stok mrket time series pttern n shpes le to profitle tre opportunity. For lst few yers mny reserh hve een onute to reognize meningful ptterns from time series t. We fin tht mny omposite ptterns whih frequently ourre in the time series n e forme y simply omining simple si time series ptterns. As fr we re onerne tht the urrent sttes of the rt re not yet onerne out this emerging omposite. In this pper we hve worke with six si ptterns illustrte in Fig1 n the omposite ptterns generte from these six si ptterns. Sientists hve een use templte se pprohes, He n Shouler Reverse He n Shouler Fig. 1. Tripple Top Reverse Tripple Top Doule Top Reverse Doule Top Six si ptterns for stok t. rule se pprohes n neurl network se pprohes to reognize ptterns from time series t. In this pper we hve propose two novel pprohes to reognize omposite pttern from time series t. We pply vrile size sliing winow on time series t n extrt fetures from it. In our first pproh we use Spermns rnk orreltion oeffiient to reognize preferre ptterns n use rule sets to provie more ury in lssifition proess. In seon pproh we use neurl network s lssifier of vrious preferre ptterns in time series n lso use rule sets to enhne the ury of pttern reognition. II. PREVIOUS WORK Severl pprohes hve een evelope to extrting meningful ptterns from time series. Two mjor pprohes for pttern reognition in stok time series re templte se n rule se pprohes [1],[2]. In pst few yers mny pproh lso fouse on pplition of ANNs to stok mrket preition [3],[4]. Reent reserh tens re using hyriize pprohes for pttern reognition in stok time series. Tsihet l. [7] use omintion of the rulese tehnique n ANN to preit the iretion of the stok n prie 500 stok inex futures on ily sis. Shtky et l. [5] suggeste iviing time series t sequene into meningful susequene n Ds et l. [6] introue fixe length winow to segment time series into susequenes n time series ws then represente y the primitive shpe ptterns tht were forme. Chung et l. [8] introue Time series pttern mthing se on Pereptully Importnt Point (PIP) ientifition. PIP lgorithm is se on pturing the flutution of the sequene n /12/$ IEEE 173
2 ientifying the highly flutute points s PIPs. Zhng et l.[9] introue omintion of templte se n rule se pprohes for pttern mthing in stok time series. Their pproh propose flexile online ptternmthing sheme se on fixe size sliing winow, whih is involve in the whole mthing proess, inluing oth in feture point extrtion n pttern mthing. Zhng et l.[9] use PIP onept, introue y Chung et l. [8] for feture point extrtion from the time series t within sliing winow.sine the urrent sttes of the rt re not yet onerne out this emerging omposite ptterns,in this pper we hve propose two novel pprohes to reognize omposite pttern from time series t. III. COMPOSITE PATTERN MATCHING APPROACHES In this setion we will give rief esription out two propose omposite pttern mthing pprohes. As shown in Fig.1 eh pproh hs three steps. Both of this pproh is se on vrile size sliing winow. On the first step, we extrt the feture points from time series t in vrile length sliing winow. The feture point extrtion metho is se on fining Pereptully Importnt Points (PIP)[8] from time series t. On the next step, for our first pproh we reognize omposite ptterns se on Spermns Rnk Correltion Coeffiient. For our seon pproh we propose pttern mthing sheme relying on neurl network where the inputs of the network re the normlize PIP points. On the thir step for oth of our pprohes we use the rule sets to improve the ility of ientifying ptterns n istinguish them more effetively. In oth of our pprohes we try to mth si pttern in sliing winow whih hs fixe initil length n we will use the nottion of primry winow length for this fixe winow length throughout the pper. However if we fil to fin ny si pttern in primry winow, then we inrese the winow length inrementlly to threshol vlue. But if the length of winow rehes to tht threshol vlue n no preferre si pttern is mthe in tht winow then we move the sliing winow to the next rw t where the length of the sliing winow is set equl to primry winow length gin. However, if mth is foun in tht sliing winow, then we move leftmost sie of sliing winow over the rw t epening on whih si pttern is mthe n the length of the sliing winow is set equl to primry winow length. If ny preferre si pttern is mthe for this new sliing winow, omposite pttern is foun. This omposite pttern is onstitute y these two si mthe ptterns. A. Feture extrtion A time series is olletion of oservtions of wellefine t items otine through repete mesurements over time. for exmple Stok time series is urve where xoorinte represents the tring ys while the yoorinte the losing pries. Time series sequene ontins lrge numer of time points. So, it is ostly n time onsuming to nlyze the ptterns from the time series iretly. A simple n effiient metho is neee for representtion or pproximtion of the time series sequene. Chung et l. [8] introue Time series pttern mthing se on Pereptully Importnt Point (PIP). In our pproh PIP is use for feture point extrtion. The PIP lgorithm is se on fining the flutution of the sequene n tkes these highly flutute points s PIPs. Initilly, the first two PIPs re efine s the first n lst point of input sequene (P ) where input sequene (P ) is tully the time series t within sliing winow(sw). The next PIP will e the point in P with mximum istne D to the first two PIPs. The fourth PIP will e the point in input sequene P with mximum istne D to its two jent PIPs. In this wy we extrt the PIPs from the input sequene P where the numer of PIPs(N) is user efine n we will ll this series s extrte series(sp). Chung et l. [8] pplie ifferent forms of mximum istne D n foun tht tht it ws effiient n effetive to extrt the feture points when D ws perpeniulr istne etween the test point n the line onneting the two jent PIPs. Hene, perpeniulr istne is use s D in PIP lgorithm. The pseuo oe of extrting Pereptully Importnt Point (PIP) is stte elow: 1: proeure EXTRACTING PERCEPTUALLY IMPOR TANT POINTS(P [1 : n]) Input sequene (P[1:n]) of stok time series 2: SP[1] P [1] The first point of input sequene 3: SP[N] P [N] The lst point of input sequene 4: repet 5: Selet P [i] with mximum perpeniulr istne 6: PD to the jent PIP points in P 7: SP[j] P [i] 8: until j = N 9: en proeure B. Rule Sets For Bsi Ptterns In Spermns rnk se si pttern reognition pproh, there is loss of informtion when the t re onverte to rnks. Also in our pproh of si pttern reognition using neurl network hs some error. So, we efine set of rules for eh si ptterns. These rules esrie the si ptterns more expliitly. Using rulese metho we n eliminte the error ours in rnk se n neurl network se tehniques, s this pproh istinguishe eh pttern more urtely /12/$ IEEE 174
3 Suh s in He n Shoulers pttern mplitue ifferene etween two shoulers will e elow 15%. In our pproh if potentil si pttern is mthe s output either from neurl network se or rnk se pproh, we pply previously efine rules on extrte PIP series of tht winow. The preefine rules for six si ptterns re stte elow. He & Shoulers Pttern SP[2] SP[6] <15% SP[4] is the top most point SP[2] n SP[6] must e the seon n thir top point SP[1] n SP[7] must e the lowest two points He & Shoulers Pttern (Reverse) SP[2] SP[6] <15% SP[4] is the lowest point SP[2] n SP[6] must e the seon n thir lowest point. SP[1] n SP[7] must e the highest two points Doule Top Pttern(UP) Differene etween the top two points < 15% SP[3] n SP[5] re the top two points. SP[2] is higher thn SP[1] SP[6] is higher thn SP[7] Doule Top Pttern(DOWN) Differene etween the top two points < 15% SP[3] n SP[5] re lowest two points. SP[2] is lower thn SP[1] SP[6] is lower thn SP[7] Triple Tops Pttern(UP) Mx( SP[2] SP[4], SP[2] SP[6], SP[4] SP[6] ) < 15% Sp[2],sp[4], sp[6] must e three highest points Triple Tops Pttern(DOWN) Mx( SP[2] SP[4], SP[2] SP[6], SP[4] SP[6] ) < 15% Sp[2],sp[4], sp[6] must e three lowest points C. Pttern reognition se on Spermns rnk orreltion oeffiient The Spermn rnk orreltion oeffiient is nonprmetri tehnique whih evlute the egree of orreltion etween two vriles. This tehnique works on the rnks of the time series t rther thn the rw time series t. In our first pproh we onvert the extrte feture points SP[1 : n] from eh sliing winow into rnk vlues. In Tle I rnk onversion for eh of the si ptterns is shown. Eh of the six preferre si ptterns in Fig1 hs preefine rnk vlues. Converte rnk vlues from eh sliing winow is then ompre with the rnk vlues of eh preferre si ptterns. As in (1) we lulte the Spermns Correltion Coeffiient etween rnk vlues of preferre si ptterns n the onverte rnk vlues from sliing winow. Here where i is the ifferene etween rnks for eh x i, y i t pir, n n is numer of t pirs. γ =1 6 n i=1 2 i n(n 2 1) (1) For preferre si pttern, If vlue of γ is more then threshol vlue then rule sets for tht preferre si pttern is pplie on SP[1 : n] vlues of sliing winow. If this SP[1 : n] vlues psse the rule sets, tht preferre si pttern is onsiere to e mthe in this sliing winow. D. Pttern reognition using lssifition neurl network In vrious time series sequene t points vry extensively. For exmple in stok time series the vrine of prie of extrte PIPs will epen upon vrious prmeters of rel stok mrket. Hene we normlize the prie of PIPs into uniform intervl ([0, 1]) to eliminte the influenes use y this vrine. Suppose extrte PIP series SP[1 : N]. SP[i] is the highest prie point n SP[j] is the lowest prie point in stok time series. Then SP hight = SP[i] SP[j]. We get the normlize extrte series SN[1 : N], where for every k =1to N, SN[k] =(SP[k] SP[j])/SP hight. In our propose pproh we investigte the six (6) kins of si ptterns of time series. Our pproh is proess of lssifition using threelyer feeforwr neurl network, whose inputs re extrte normlize series SN[1:N] efine in setion IIIA. n outputs will e the preefine si pttern shown in Fig1. A threelyer feeforwr neurl network is typilly ompose of one input lyer, one output lyer n one hien lyers. In the input lyer, eh neuron orrespons to feture; while in the output lyer, eh neuron orrespons to preefine si pttern. Clssifition proess strts with trining the neurl network with group of trining smples. Every trining smple elongs to ertin preefine si pttern. Then the testing smples re use to test the performne of the trine network. For input feture vetor the est output woul e output vetor with ll elements s zero, exept one orresponing to whih si pttern the input smple elongs to. But, ue to lssifition errors some smple input oul not give the expete output. In our experiment, if ny output neuron of network gives more thn threshol perent similrity, then tht lss of si pttern is the potentil mth for input smple. In our pprohes primry winow length is W 0.Both /12/$ IEEE 175
4 TABLE I RANK OF BASIC PATTERNS Ptterns Pttern Figure Position Rnk Nme Orer He n He n Shouler [6241 [ Shouler 537] ] 6.5] 1 2 Doule Doule Top [6413 [ Top 257] ] 6.5] Triple Tripple Top [6142 [6.5 2 Top 537] ] 6.5] Reverse 7 Reverse He n Shouler [1537 [ He n 462] ] Shouler 1.5] Reverse Reverse Tripple Top [1536 [1.5 6 Triple 472] ] Top 1.5] Reverse Reverse Doule Top [1365 [ Doule 742] ] Top 1.5] 6 of our Spermns rnk orreltion oeffiient pproh n neurl network se pproh strts with pplying W = W 0 length sliing winow SW[1 : W ] on time series t S[1 : n]. Then we extrt feture points SP[1 : n]. For Spermns rnk orreltion oeffiient pproh we extrt rnk vlues from sliing winow SW. Then we ompre the rnk vlues extrte from eh sliing winow with the preefine rnk vlues of eh of the preferre si ptterns. If Spermns rnk orreltion oeffiient γ for ny of the preferre si pttern is more then threshol vlue then the orresponing input time series within the sliing winow (SW) is the potentil si mthe pttern. For our neurl network se pproh we extrt normlize feture points SN[1 : N] from sliing winow SW.Then we pply SN[1 : N] s input vetor of trine neurl network. If ny of the six (6) output neurons gives lssifition ury more thn user efine threshol in perentge (i.e. 90 perent), then the orresponing input time series within the sliing winow (SW) is the potentil si mthe pttern. After tht, for oth of our pprohes we pply previously efine rules in setion IIIB on SP[1 : N] of tht sliing winow for potentil si pttern. If SP[1 : N] n pss these rules, then we onsier preefine si pttern is foun n then we move leftmost sie of winow over the rw t epening on whih si preferre pttern is mthe. If we fin He n Shouler or Reverse He n Shouler or Tripple Top or Reverse Tripple Top pttern we move leftmost sie of the winow over the rw t to the thir extrte point SP[3] of SP[1 : N] n the length of the winow is set equl to primry winow length. If we fin Doule Top or Reverse Doule Top pttern, we move leftmost sie of winow over the rw t to the fourth extrte point SP[4] of SP[1 : N] n the length of the winow is set equl to primry winow length. If ny preferre si pttern is mthe for this new sliing winow, omposite pttern is foun. However if we fil to fin ny pttern in primry winow, then we inrese the winow length inrementlly to threshol vlue. But if the length of winow rehes to tht threshol vlue n no preferre pttern is foun in tht winow then we move the winow to the next rw t where the length of the winow is set equl to primry winow length W 0. Then the sme proess will e gin pplie on the new winow. This will ontinue until the en of the Stok time series S. In Fig2() for winow etween the points n we fin He n Shouler pttern. Hene move leftmost sie of winow over the rw t to the thir extrte point SP[3] whih is point. For winow etween the points n we fin Tripple Top pttern. These /12/$ IEEE 176
5 () He n Shouler n Tripple top omposite pttern () Reverse He n Shouler (e) Two Reverse tripple (f) Fig. 2. n Reverse Tripple Top omposite pttern () Doule Top n Tripple Top omposite pttern top omposite pttern () Tripple top n He n Shouler omposite pttern Reverse trippe top n Reverse He n Shouler omposite pttern Some exmple of omposite ptterns. two ptterns onstitute He n Shouler n Tripple top omposite pttern. Also in Fig2() for winow etween the points n we fin Doule Top pttern. Hene move leftmost sie of winow over the rw t to the fourth extrte point SP[4] whih is point. For winow etween the points n we fin Tripple Top pttern. These two ptterns onstitute Doule Top n Tripple top omposite pttern. The pseuo oe of overll pproh of omposite pttern reognition is stte elow: 1: proeure COMPOSITE PATTERN MATCHING ON SLIDING WINDOW(S[1 : n]) full time series t 2: Set primry Winow With, W 0 3: Set Winow With, W = W 0 4: Threshol Winow Size W t 5: Set the numer of feture points extrte from 6: time series within sliing winow, N 7: repet 8: Apply sliing winows on S[1 : n] to extrt 9: feture points SP[1 : N] 10: For neurl network se pproh extrt 11: normlize feture points SN[1 : N], within 12: sliing winow, SW[1 : W ] 13: 14: Apply normlize feture points SN[1 : N] 15: s inputs of neurl network n hek the 6 16: outputs. If ny of the output gives more thn 17: 90% mth, then this pttern lss is 18: onsiere s potentil mthe pttern 19: (MP). 20: 21: For rnk se pproh extrt 22: rnk vlues from feture points SP[1 : N], 23: within sliing winow, SW[1 : W ] 24: If Spermns rnk orreltion oeffiient 25: with ny of the preferre si pttern is 26: more then threshol vlue then this si 27: pttern lss isonsiere s potentil 28: mthe pttern (MP). 29: 30: Chek whether SP[1 : N] n pss the 31: efine rules for MP pttern. 32: if pttern mth foun then 33: Move the winow epening on whih 34: si pttern is mthe with winow 35: withw = W 0 36: if If ny si pttern mthe for this 37: winow then 38: A omposite pttern is mthe 39: en if 40: else if winow with W<W t then 41: Inrese the winow with, 42: W = W + next rw t 43: else if winow with W equl W t then 44: Move the winow with 45: step=next rw t SW[1] 46: en if 47: until finish the time series S 48: en proeure IV. EXPERIMENTAL RESULT In this setion we present the experimentl results tht we onute on our propose pproh. We hve implemente our lgorithm in MATLAB n run extensive simultion on PC with Intel ore i5 proessor with lok spee 2.3GHz n 4 GB memory. We hve uploe our oe, whih is pulily ville to ess, t [12]. We hve performe extensive experiments n ompre our two propose pprohes. We run experiments on two rel stok prie tset nmely Dow Jones Inustril Averge [10] (20904 t points) n Generl Eletri Compny (GE) [11] (12691 t points). Aoring to the experiment on oth tsets, winow length of 15 to 20 t gives the est results for our oth pprohes. A. Neurl network n rule se pproh For trining the neurl network we prtition the tset of oth [10] n [11] tset into trining n testing tset. For tset [10] the trining tset ontins first points n rest of the t elongs to testing tset. Similrly,we prtition first points of tset [11] s trining tset n rest of the t s testing tset. We trin neurl network using vrious numer of neurons in hien lyer n vrious numer of itertion on trining t n then pply our neurl network n rule se pproh with vrile winow length with initil winow length of 15 t n inrese winow length y one rw t until winow length rehe the threshol Winow Length of 20 t on test t. Numer of omposite ptterns foun from Dtset [11] for using vrious numer of hien lyer n vrious numer of itertion is shown in Fig4. From Dtset [10] for trining feeforwr neurl network of 40 neurons in hien lyer n 4500 itertion on trining t we fin highest verge of 25 ptterns. An From Dtset [11] for trining feeforwr neurl network of 35 neurons in hien /12/$ IEEE 177
6 30 25 COMPARISON BETWEEN TWO APPROACH se on vrile length sliing winow. Our hyri pprohes n effiiently reognize omposite ptterns. In Neurl network n rule se pproh Numer of omposite ptterns Dow Jones Inustril Averge Generl Eletri Compny Dt set Numer of Composite ptterns Numer of hien lyer neuron Numer of itertion Fig. 3. Comprison of two pprohes. On the left neurl network se pproh n on the right rnk se pproh TABLE II ERROR OF TWO APPROACHES(IN PERCENTAGE) Stok Time Neurl network n Rnk se n Series Rule se Rule se Dow Jones Inustril Averge Generl Eletri Compny lyer n 3500 itertion on trining t we fin highest verge of 28 ptterns. B. Spermns rnk se n rule se pproh In this omposite pttern reognition pproh we extrt seven (7) feture points from eh sliing winow. In this pproh initil winow length of sliing winow is 15 t n inrese winow length y one rw t until winow length rehe the threshol Winow Length of 20 t on test t. From test tset of Dtset [10] using this Spermns rnk se n rule se pproh we fin 20 omposite ptterns n from test tset of Dtset [11] using this Spermns rnk se n rule se pproh we fin 21 omposite ptterns Fig3 epits omprison of the numer of omposite ptterns foun using our vrious pprohes. Atul numer of Composite pttern in [10] Dtset is 23 n tul numer of Composite pttern in [11] Dtset is 26. Tle II epits the error of our propose two pprohes. V. CONCLUSIONS In this pper we introue omposite ptterns n propose two hyri omposite pttern mthing pproh Fig. 4. Composite ptterns foun in Dtset of Generl Eletri Compny using neurl network pproh this pper we work with si six ptterns n omposite ptterns originte from them. There re severl more si ptterns n vrious omposite struture n e generte from them. In future work n e one to reognize these severl other ptterns using these hyri pprohes. REFERENCES [1] C. L. Osler, n P. H. K. Chng, He n Shoulers: Not Just Flky Ptternl, Stff Report No.4, Feerl Reserve Bnk of New York. [2] F. Collopy, n J. S. Armstrong, Rulese foresting:development n vlition of n expert systems pproh to omining time series extrpoltions, Mngement Siene, vol. 38, pp , Otoer [3] H. Ahmi, Testility of the ritrge priing theory y neurl networks, in Proeeings of the Interntionl Conferene on Neurl Networks, Sn Diego, CA, 1990, pp [4] J.H. Choi, M.K. Lee, M.W. Rhee, Tring S& P 500 stok inex futures using neurl network, in Proeeings of the Annul Interntionl Conferene on Artiil Intelligene Applitions on Wll Street, New York, 1995, pp [5] H. Shtky, S. B. Zonik, Approximte queries n representtions for lrge t sequenes, in Proeeings of Interntionl Conferene on Dt Engineering, Los Almitos, CA: IEEE Computer Soiety Press, 1996, pp [6] G. Ds, K. I. Lin,H. Mnnil, Rule isovery from time series, in Proeeings of the ACM SIGKDD Interntionl Conferene on Knowlege Disovery n Dt Mining, 1998, pp [7] R. Tsih, Y. Hsu, C.C. Li, Foresting S&P 500 stok inex futures with hyri AI system, Deision Support Systems., vol. 23, pp , June [8] T. C. Fu, F. L. Chung, R. Luk, n C. Ng, Stok time series pttern mthing: Templtese vs. rulese pprohes, Engineering Applitions of Artifiil Intelligene., vol. 20(3), pp , April [9] Z. Zhng, J. Jing, X. Liu, R. Lu, H. Wng, R. Zhng, A Rel Time Hyri Pttern Mthing Sheme for Stok Time Series, in Pro. ADC2010, [10] DJI+Historil+Pries; Lst esse : June 25, 2012, 1 m GMT. [11] Lst esse : June 25, 2012, 1 m GMT. [12] Lst esse : June 25, 2012, 1mGMT /12/$ IEEE 178
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