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3$GDfÔDf7fGGD($$ÔG9$D(wG9pG`GfÂGDăiÔDB e eT S X P R C b E e C R SF C X H 8F E C B @ XT e e V e e C (DoDGso`(h#Ôsay$9oi(#9`~ÔG9$D(G9DăƯDwDăÊ w#ÂGGq$idDfD`ă9(i`GDD(`Aă9sAÔ($$($|GdcÔÔa`X TF X C CF R B e e V @ U RT XT B @ B X V e V b R V S V RT PT b @ C e U RT V e C eT X V E V e V S T X X V H V RT X R B e e V @ U R D|(iƯo(#(Dcsd`$9$t19dÂG``$g|õGi9DfD`1Ư9GT r XT B @ B X S R Q C e B X V CFF V FF VT e R e C @ SF C e w X CT GD(D(`Ư9Dsf`9ỏiGăgcG$iDÔD$ad(#qqÔ9#G r E C eT x XT H eT B C UF V R V b P C eTFT e w R CT e R e e ($jDc9Gk9DcD$$G$|ă|(`X $d!cGGD(f97q3$GDfD`ăV X X 8F B VP S T b B X V X R B e e V @ U RT e X B e RT B C U RT XT B @ B `ÔGpăheÔÂGÔÔÔDW$Ư9DfD`1Ư9GDÔDfDGoă{(i`GDD(`X FF V U RT e V B H R P C H 8F E C B @ e e X V B e R C b R w ị ò iăt9GD1tfp9ÔW$ÔG(#D(|(Ds$t`#Ôệ4'fị #q1cuiÔƯoDDăgtcÔÂGD1fDhí9WGvƯ$e$GDfD`ăV ị SF Q B e V H F T e VF B V C R XT S R V R CT e R e e b H S T b B X V e R e R C b E B x w wTu X V E V e V S X 8T (ÂGÔÔÔD7ăƯyÔD$Ôpg`f9y#8 vvo`$9$t19sÔGDB r X HT e V RT R B e e V @ S QT b @ X V U RT S R Q P C H 8F E C B @ f`qpiDYhGDfD`ă9ÔƯcÔÔa`Y(G(Ư9ăĩÔG9$D(A975 ắ è #Ô ccắ è è è è ẹ #'`é ỉ ì ế 1c!$ăư ì Ð Ð Ú ÙÂ Ì ¾ Ù ¾¾ Ì Ì è è è è è è ô â à ắ đ #ÔÔ ì #tcyệ94ăfÂ3ẽ ể 1`9ẽ è ậ7w7$ â ă ẳ ế đ đ ê ² Ơ Í Ì Ì Í Ị Đ Á ÀÐ ẻ ấ ẫ ẫ ẩ ầặ ắ ă ăá â đ đ ưô ơô ê â ă à ả ô ả ă à â ưô â 1DAyfÂÔWc!4cf!Dwẵ Dt4c4Âà ă âô ă â ơô ă ẳô â ơô ă â â â ă ằ â ă đ à ơô ẳ D!cÂăD!f44ccw4 4#Âc4!cÂD!w4a34t1D!j34w4Ô9!cc#ÂÂà ă â â ă ơô â ă à ả ắ ă à â ẵ ă đ đ ưô ô ả ă `!!c4DÂ4Ôo1Dja Ô4!ÂqÂ4oc4f! t9cÂlwÂ4 đ ă ảô đ ơô â ă ẳ ăô à ả đ ă đ ằ ô ả â ă ê ê ÂÔjDc4ÔÂ7cÂ47ÔtwDcÂDwfÂ!pÂÔYÔ!ăÔÔ#ÔaÔGD!DffDả â ẵ â à â ưá ă ẳô â ơô â ă ê đ ă â ăô à ả ă ô ằ â ÂÔ!#AD4#Âc4!cÂsÂÔY3ÔÂƯ!Ô3DcÂDf4ADÂc$4Âà ă ăá ô ă đ â ơô ă ê ư â ơ ả â đ â ă à â ưá â ơô D#Â4 ysD!1Ôac3!Âeă!4!ÔGDa#Ô4!DƯ7!ƯƯcÂ4 â à â ăô à ả â â ô ô ă ê đ ưô ơô ê â ă Ôq4ÔÂAscÔyÔAtc#th!ÔqsÔ! cÂfÔYp!pc4!cf!DĐ w R CT e b V B e z Ơ B e V Ô F S C C B V R CT e b e #GDf$t`ƯfD(D19Ư'f(hhă#DăgƯ3#GDffDfj F V H C R r R CT e b e eF C £ 8 B z p ¢ X 8T B X HT c$g$9Aq3$GDfÔDfje4cÔÂ1q#ÔD3e(sÔÔGDf`hpG75 Keywords Ă X R CT h9lp$Y!(#GDe r V bTF @ @ r X V E V e V w w ăÔiG(9A`ăƯătăfd'f{(Ư(ƯÔ9s9f9d i Categories and Subject Descriptors w R CT e V F V F V e R HT B @ z 8 T X R e z R V eT b V C B 3$iD1ƯG$$Ô$tÔpGDfafÂG`9ÔDfd$|Dcsht$#D(@ r @ V B C P C eTFT e e e V B e X R C H S w X V E V e V S P (ăj#$h!cGGD(f9DfD1t`9#pf(Yvs#`ăƯătă9Y(De $C T X e RT B V RTF b V @ X S R V HT e RT S RT H B e S E R V ÔG`W9D|GYă(iGiÔ$9`9$ipGDGg(ipDDf(ia{ăb X V E V e V S R V RT X R B e e V @ FF V B CP XT B @ B X P C B `ăƯ$t19f(hvGf9DD`ăƯ9De iăoăh`GDD(`s$D(`X r V H V S 8e b BeX R C b R 8 X V 8Be z p X 6e b R } w X RB ăÔpDf9D`(#ÔÔÔaE $9wÔD`i(`7(D7Ô9Ô(DfDe r e V @ S B X E C R F X CT B @ P C b R x BP S e b @ z 8 `ă9ÔÂDf`9$9(c`(#GÔD(făf9Ô(DltDfÔafh9De e bT S B @ C F S C H C B V V X CFF V S R V X R B e e V @ S B fGD(dDe f(p1ÂDăghisGG${Ư$Y(DfD`ă9ÔÂDf`X r E C FF V P C b R x BP e S C b R F e R 8T b p C e 8 B e z p X ($9G$ă9Ô(ÔDl79D7Ô9fcDÔGÔpffD7fD`W(`jV X X H eT B C UF V B } w V e V S F V H B C R S B X E C F X CT B @ P Ô`(~(DcD$#Gă(tă9($gDă9WÂDf`(#iG`(#GÔD(Ư$C R CT e b 8FF C b V H eT B C UF V e X T U F @ HT X B X e S V e X R $iDÔGi$ÔiI9DcD$$iăj(D7ÔÂG#pc(pi`7f`9A9Dp#D(! w e B @ z RT V H C S V H C BP eT bTF C e 8F ET X X C @ HT E V H bT `fafWiăg#j#DcÔGGÔAD7i(G``#apG7aYÔgtG9s #`GD(D`s$v$iDc(ƯfocÔGG9fvă|9GDc9DYă9s$g$$te XT B @ B X P C R CT eT R Q S eT bTF @ z R V U RT BT x B e C R P C U V r(ă##Y(DqăƯ|#GDă9G(7st19ÔÔ`dc`9$iÔDYp#`X R V S V e X V R CT e C R XT w V e V S R 8 X F X CT B @ H C R T U b R V b E S e b @ z e V e H C BP FF VT e R V e X E X X B fÂG#3#Ô9ăƯt{Dffa(YăƯDy$DlciăiDăt9(`WDhP rPT S b R B B b b C X eT P C b R x BP e PT U RT XT B @ B X R B e e V lc(Ô9fD`(ÔÔyDcăpf9f9Dls9Dci(G`iDD(`gDfD`1Ư@ V X R Q S e V e xT R b e F C R V b S C B e RT X R CT e V e iÔ(Ưfo1ƯDo9i9(fDyÔÂ1(Ô((D`Gdqi(#GDătcT r HTF X e H C b B C C w X e X V e V S T X X V H C e 8F V b X e C oGGo`Ô9Dip#ÔDf#ăhÔDf`$t19gÂG``ăghDpG$`Yă9R C S B C x S R XT B @ B X P C R CT e C R S eT HTF B V X X 8T B i$ă9ƯăV #`GD(D`w$v$GD$9DcpGi`f#hg`9WÔGDf`X HT e RT X R B e e V @ U RT XT B @ B X U RT S R Q e V X e @ H e e V X CT pGDuG9DfD`1Ưt9G`GD(D`t9G(9ƯăD(pfD`ăd9#G r B @ FF r w xT R b e b B V X e R 8T b p R V S R V n XT B @ B X m P fD9GAs#9i9(ÔDotDăÔ`qÔGÔpo$p9$(f`iDD(`4s$C R CT eT R Q F P U RT R V H V X BT x B H 8F E C B @ XT w R CT e R #GDc9Ư(S 9l$(i($ppffDG(Dkfi(#DjG97f#GDÔDe r e V X X 8F B VP S T b B X V X R B e e V @ U RT e X B e RT B C U RT XT B `ăi`ÔGWăhÂGÔfÔDf$Ưf(DfD`ă9g9GDÔDDGW$h9G`GD(@ r`(`fGăe9GDătfp(ÔW$dÔG9#Dăt`$apG9Dq$t`e B X FF V U RT e V B H R P C H 8F E C B @ e R V e B C @ HT e e X V B r($Ô!YiÔ9WDDăgcÔÂGD1fD9iƯă$GDfD`ăV R C b R w SF Q B e V H F T e VF B V C R XT S R V R CT e R e e b H S T b B X V e R e R C b E B x w wTu X V E V e V S X 8T (gÂGÔÔfD7$ƯfD$Ôgp`f(y#8 vvp`$9$t19sÔGDB r X HT e V RT R B e e V @ S QT b @ X V U RT S R Q P C H 8F E C B @ f`qpiDYhGgDfD`1ƯdÔƯcÔÔa`YW9G(9ƯăIÔG9$D(A975 ABSTRACT INTRODUCTION Department of Computer Science and Engineering University of California Riverside, CA 92521 " © Ơ & % #$! ă('Â##ă Stefano Lonardi " © ##4 ă(3Â11) " â Đ Đ Ơ Ê Ă $#! ăÂÂăƯÔ Eamonn Keogh Bill ‘Yuan-chi’ Chiu Finding Surprising Patterns in a Time Series Database in Linear Time and Space eT B VFT HT X e B C @ @ X C e X 8T B 8 HT e S T e B b XT S X C eT !cDăiGpG`s`ăa99`qDsÔGDf`X pGDYÔÔGDfDf`G(q`9q9s4c9R r H H C b U RT RT H V e V S e P C R CT e R e e V e S B e @ V b C XF p#fi(i(Gptă(j9D$h$GDfD`ăf(DDD($Ôo`G$V X V R CT e V e R X B @ B w 8T B C T e X V z R V B C $9$GDătÔ`ÔDÔD{(7íAfGDfÂ1ÂGD9$9fẽ$ăhP w ị 8  u w b e B e XT H b RT bT S H H C R C B e X V U RT S F b R ăĂcYÔw#Df$``GpÔ9tÂ#(GÔG(p#i#(#D`ăf9G(9GÔ9GT X SF Q X B T S RT R CT e R e e V b H S T b B X V e E V Ô(iÔ9`Df#iiẽ$iDÔD`1ẽ(ệÂGÔfÔDdăƯdfa$99@ rF V eT R Q V C e RT X 8T B X HT e U RT T e B b XT S P c$iDG(ƯogDGjÔGDf`YpGD(ifiDDf`G(q$C ÔG9$D(W975 H 8F E C B @ w RB 8ee V @ R 8X R 3DD`ăƯdÔÔ`(9 F X CT B @ V P C b R B B b b C P C eTFT E V E C B @ S e b @ z 8 c`9#GÔDgq$Ô9ÔD`ÔÔsăv!cGG9ăƯ#DDffa(p9De e V HT e X C e XF S C H 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w X R B e e V @ n U RT XT B @ B X m X CT Ô9DfD`1Ưp#(G`iDD(`4(#GDB r @ X 8F E V B H R RT E S HF B C E C e e b @ z R V b ((`fG9$tp99GddpGÔ9s`f#ăYapDsfÔafăY7 ÔDf`$t19yÂG``$gsDyG$Ô`qD(pfD`ăy7ăă3Ô(DăÔpD1i$V X e X V e V S T X X V H C e 8F V b X C e e @ H e e V X V R e X H B VF XF VP B V b V C B @ @ V B C E S U U V X R B e e V @ P C R CT e b V B `G$hhDăăÂD9$o($t$#$Ư'(DfD`ă9j$#GDfătlP FG$g`htfÂÔwd4cGDffif`WX s5T5p (i`9$ÔgD{f9R F V H X V R P w eT T e b 8F X ã h B ST X R C b C e S 8 C XF V B C X R B e e V @ U RT XT B @ B X S R Q C e h `G${7dfÂÔq9AÔ9DfD`1Ư9G`GD(D(`u9ƯtD5(@p P C eTFT E V e e V B e X R C H S X e R HT B @ z X CT B @ ă!cGi($t(D{D1t`9#pf(gDÔpGDfaf|(#GÔD(975 I ) I y A $G h $ ă ỏBƯh1êrơ@uYW9Â927$ A A A A A D ) & @yl$f3Ư|Ô9Ô9ềBƯ{(gdW7YấĂ D ) & & $ " hfiấhĂh(B9ĂÔaỡỏ1Ăr5 1l p IMM C TSA-Tree 3 & A 3hĂh(B9ĂolsădÔÔ(sĂos I 9Â927$ ă #Bl(d @dõ1#ỡĩĂẫ ÔƯÔ(Ơ2iD ) & V A 3 ) A @B¦1 3 ) A & D Ư12lhĂ91hah#1âuF ÊÔ9s9Ô(A o 3 ¥#WD ) A A B9ă I C#{1ẽhấƯÂ927$ BsĐc 33 ă A ) º 33 c ) ºu c ) & $ " $dÔf9sêƠ2A2iâx9 '#ọƯ(ădad|rri 1l Tarzan d |R| 0.005 128 256 512 1024 2048 4096 8192 16384 32768 65536 0.01 0.015 0.02 average of |z(w)| 0.025 0.03 0.035 0.04 0.045 random.dat 0.05 ắ (Ôă(Âđrc$â c{ é y â è è è ắ đ ẻ ôé ê Đ ắ â đ đ ưô ả ă ă đ ăô ả Ơ crkăr}"ăg#!Ư9ÔÂ!ÂăÂÔpc4DD4`ÂăDcDfƯễ ắ Ô ắ Ô đ ô â đ x 9qăA#ÔhÂ4ÔƯwắ ăsw#ắ ỉ Âtcc44yÂAAu t ả v ắ ễ ảô à ế ắ ế ắ c!Ây wẫ 94ÔÂcÂ4ÔdăÔ")$P è è ô â à ế ì đ đô Ê Â Ă } Ơ P r}| c Ơsur }k9Uă}{ "ă~ (scXz y ơâ ô ă đ êâă 4! #tÂ9ÔY!D4fh ắ ỉ ÂÔDÂD `ÂÂhcÔ!!ơ ặ ắ đ â ă đ ằ ă Đ ắ Đ ô â ô đ ă đ đ hccÔÂDÂ#Ôq ắ 4D1 ỉ ắ ầ đ ặ `Ô!!ÂÔgDÂÂD!ă ă ơâă ắ ả âơ ẳ ă đă â đ â ưá ă ă ả ă â đ ă ơô â à â Â4Ư9Ô4Âă l4DÂă7cÔt!v`4ÔGÂÔw4c!Â4Â!Ôư đ ư đ ă4ÔÂư ỉ h#!ÔƯ ắ ÂÔăs #ắ ỉ Âtcc44yÂAA é ắô â đ đ ả ắ ễ ảô à ế ắ ế ăx v w u t 10 REFERENCES w B @ V @ 6e R C Xe R fa$9j9Dh$7DÔpH r H C b F P 8X B B CP X 8 B 8P B X C H R C R V e R V e o#fƯ9h`9g`Âf$ljÔÔDflfDs9#p#($W9Dd9$9Dfv ACKNOWLEDGMENTS w B C B e P RT X X XT X aD$qD(DhhGqÔ9``Gj`f9De X X B S S V C e S R e RT w Þ U S 8F C R S B C b XT S P C e `ÔD(#gDh9ÔDiWvA'$âc#Gs1(ÔDfÂ1Ô`G(y$h!cT rFT E V R CT e b V e S R V XF V X XT H XT S XF VP S R V X H B VF V XF VP P GG($Ư$GDf$Y(DdƯăÔG$D`Gp`G(i`iăvd9$ApDăi$i`G$hƯ$C X e X C b bT B e H H X V 8F ET X X C @ e 8F @ H V z B C Ô w XT B V e V D#ÔfGD`fppăoG9G``#aY(DƯ#G9pă9j$(j#`GD1j1ƯDe X R CT e X x r V e H R V H e U RT X X B S S V e C eT X R B e e V (#GDÔ94ătp|$g(Dd(i``fD9$W($9DcsÔ9DfD`1Ư@ U RT XT B @ B X e U RT S R Q P C X 8T b V bT B e RT e R C F 8F C X S e V B (i`GDD(`j(D9G(9ƯsăÔGÔăGD`if(Dd$gcÔG#`hÔDăt`e r R b R C b V X R CT e V eT HTF b V @ X P C X V b E FF V RT (Ôf9#fgÂƯgq(#GDătcpGG|Ô$9`f$|`($fawciăƯGsÔ w e 8X V e V f`$t19S bT R C e X E X B C xT R b e bT T B e b V B V b C tG9sệ#dÔadDă7g(i(9tÔDệG9sÔGDfDfătăƯttDe e @ H e e V S R V X B C e @T B b X S B 8T B C ¤ S R V X e 8F V X V b pÔD`ă{Ư$ƯÔD$D(GDf`f(ifGD($99$WDfGÔÂwfăvt9`X X xT R b e B e C e V UT e X RT C e U RT e X B e RT E SF C e Ô((9tÔDWf9DăD1ÂGDÔÂGgDg(iDfDfDipavi(#7YcT B C w X @ CF X F V b CF R C S X V xT R b e R CT e b V B e z fÂÔqvÔfa#G`w$Gt$eÔ`$ƯE $9i99tÔDv$iD$t`f8 8B e V 8P R D(D1hv(#C ÔDf(i`9$ÔG(#D$qG(D4cÔGi(pG`{ă9Ô S B ST X R C b F R C B C XT e eT bTF @ HT X B C w X e RT V B e X R C b S X V E RT V H C S S R V b V E S 8P B X ÔDG$t`(#Ôd`$9hG$g$(h9$dăƯÔhw`9 U RT e V B C @ B C b RT P C eTFT ET X X C @ e e V UT e X RT C e S R e RT (iD1t$aDăÔ9Gsă!cGi(G``#a(DDă#GDÔÂGiDoƯfDGA7 U V e R V S V e V B U V X V R CT e R B e RT B X e C eT X R B ##ăt$$(#hăÔD$$õ#GDÔÂDfDGgf`(d#(DGso(DfDe r e V @ U RT XT B @ B X S R Q C e eTFT E V ã h 8 X U C eF `ă9A(i`GDD(`fƯ9qDf4GGG9ăƯX s@(5Y f`q7f$9#(DcAr I w eT T e b 8F X S R V eT T eT X R X B UT !ciDÔGÔ`d9$h!ciDc`(Ô`sf9$G96 b H V C eT S R CP S R V V e V S bT e e R X S R V F V B e C (wÂ9jDe GWƯ(#hWƯ$Ât19sGDf9Di9$9$DWD$aE R C X H eT B C UF V B e C C e C e eT S B V @ H C b w b R 8T B $ip(DcD$#Găof(D$|q!gDYcDă9p#Ôgh#Ô(ÔGDfa@ rfq9#GÔD|ÔÂG#gDÔaf1ƯDe #DgcDăDăADfjcT z X CT B @ R T U S e b @ z e V H C BP F e V B U X B T S e B e R C b R 8 bT eT b R x BP e PT U RT XT B @ B X X fD9$Ô9fiqgG9s|Dcsh9Ô(ÔDlf9Dc(G`iDD(`A$V R B e e V @ V U RT ET B b X S e R S R @ S RT RT V H C S S R V F V B R DD`ăƯd|9G9GDf`f(f(ƯfaÔ(9i{G$g#vƯăqătf9f#U XG{(i`GDD(`jă$GDG(Ưfp#pGDe9$gf$Ư`g19GGF T U RT XT B @ B X P C R CT eT R Q S B } w HT e S R V b V @ X B V RT RT X V E V e V S X 8T B X HT e V RT X R B e e V @ U RT XT B @ B X X e b e GW`$9$tă(jÔGDf`YpGDGA(DfD`ă9g9G`GD(D(`qDfÔD(S e V e H eT B C UF V R V h S b S C B e RT B @ V @ XT e R ă9D(DGDă#G$găs5T5Y ÔÔ9D`Gq7fa$9qG9Di! 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