7Ï07ҲT LUҰ19Ă1 Dͷ li͏u chu͟i thͥi thͥi gian time series data Oj Pӝt chuӛi dӳ liӋu dҥng ÿLӇmÿѭӧFÿRWKHRWӯng khoҧng thӡi gian liӅn nhau theo mӝt tҫn suҩt nhҩWÿӏnhÿmYjÿDQJÿѭӧc ӭng dөng trong
Dӳ liӋu chuӛi thӡi gian
Dӳ liӋu chuӛi thӡi gian ܺ OjPӝt tұp hӧp nhiӅu m̳u dͷ li u (data samples), mӛi mүXOjPӝt bӝ ሺܶǡ ܸሻ Trong ÿyܶ OjWKӡLÿLӇm tiӃQKjQKTXDQViWܸ OjJLiWUӏ TXDQViW, ݊ OjVӕ lҫQÿRÿҥt lҩy mүu.êKLӋu chuӛi thӡLJLDQFyGҥng: ܺ ൌ ൫ሺܶ ଵ ǡ ܸ ଵ ሻǡ ሺܶ ଶ ǡ ܸ ଶ ሻǡ ǥ ǡ ሺܶ ǡ ܸ ሻ൯
Chuӛi thӡi gian ܺ OjPӝWYpF-WѫWURQJNK{QJJLDQ݇ chiӅXFyGҥng: ܺ ൌ ሺݔ ଵ ǡ ݔ ଶ ǡ ǥ ǡ ݔ ሻ
7URQJÿyJLiWUӏ ݇ ൌ ͳ ÿѭӧc sӱ dөng rӝQJUmLQKҩt, vӟi k WKu ܺ ÿѭӧc gӑLOjchu͟i thͥLJLDQÿ˯Qbi͇n (uni-variate time series) 9tGө QKѭJLiFKӭQJNKRiQWtQKLӋu ÿLӋQWkPÿӗ, sӕ OѭӧQJVLQKYLrQWӕt nghiӋp TXDFiFQăPOѭӧQJPѭDÿӝ ҭm +uQK 1.1 minh hӑa dӳ liӋu chuӛi thӡi gian vӅ kӃt quҧ EiQUѭӧXÿӓ ӣ Australia tӯ WKiQJ- ÿӃQWKiQJ-1991
NӃu ݇ ͳ WKuܺ ÿѭӧc gӑL Ojchu͟i thͥL JLDQ ÿD bi͇n (multi-variate time series), ÿѭӧc GQJÿӇ P{KuQKKyDYjJLҧLWKtFKVӵ WѭѫQJWiFYjOLrQTXan lүn nhau cӫa mӝWQKyPFiFGӳ liӋu chuӛi thӡi gianYtGө WLrXELӇXQKѭGӳ liӋu vӅ WLrXGQJ YjWKXQKұSJLiFә phiӃXYjFә tӭFOmLVXҩWWăQJWUѭӣQJYjOҥPSKiW
NӃu thӡLÿLӇP[iFÿӏQKFiFJLiWUӏ ܸ trong ܺ OjFiFKÿӅXQKDXWKuFKXӛi thӡi gian ܺ ÿѭӧc gӑLOjÿ͛ng nh̭t (uniform).KLÿyta FyWKӇ NK{QJTXDQWkPÿӃnܶ Trong luұQYăQQj\, FK~QJW{L tұSWUXQJQJKLrQFӭu chuӛi thӡLJLDQÿѫQbiӃn ÿӗng nhҩt TӭFOjFKXӛi thӡi gian ܺ ÿѭӧc biӇu diӉQGѭӟi dҥng vec-WѫJLiWUӏ ݊ chiӅu (݇ ൌ ͳ, ݐ FiFKÿӅu nhau) ܺ ൌ ሺݔ ଵ ǡ ݔ ଶ ǡ ǥ ǡ ݔ ሻ
+uQK1.1 KӃt quҧ EiQUѭӧXÿӓ ӣ Australia tӯ WKiQJ-1980 ÿӃQWKiQJ-1991 [13]
.KiLQLӋPFKtQKVӱ dөQJWURQJÿӅ WjL : x T̵p hṷn luy n ( training set)
/jWұSFiFGӳ liӋXÿmÿѭӧFSKkQOӟSÿӇ phөc vө cho viӋF[k\GӵQJP{KuQKGӵ ÿRiQQKmQ x PKkQOͣp ( Classification)
&KRWUѭӟc mӝt chuӛi thӡi gian Q FK˱DJiQQKmQ XQODEHOHGYjM lӟp, mӛi lӟp chӭa k chuӛi thӡL JLDQ Fy FQJ Pӝt sӕ ÿһF WUѭQJ QKҩW ÿӏnh dӵD WUrQ ÿӝ ÿR khoҧQJFiFKÿmÿӏQKQJKƭDWUѭӟF%jLWRiQSKkQOӟp tiӃQKjQKSKkQORҥi chuӛi thӡi gian Q YjRPӝt trong sӕ M lӟSÿy x Ĉ͡ ÿRNKR̫QJFiFK ( Distance measure)
/jSKѭѫQJSKiSWtQKWRiQNKRҧQJFiFKJLӳa 2 chuӛi thӡi gian Q YjC Hai chuӛi thӡLJLDQÿѭӧF[HPOjWѭѫQJWӵ nhau khi khoҧQJFiFKJLӳDFK~QJWLӃn vӅ 0 Mӝt sӕ NKiLQLӋPNKiFOLrQTXDQ : x Gom cͭm ( clustering)
Gom cөP Oj SKkQ KRҥch dӳ liӋu chuӛi thӡL JLDQ WKjQK FiF QKyP VDR FKR FiFWKjQKSKҫn trong cөP OjWѭѫQJWӵ QKDX FzQ FiF WKjQKSKҫQ NKiF FөPOjUҩWNKiF nhau
&KRWUѭӟc mӝt chuӛi thӡi gian ܳFy݊ ÿLӇm dӳ liӋX %jL WRiQ VӁ dӵ EiR JLi WUӏ cӫa chuӛi thӡLJLDQOLrQWLӃp tӯ thӡLÿLӇm ݊ ͳ ÿӃn ݊ ݇ x 3KiWKL n b̭WWK˱ͥng ( novelty detection)
%jL WRiQ Qj\ [iF ÿӏQK FiFchu͟i con b̭W WK˱ͥng (unusual/ abnormal/ discord/ novel) OjFKXӛLFRQNKiFQKҩt so vӟLFiFFKXӛLFRQNKiFWURQJFKXӛi thӡi gian x 3KiWKL QP{WtS motif detection)
%jLWRiQQj\ [iF ÿӏQKFiF P{WtSPүu lһSOjFKXӛLFRQ WKѭӡng lһp lҥi nhiӅu nhҩt trong chuӛi thӡi gian
1JRjLFiFEjLWRiQNӇ WUrQӭng dөng khai pKiGӳ liӋu chuӛi thӡLJLDQFzQWӗn tҥi mӝt sӕ EjLWRiQNKiFQKѭNKDLSKiOX̵t k͇t hͫp (association rules mining), truy v̭n dDWUrQQ͡i dung (query by content)ô 7X\QKLrQÿӅ WjLQj\chӍ tұSWUXQJYjR F{QJ
3KѭѫQJSKiS SAX-960FKRFK~QJWDPӝWFiLQKuQtriӇn vӑng WURQJEjLWRiQ SKkQOӟp dӳ liӋu chuӛi thӡi gian7URQJNKLFiFJLҧi thuұWSKkQOӟp cә ÿLӇn gһp vҩQÿӅ vӅ dӳ liӋu nhiӉu hoһFFKLSKtFDRQKѭJLҧi thuұt 1-NN rҩt nhҥy cҧm vӟi dӳ liӋu nhiӉX Yj QӃu chuӛi thӡL JLDQ GjL WKu FKL SKt Fӫa 1-NN sӁ rҩt cao WKu SAX-VSM lҥLFyÿӝ phӭc tҥSOjWX\ӃQWtQKFNJQJJLӕng SKѭѫQJSKiSW~Lÿng m̳u (Bag of patterns - BOP) Oj FKX\ӇQ ÿәi tҩt cҧ FiF FKXӛi thӡi gian huҩn luyӋn WKjQK W~L Wӯ Yj Vӱ dөng P{ KuQK NK{QJ JLDQ YHFWRU ÿӇ SKkQ Oӟp Tuy QKLrQWKD\YuBOP [k\Gӵng n W~L FKR FKXӛi thӡi gian tұp huҩn luyӋn, SAX-
690[k\Gӵng mӝWW~LWӯ duy nhҩWFKRFiFOӟp, cung cҩp mӝWFiFKKLӋu quҧ mӝWYHFWѫWUӑQJOѭӧng N (N OjVӕ Oѭӧng lӟSYjWKӡLJLDQSKkQORҥi nhanh x é nghƭa thc ti͍n
7K{QJTXDWKӵc nghiӋm, FK~QJW{LVӁ ÿѭDUDNӃt luұn vӅ WtQKFKtQK[iFFӫa viӋc SKkQOӟp khi sӱ dөng SKѭѫQJSKiS SAX-VSMFNJQJQKѭVRViQKÿӝ FKtQK[iFSKkQOӟp vӟi hai giҧi thuұt 1NN-'7:YjW~Lÿӵng mүu (Bag of patterns)
MөF WLrX FKtQK FӫD ÿӅ WjL Oj WuP KLӇX SKkQ lӟp dӳ liӋu chuӛi thӡi gian sӱ dөng SKѭѫQJ SKiSx̭p x͑ g͡S Nê KL X KyD (SymbolicAggregate approXimation-
SAX) kӃt hӧp vӟi P{KuQKNK{QJJLDQYHFWRU (Vector Space Model-VSM)
&iFF{QJYLӋFÿѭӧc thӵc hiӋQWURQJÿӅ WjLJӗPFy : x 1JKLrQ FӭX thu gi̫m s͙ chi͉u b̹QJ SK˱˯QJ SKiS [̭p x͑ g͡p tͳQJ ÿR̩n (Piecewise Aggregate Approximation - PAA) Yj FiFK WKӵF KLӋQ WtQK WRiQ YӟL FKXӛLGӳOLӋX x 1JKLrQ FӭX YӅ pKѭѫQJ SKiS x̭p x͑ g͡S Nê KL X KyD(Symbolic Aggregate approXimation - SAX) biӃQÿәi chuӛi thӡLJLDQWKjQKPӝt chuӛLFiFNêWӵ x 1JKLrQ FӭXYӅ YLӋF VӱGөQJP{KuQKNK{QJ JLDQYHFWRU (Vector Space Model-
VSM) ÿӇ SKkQOӟp x +LӋQWKӵFFKѭѫQJWUuQKSKҫQPӅPYjWKӱQJKLӋPWUrQFiFEӝGӳOLӋXPүXÿӇVR ViQK KLӋX VXҩW JLӳD SKѭѫQJ SKiS SKkQ OӟS 6$;-960 YӟL SKѭѫQJ SKiS 11- '7:YjBag of patterns x %iRFiRNӃWTXҧÿҥWÿѭӧFWK{QJTXDWKӵFQJKLӋPYӟLQKLӅXEӝGӳOLӋXNKiFQKDX
- Giҧm sӕ chiӅu cho chuӛi thӡi gian, qua thӵc nghiӋm vӟLFiFgiҧi thuұWSKkQOӟp NKiF QKDX Yj QKLӅu bӝ dӳ liӋX NKiF QKDX FK~QJ W{L QKұn thҩy rҵng viӋc thu giҧm sӕ chiӅu thӵc sӵ hiӋu quҧ YjFҧi thiӋn tӕFÿӝ WtQK
- VӅ giҧi thuұWSKkQOӟp 1NN-DTW kӃt quҧ mang lҥi vӟLÿӝ FKtQK[iFNKiFDRWX\ QKLrQÿӕi vӟi chuӛi thӡLJLDQGjLthӡi gian thӵFWKLWKuOҥi mҩt nhiӅu thӡi gian KѫQVRYӟi Bag of patterns Yj6$;-VSM
- Bag of patterns, SAX-VSM qua thӵc nghiӋm mang lҥi kӃt quҧ NKiWӕWWX\QKLrQ so vӟi viӋc tҥRUDQW~LQKѭJLҧi thuұt Bag of patterns WKuJLҧi thuұt SAX-VSM gӝSFiFOӟSFKXQJYjRPӝWW~LPDQJÿӃn thӡi gian thӵc thi tӕWKѫQ
LuұQYăQÿѭӧc bӕ cөFWKHRFiFQӝLGXQJFKtQKWURQJWӯQJFKѭѫQJQKѭVDX
&KѭѫQJQj\JLӟi thiӋu sѫ OѭӧFFiFÿӏQKQJKƭDFiFYҩQÿӅ FyOLrQTXDQÿӃn ÿӅ WjL, mөFWLrXYjnhiӋm vө cӫDÿӅ WjLWyPOѭӧFFiFNӃt quҧ ÿҥWÿѭӧc Yjbӕ cөc luұQYăQ
&KѭѫQJQj\WUuQKEj\FKLWLӃt vӅ FiFFѫVӣ OêWKX\ӃWÿѭӧFiSGөQJWURQJÿӅ WjLQKѭWKXJLҧm sӕ chiӅu sӱ dөQJSKѭѫQJSKiS[ҩp xӍ gӝp tӯQJÿRҥn (PAA), xҩp xӍ gӝSNêKLӋXKyD6$;P{KuQKNK{QJJLDQYHFWRU960Yj giӟi thiӋu mӝt sӕ F{QJWUuQKQJKLrQFӭXOLrQTXDQÿӃn ÿӅ tjL
&KѭѫQJQj\JLӟi thiӋu Kѭӟng tiӃp cұn cӫa FK~QJW{LÿӇ thӵc hiӋQÿӅ WjL
&+ѬѪ1*4: HIӊN THӴ&9ơTHӴC NGHIӊM
&KѭѫQJQj\WLӃQKjQKWKӵc nghiӋPWUrQQKLӅu bӝ dӳ liӋXNKiFQKDXFKRTXi WUuQKSKkQOӟp YjVRViQKvӟi SKѭѫQJSKiSSKkQOӟSNKiF dӵDWUrQWKӡi gian thӵc thi Yjÿӝ FKtQK[iF Mӝt sӕ kӃt luұn YjÿӅ xuҩt sӁ ÿѭӧFQrXOrQGӵDWUrQFiFNӃt quҧ thӵc nghiӋm
&KѭѫQJ Qj\ WUuQK Ej\ tәQJ Oѭӧc lҥL WRjQ Eӝ nӝi dung quan trӑng cӫa luұn YăQFiFÿyQJJyS FKtQKFӫDÿӅ WjLYjKѭӟQJSKiWWULӇn
&KѭѫQJQj\JLӟi thiӋXVѫOѭӧc mӝt sӕ QJKLrQFӭXOLrQTXDQ ÿӃn ÿӝ ÿRNKRҧng FiFKYjSKѭѫQJSKiSSKkQOӟp
.KLSKkQOӟSGӳOLӋXFKXӛLWKӡLJLDQPӝWWURQJQKӳQJPӕLTXDQWkPFҫQÿѭӧF QKҳFÿӃQOjÿ͡ÿRNKR̫QJFiFKGLVWDQFHPHDVXUHVDRFKRSKKӧSYӟLNLӇXGӳOLӋX FKXӛLWKӡLJLDQ+DLÿӝÿRSKәELӃQÿѭӧF[pWÿӃQWURQJEiRFiRQj\OjÿӝÿRNKRҧQJ FiFK(XFOLGYjÿӝÿR[RҳQWKӡLJLDQÿӝQJ'7:
2.1.1 Ĉӝ ÿRNKRҧQJFiFK(XFOLG(' ĈӝÿRNKRҧQJFiFK(XFOLGÿѭӧFGQJÿӇÿRÿӝNKiFELӋWJLӳDKDLFKXӛLWKӡL JLDQĈk\OjÿӝÿRNKRҧQJFiFKÿѫQJLҧQQKҩWYjGӉWtQKWRiQQKҩW
&KRKDLFKXӛLWKӡLJLDQ& ^F F ôF Q `Yj4 ^T T ôT Q `NKRҧQJFiFK
(XFOLGJLӳDKDLFKXӛLWKӡLJLDQ&Yj4ÿѭӧFWtQKEҵQJF{QJWKӭFVDX Ĉӝ ÿR NKRҧQJ FiFK (XFOLG Fy ѭX WKӃ Oj ÿѫQ JLҧQ GӉ KLӋQ WKӵF Yj WKӡL JLDQ WKӵFWKLWKҩS7X\QKLrQÿӝÿR(XFOLGFyQKѭӧFÿLӇPOjQKҥ\FҧPYӟLQKLӉXYjNpP WtQKOLQKKRҥWYuÿӝÿRQj\\rXFҫXKDLFKXӛLWKӡLJLDQFyFKLӅXGjLEҵQJQKDX
2.1.2 Ĉӝ ÿR[Rҳn thӡLJLDQÿӝng (Dynamic Time Warping ± DTW) Ĉӝ ÿR[Rҳn thӡLJLDQÿӝng (Dynamic Time Warping ± DTW) ÿѭӧFÿӅ xuҩt bӣi
%HUQWYj&OLIIRUG>4] FyÿһFÿLӇPFKtQKOjviӋFiQK[ҥ NK{QJWX\ӃQWtQKNKL VRViQKJLӳa hai chuӛi thӡLJLDQ&{QJWKӭFWtQKWRiQQKѭVDX
Giҧ sӱ FyKDLFKXӛi thӡi gian ܳ Yjܥ FyFKLӅXGjLOҫQOѭӧWOj݊ Yj݉vӟi: ܳ ൌ ݍ ଵ ǡ ݍ ଶ ǡ ǥ ǡ ݍ ǡ ǥ ǡ ݍ ܥ ൌ ܿ ଵ ǡ ܿ ଶ ǡ ǥ ǡ ܿ ǡ ǥ ǡ ܿ
8 ĈӇ WtQKWRiQNKRҧQJFiFKDTW giӳa hai chuӛL WUrQ WD [k\ Gӵng mӝt ma trұn ܦ FyNtFKWKѭӟc ݉ ൈ ݊ gӑLOjma tr̵n xo̷n (warping matrix)
7URQJÿySKҫn tӱ ܦ ൌ ݀ሺݍ ǡ ܿ ሻ Oj NKRҧQJ FiFK JLӳD KDL ÿLӇm ݍ Yjܿ (vӟi kho̫QJ FiFK (XFOLG WKu݀ሺݍ ǡ ܿ ሻ ൌ ሺݍ Ȃܿ ሻ ଶ ) Ĉ˱ͥng xo̷n W (warping path)
OjPӝt tұSFiFSKҫn tӱ OLrQWөc cӫa ma trұQÿӏQKQJKƭDPӝWiQK[ҥ giӳa ܳ Yjܥ Phҫn tӱ thӭ ݇ cӫa ܹ ÿѭӧFÿӏQKQJKƭDOjݓ ൌ ሺ݅ǡ ݆ሻ , YuYұ\WDFy ܹ ൌ ݓ ଵ ǡ ݓ ଶ ǡ ǥ ǡ ݓ ଷ ǡ ǥ ǡ ݓ vӟi ݉ܽݔሺ݊ǡ ݉ሻ ܭ ݉ ݊Ȃ ͳ
7KHRÿӏQKQJKƭDÿѭӡng xoҳn tӕLѭXOjÿѭӡng xoҳQFKRJLiWUӏ khoҧQJFiFK xoҳn nhӓ nhҩt: ܦܹܶሺܳǡ ܥሻ ൌ ݉݅݊ ە ۔ ۓ ඩ ݓ ୀଵ
7URQJ ÿyFKLSKt[Rҳn cӫa mӝWÿѭӡng xoҳQOjWәng khoҧQJFiFK FӫD FiF cһSÿLӇPWѭѫQJӭng vӟLFiF{QҵPWUrQÿѭӡng xoҳQÿy
+uQh 2.1&iFKWtQKNKRҧQJFiFKÿӝ ÿR[Rҳn thӡLJLDQÿӝng [6]
(A) Hai chu͟i thͥi gian ࡽ Yj B) Ma tr̵QWtQK'7:&.͇t qu̫ iQK[̩ ÿL͋m trong DTW) Ĉѭӡng xoҳn tӕLѭXQj\FyWKӇ WuPÿѭӧc bҵQJFiFKVӱ dөQJSKѭѫQJSKiS quy ho̩FKÿ͡ng (dynamic programming) &{QJWKӭc truy hӗi cho kho̫QJFiFKWtFKONJ\cumulative distance) ߛሺ݅ǡ ݆ሻ ÿѭӧc ÿӏQKQJKƭDQKѭVDX
7URQJ ÿykho̫QJ FiFK WtFK ONJ\ ߛሺ݅ǡ ݆ሻ tҥL {ሺ݅ǡ ݆ሻ cӫa ma trұQ ÿѭӧF WtQK bҵng khoҧQJFiFK݀ሺ݅ǡ ݆ሻ cӫD{WѭѫQJӭng cӝng vӟLJLiWUӏ nhӓ nhҩt cӫa khoҧQJFiFK WtFK ONJ\ FӫD FiF { OLӅn kӅ WUѭӟF { ÿy KRҧQJ FiFK [Rҳn thӡL JLDQ ÿӝng cӫa hai chuӛi thӡi gian ܳ Yjܥ OjFăQEұc hai cӫa khoҧQJFiFKWtFKONJ\WҥL{FyFKӍ sӕ Oj ሺ݉ǡ ݊ሻ+uQK2.1 minh hӑDFiFKWtQKNKRҧQJFiFKFӫDÿӝ ÿR[Rҳn thӡLJLDQÿӝng ĈӇ hҥn chӃ sӕ OѭӧQJÿѭӡng xoҳQZDUSLQJSDWKWURQJTXiWUuQKWuPWѭѫQJ tӵÿѭӡng xoҳn W phҧLFyÿӫ 3 yӃu tӕ VDXÿk\ x ĈL͉u ki QELrQ ݓ ଵ ൌ ሺͳǡ ͳሻ Yjݓ ൌ ሺ݉ǡ ݊ሻ, UjQJEXӝFQj\\rXFҫXÿѭӡng xoҳn phҧi bҳWÿҫu YjNӃWWK~Fӣ KDLJyFÿӕi diӋn cӫa ma trұn xoҳn x 7tQK OLrQ WͭF cho ݓ ൌ ሺܽǡ ܾሻ WKuݓ ିଵ ൌ ሺܽ ᇱ ǡ ܾ ᇱ ሻ WURQJ ÿyܽȂ ܽ ᇱ ͳ Yj ܾ െ ܾǯ ͳ5jQJEXӝFQj\\rXFҫXÿѭӡQJ[RҳQSKҧLGLFKX\ӇQJLӳDQKӳQJ{ OLӅQNӅNӇFҧQKӳQJ{OLӅQNӅWKHRÿѭӡQJFKpR x 7tQKÿ˯QÿL XWăQJ cho ݓ ൌ ሺܽǡ ܾሻWKuݓ ିଵ ൌ ሺܽ ᇱ ǡ ܾ ᇱ ሻ vӟi ܽȂ ܽ ᇱ Ͳ Yj ܾȂ ܾ ᇱ Ͳ5jQJEXӝFQj\\rXFҫXFiFÿLӇm trong ܹ SKҧLWăQJÿѫQÿLӋXWKHR WKӡLJLDQ
Giҧi thuұWÿѭӧc thӵc hiӋQQKѭVDX:
Input : Q: array [1 ôQ], C: array [1 m], DTW: array [1 ôQ, 1 ôP]
3 DTW [i, j] = (Q [i] ± C [j]) 2 + min (DTW [i - 1, j], DTW [i, j - 1], DTW [i - 1, j - 1])
10 6DXÿk\VӁ OjYtGө cho viӋFWtQKNKRҧQJFiFK'7:JLҧ sӱ WDFyKDLFKXӛi thӡLJLDQQKѭVDX
+uQK2.2 WUuQKEj\ÿѭӡng cong biӇu diӉn hai chuӛi thӡi gian Q YjC
ộ NGHƬA CӪ$Ĉӄ 7ơ,
3KѭѫQJSKiS SAX-960FKRFK~QJWDPӝWFiLQKuQtriӇn vӑng WURQJEjLWRiQ SKkQOӟp dӳ liӋu chuӛi thӡi gian7URQJNKLFiFJLҧi thuұWSKkQOӟp cә ÿLӇn gһp vҩQÿӅ vӅ dӳ liӋu nhiӉu hoһFFKLSKtFDRQKѭJLҧi thuұt 1-NN rҩt nhҥy cҧm vӟi dӳ liӋu nhiӉX Yj QӃu chuӛi thӡL JLDQ GjL WKu FKL SKt Fӫa 1-NN sӁ rҩt cao WKu SAX-VSM lҥLFyÿӝ phӭc tҥSOjWX\ӃQWtQKFNJQJJLӕng SKѭѫQJSKiSW~Lÿng m̳u (Bag of patterns - BOP) Oj FKX\ӇQ ÿәi tҩt cҧ FiF FKXӛi thӡi gian huҩn luyӋn WKjQK W~L Wӯ Yj Vӱ dөng P{ KuQK NK{QJ JLDQ YHFWRU ÿӇ SKkQ Oӟp Tuy QKLrQWKD\YuBOP [k\Gӵng n W~L FKR FKXӛi thӡi gian tұp huҩn luyӋn, SAX-
690[k\Gӵng mӝWW~LWӯ duy nhҩWFKRFiFOӟp, cung cҩp mӝWFiFKKLӋu quҧ mӝWYHFWѫWUӑQJOѭӧng N (N OjVӕ Oѭӧng lӟSYjWKӡLJLDQSKkQORҥi nhanh x é nghƭa thc ti͍n
7K{QJTXDWKӵc nghiӋm, FK~QJW{LVӁ ÿѭDUDNӃt luұn vӅ WtQKFKtQK[iFFӫa viӋc SKkQOӟp khi sӱ dөng SKѭѫQJSKiS SAX-VSMFNJQJQKѭVRViQKÿӝ FKtQK[iFSKkQOӟp vӟi hai giҧi thuұt 1NN-'7:YjW~Lÿӵng mүu (Bag of patterns)
MөF WLrX FKtQK FӫD ÿӅ WjL Oj WuP KLӇX SKkQ lӟp dӳ liӋu chuӛi thӡi gian sӱ dөng SKѭѫQJ SKiSx̭p x͑ g͡S Nê KL X KyD (SymbolicAggregate approXimation-
SAX) kӃt hӧp vӟi P{KuQKNK{QJJLDQYHFWRU (Vector Space Model-VSM)
&iFF{QJYLӋFÿѭӧc thӵc hiӋQWURQJÿӅ WjLJӗPFy : x 1JKLrQ FӭX thu gi̫m s͙ chi͉u b̹QJ SK˱˯QJ SKiS [̭p x͑ g͡p tͳQJ ÿR̩n (Piecewise Aggregate Approximation - PAA) Yj FiFK WKӵF KLӋQ WtQK WRiQ YӟL FKXӛLGӳOLӋX x 1JKLrQ FӭX YӅ pKѭѫQJ SKiS x̭p x͑ g͡S Nê KL X KyD(Symbolic Aggregate approXimation - SAX) biӃQÿәi chuӛi thӡLJLDQWKjQKPӝt chuӛLFiFNêWӵ x 1JKLrQ FӭXYӅ YLӋF VӱGөQJP{KuQKNK{QJ JLDQYHFWRU (Vector Space Model-
VSM) ÿӇ SKkQOӟp x +LӋQWKӵFFKѭѫQJWUuQKSKҫQPӅPYjWKӱQJKLӋPWUrQFiFEӝGӳOLӋXPүXÿӇVR ViQK KLӋX VXҩW JLӳD SKѭѫQJ SKiS SKkQ OӟS 6$;-960 YӟL SKѭѫQJ SKiS 11- '7:YjBag of patterns x %iRFiRNӃWTXҧÿҥWÿѭӧFWK{QJTXDWKӵFQJKLӋPYӟLQKLӅXEӝGӳOLӋXNKiFQKDX
- Giҧm sӕ chiӅu cho chuӛi thӡi gian, qua thӵc nghiӋm vӟLFiFgiҧi thuұWSKkQOӟp NKiF QKDX Yj QKLӅu bӝ dӳ liӋX NKiF QKDX FK~QJ W{L QKұn thҩy rҵng viӋc thu giҧm sӕ chiӅu thӵc sӵ hiӋu quҧ YjFҧi thiӋn tӕFÿӝ WtQK
- VӅ giҧi thuұWSKkQOӟp 1NN-DTW kӃt quҧ mang lҥi vӟLÿӝ FKtQK[iFNKiFDRWX\ QKLrQÿӕi vӟi chuӛi thӡLJLDQGjLthӡi gian thӵFWKLWKuOҥi mҩt nhiӅu thӡi gian KѫQVRYӟi Bag of patterns Yj6$;-VSM
- Bag of patterns, SAX-VSM qua thӵc nghiӋm mang lҥi kӃt quҧ NKiWӕWWX\QKLrQ so vӟi viӋc tҥRUDQW~LQKѭJLҧi thuұt Bag of patterns WKuJLҧi thuұt SAX-VSM gӝSFiFOӟSFKXQJYjRPӝWW~LPDQJÿӃn thӡi gian thӵc thi tӕWKѫQ
LuұQYăQÿѭӧc bӕ cөFWKHRFiFQӝLGXQJFKtQKWURQJWӯQJFKѭѫQJQKѭVDX
&KѭѫQJQj\JLӟi thiӋu sѫ OѭӧFFiFÿӏQKQJKƭDFiFYҩQÿӅ FyOLrQTXDQÿӃn ÿӅ WjL, mөFWLrXYjnhiӋm vө cӫDÿӅ WjLWyPOѭӧFFiFNӃt quҧ ÿҥWÿѭӧc Yjbӕ cөc luұQYăQ
&KѭѫQJQj\WUuQKEj\FKLWLӃt vӅ FiFFѫVӣ OêWKX\ӃWÿѭӧFiSGөQJWURQJÿӅ WjLQKѭWKXJLҧm sӕ chiӅu sӱ dөQJSKѭѫQJSKiS[ҩp xӍ gӝp tӯQJÿRҥn (PAA), xҩp xӍ gӝSNêKLӋXKyD6$;P{KuQKNK{QJJLDQYHFWRU960Yj giӟi thiӋu mӝt sӕ F{QJWUuQKQJKLrQFӭXOLrQTXDQÿӃn ÿӅ tjL
&KѭѫQJQj\JLӟi thiӋu Kѭӟng tiӃp cұn cӫa FK~QJW{LÿӇ thӵc hiӋQÿӅ WjL
&+ѬѪ1*4: HIӊN THӴ&9ơTHӴC NGHIӊM
&KѭѫQJQj\WLӃQKjQKWKӵc nghiӋPWUrQQKLӅu bӝ dӳ liӋXNKiFQKDXFKRTXi WUuQKSKkQOӟp YjVRViQKvӟi SKѭѫQJSKiSSKkQOӟSNKiF dӵDWUrQWKӡi gian thӵc thi Yjÿӝ FKtQK[iF Mӝt sӕ kӃt luұn YjÿӅ xuҩt sӁ ÿѭӧFQrXOrQGӵDWUrQFiFNӃt quҧ thӵc nghiӋm
&KѭѫQJ Qj\ WUuQK Ej\ tәQJ Oѭӧc lҥL WRjQ Eӝ nӝi dung quan trӑng cӫa luұn YăQFiFÿyQJJyS FKtQKFӫDÿӅ WjLYjKѭӟQJSKiWWULӇn
&KѭѫQJQj\JLӟi thiӋXVѫOѭӧc mӝt sӕ QJKLrQFӭXOLrQTXDQ ÿӃn ÿӝ ÿRNKRҧng FiFKYjSKѭѫQJSKiSSKkQOӟp
.KLSKkQOӟSGӳOLӋXFKXӛLWKӡLJLDQPӝWWURQJQKӳQJPӕLTXDQWkPFҫQÿѭӧF QKҳFÿӃQOjÿ͡ÿRNKR̫QJFiFKGLVWDQFHPHDVXUHVDRFKRSKKӧSYӟLNLӇXGӳOLӋX FKXӛLWKӡLJLDQ+DLÿӝÿRSKәELӃQÿѭӧF[pWÿӃQWURQJEiRFiRQj\OjÿӝÿRNKRҧQJ FiFK(XFOLGYjÿӝÿR[RҳQWKӡLJLDQÿӝQJ'7:
2.1.1 Ĉӝ ÿRNKRҧQJFiFK(XFOLG(' ĈӝÿRNKRҧQJFiFK(XFOLGÿѭӧFGQJÿӇÿRÿӝNKiFELӋWJLӳDKDLFKXӛLWKӡL JLDQĈk\OjÿӝÿRNKRҧQJFiFKÿѫQJLҧQQKҩWYjGӉWtQKWRiQQKҩW
&KRKDLFKXӛLWKӡLJLDQ& ^F F ôF Q `Yj4 ^T T ôT Q `NKRҧQJFiFK
(XFOLGJLӳDKDLFKXӛLWKӡLJLDQ&Yj4ÿѭӧFWtQKEҵQJF{QJWKӭFVDX Ĉӝ ÿR NKRҧQJ FiFK (XFOLG Fy ѭX WKӃ Oj ÿѫQ JLҧQ GӉ KLӋQ WKӵF Yj WKӡL JLDQ WKӵFWKLWKҩS7X\QKLrQÿӝÿR(XFOLGFyQKѭӧFÿLӇPOjQKҥ\FҧPYӟLQKLӉXYjNpP WtQKOLQKKRҥWYuÿӝÿRQj\\rXFҫXKDLFKXӛLWKӡLJLDQFyFKLӅXGjLEҵQJQKDX
2.1.2 Ĉӝ ÿR[Rҳn thӡLJLDQÿӝng (Dynamic Time Warping ± DTW) Ĉӝ ÿR[Rҳn thӡLJLDQÿӝng (Dynamic Time Warping ± DTW) ÿѭӧFÿӅ xuҩt bӣi
%HUQWYj&OLIIRUG>4] FyÿһFÿLӇPFKtQKOjviӋFiQK[ҥ NK{QJWX\ӃQWtQKNKL VRViQKJLӳa hai chuӛi thӡLJLDQ&{QJWKӭFWtQKWRiQQKѭVDX
Giҧ sӱ FyKDLFKXӛi thӡi gian ܳ Yjܥ FyFKLӅXGjLOҫQOѭӧWOj݊ Yj݉vӟi: ܳ ൌ ݍ ଵ ǡ ݍ ଶ ǡ ǥ ǡ ݍ ǡ ǥ ǡ ݍ ܥ ൌ ܿ ଵ ǡ ܿ ଶ ǡ ǥ ǡ ܿ ǡ ǥ ǡ ܿ
8 ĈӇ WtQKWRiQNKRҧQJFiFKDTW giӳa hai chuӛL WUrQ WD [k\ Gӵng mӝt ma trұn ܦ FyNtFKWKѭӟc ݉ ൈ ݊ gӑLOjma tr̵n xo̷n (warping matrix)
7URQJÿySKҫn tӱ ܦ ൌ ݀ሺݍ ǡ ܿ ሻ Oj NKRҧQJ FiFK JLӳD KDL ÿLӇm ݍ Yjܿ (vӟi kho̫QJ FiFK (XFOLG WKu݀ሺݍ ǡ ܿ ሻ ൌ ሺݍ Ȃܿ ሻ ଶ ) Ĉ˱ͥng xo̷n W (warping path)
OjPӝt tұSFiFSKҫn tӱ OLrQWөc cӫa ma trұQÿӏQKQJKƭDPӝWiQK[ҥ giӳa ܳ Yjܥ Phҫn tӱ thӭ ݇ cӫa ܹ ÿѭӧFÿӏQKQJKƭDOjݓ ൌ ሺ݅ǡ ݆ሻ , YuYұ\WDFy ܹ ൌ ݓ ଵ ǡ ݓ ଶ ǡ ǥ ǡ ݓ ଷ ǡ ǥ ǡ ݓ vӟi ݉ܽݔሺ݊ǡ ݉ሻ ܭ ݉ ݊Ȃ ͳ
7KHRÿӏQKQJKƭDÿѭӡng xoҳn tӕLѭXOjÿѭӡng xoҳQFKRJLiWUӏ khoҧQJFiFK xoҳn nhӓ nhҩt: ܦܹܶሺܳǡ ܥሻ ൌ ݉݅݊ ە ۔ ۓ ඩ ݓ ୀଵ
7URQJ ÿyFKLSKt[Rҳn cӫa mӝWÿѭӡng xoҳQOjWәng khoҧQJFiFK FӫD FiF cһSÿLӇPWѭѫQJӭng vӟLFiF{QҵPWUrQÿѭӡng xoҳQÿy
+uQh 2.1&iFKWtQKNKRҧQJFiFKÿӝ ÿR[Rҳn thӡLJLDQÿӝng [6]
(A) Hai chu͟i thͥi gian ࡽ Yj B) Ma tr̵QWtQK'7:&.͇t qu̫ iQK[̩ ÿL͋m trong DTW) Ĉѭӡng xoҳn tӕLѭXQj\FyWKӇ WuPÿѭӧc bҵQJFiFKVӱ dөQJSKѭѫQJSKiS quy ho̩FKÿ͡ng (dynamic programming) &{QJWKӭc truy hӗi cho kho̫QJFiFKWtFKONJ\cumulative distance) ߛሺ݅ǡ ݆ሻ ÿѭӧc ÿӏQKQJKƭDQKѭVDX
7URQJ ÿykho̫QJ FiFK WtFK ONJ\ ߛሺ݅ǡ ݆ሻ tҥL {ሺ݅ǡ ݆ሻ cӫa ma trұQ ÿѭӧF WtQK bҵng khoҧQJFiFK݀ሺ݅ǡ ݆ሻ cӫD{WѭѫQJӭng cӝng vӟLJLiWUӏ nhӓ nhҩt cӫa khoҧQJFiFK WtFK ONJ\ FӫD FiF { OLӅn kӅ WUѭӟF { ÿy KRҧQJ FiFK [Rҳn thӡL JLDQ ÿӝng cӫa hai chuӛi thӡi gian ܳ Yjܥ OjFăQEұc hai cӫa khoҧQJFiFKWtFKONJ\WҥL{FyFKӍ sӕ Oj ሺ݉ǡ ݊ሻ+uQK2.1 minh hӑDFiFKWtQKNKRҧQJFiFKFӫDÿӝ ÿR[Rҳn thӡLJLDQÿӝng ĈӇ hҥn chӃ sӕ OѭӧQJÿѭӡng xoҳQZDUSLQJSDWKWURQJTXiWUuQKWuPWѭѫQJ tӵÿѭӡng xoҳn W phҧLFyÿӫ 3 yӃu tӕ VDXÿk\ x ĈL͉u ki QELrQ ݓ ଵ ൌ ሺͳǡ ͳሻ Yjݓ ൌ ሺ݉ǡ ݊ሻ, UjQJEXӝFQj\\rXFҫXÿѭӡng xoҳn phҧi bҳWÿҫu YjNӃWWK~Fӣ KDLJyFÿӕi diӋn cӫa ma trұn xoҳn x 7tQK OLrQ WͭF cho ݓ ൌ ሺܽǡ ܾሻ WKuݓ ିଵ ൌ ሺܽ ᇱ ǡ ܾ ᇱ ሻ WURQJ ÿyܽȂ ܽ ᇱ ͳ Yj ܾ െ ܾǯ ͳ5jQJEXӝFQj\\rXFҫXÿѭӡQJ[RҳQSKҧLGLFKX\ӇQJLӳDQKӳQJ{ OLӅQNӅNӇFҧQKӳQJ{OLӅQNӅWKHRÿѭӡQJFKpR x 7tQKÿ˯QÿL XWăQJ cho ݓ ൌ ሺܽǡ ܾሻWKuݓ ିଵ ൌ ሺܽ ᇱ ǡ ܾ ᇱ ሻ vӟi ܽȂ ܽ ᇱ Ͳ Yj ܾȂ ܾ ᇱ Ͳ5jQJEXӝFQj\\rXFҫXFiFÿLӇm trong ܹ SKҧLWăQJÿѫQÿLӋXWKHR WKӡLJLDQ
Giҧi thuұWÿѭӧc thӵc hiӋQQKѭVDX:
Input : Q: array [1 ôQ], C: array [1 m], DTW: array [1 ôQ, 1 ôP]
3 DTW [i, j] = (Q [i] ± C [j]) 2 + min (DTW [i - 1, j], DTW [i, j - 1], DTW [i - 1, j - 1])
10 6DXÿk\VӁ OjYtGө cho viӋFWtQKNKRҧQJFiFK'7:JLҧ sӱ WDFyKDLFKXӛi thӡLJLDQQKѭVDX
+uQK2.2 WUuQKEj\ÿѭӡng cong biӇu diӉn hai chuӛi thӡi gian Q YjC
+uQK2.2 Hai chuӛi thӡi gian Q YjC ĈӇ WtQKNKRҧQJFiFK'7:JLӳa hai chuӛi thӡLJLDQWUrQWD[k\Gӵng ma trұn xoҳQOѭXNKRҧQJFiFKWtFKONJ\QKѭKuQK2.3 MӛL{WURQJPDWUұQQj\FKӭa khoҧng FiFKWtFKONJ\Fӫa tӯng cһSÿLӇPWѭѫQJӭng
+uQK2.3 Ma trұn biӇu diӉn FiFKWtQK'7:FKRKDLFKXӛi thӡi gian
11 Trong ma trұQWUrQJLiWUӏ cӫDFiF{ÿѭӧFWtQKQKѭVDX x ߛሺͳǡ ͳሻ ൌ ሺܳ ଵ െ ܥ ଵ ሻ ଶ x ߛሺͳǡ ݅ሻ ൌ ߛሺͳǡ ݅ െ ͳሻ ሺܳ ଵ െ ܥ ሻ ଶ x ߛሺ݅ǡ ͳሻ ൌ ߛሺ݅ െ ͳǡ ͳሻ ሺܳ െ ܥ ଵ ሻ ଶ x ߛሺ݅ǡ ݆ሻ ൌ ݉݅݊ሼߛሺ݅ െ ͳǡ ݆ሻǡ ߛሺ݅ǡ ݆ െ ͳሻǡ ߛሺ݅ െ ͳǡ ݆ െ ͳሻሽ ൫ܳ െ ܥ ൯ ଶ
6DXNKLWtQKÿѭӧc JLiWUӏ cho tҩt cҧ FiF{WDFyÿѭӡng xoҳn bao gӗPFiF{ WKDPJLDWtFKONJ\JLiWUӏ FKR{ሺͳͲǡ ͳͲሻ7URQJYtGө WUrQÿѭӡng xoҳQOjFiF{ÿѭӧc W{ÿӓ Vұy khoҧQJFiFKDTW cӫa hai chuӛi ܳ Yjܥ OjξͳͲ ൎ ͵Ǥͳ ѬXÿLӇPĈӝÿR'7:SKKӧSYӟLFiFGӳOLӋXFKXӛLWKӡLJLDQFyKuQKGҥQJ WѭѫQJWӵQKDXQKѭQJÿӝGjLWKӡLJLDQNKiFQKDXKRһF³OӋFKQKDX´YӅPһWWKӡLJLDQ
1KѭӧFÿLӇP 1KѭӧF ÿLӇP OӟQ QKҩW FӫD NKRҧQJ FiFK '7: Oj ÿӝ SKӭF WҥS WtQKWRiQOӟQ9ӟLKDLFKXӛLQ YjC FyFKLӅXGjLOҫQOѭӧWOjm YjnÿӇWtQK NKRҧQJ FiFK'7:FӫDKDLFKXӛLQj\WDSKҧL[k\GӵQJPDWUұQD FyNtFKWKѭӟFm ợn Yj
WtQKNKRҧQJFiFKWtFKONJ\WѭѫQJӭQJYӟLKjPȖ FKRPӑL{WURQJPDWUұQÿy1KѭYұ\ ÿӝ SKӭF WҥS WtQK WRiQ FӫD JLҧL WKXұW WtQK '7: Vӱ GөQJ SKѭѫQJ SKiS TX\ KRҥFK ÿӝQJOjO(mn)
9LӋFWtQKÿӝÿR[RҳQWKӡLJLDQÿӝQJFyFKLSKtOӟQYuSKҧLWuPÿѭӡQJ[RҳQ ÿҥWJLiWUӏQKӓQKҩWWURQJPDWUұQEҵQJSKѭѫQJSKiSTX\KRҥFKÿӝQJĈӝSKӭFWҥS FӫDJLҧLWKXұWQj\OjO(mn)7X\QKLrQGӵDWUrQêWѭӣQJFѫEҧQOjJLӟLKҥQÿѭӡQJ [RҳQEҵQJFiFKWKrPYjRFiFJLӟLKҥQFөFEӝWUrQWұSKӧSFiFEѭӟFVӁ[HP[pWÿm FyKDLUjQJEXӝFYӅÿѭӡQJ[RҳQSKәELӃQOjUjQJEXӝF6DNRH-&KLEDYjUjQJEXӝF KuQKEuQKKjQK,WDNXUD
BӔ CӨC LUҰ19Ă1
Ĉӝ ÿRNKRҧQJFiFK(XFOLG('
ĈӝÿRNKRҧQJFiFK(XFOLGÿѭӧFGQJÿӇÿRÿӝNKiFELӋWJLӳDKDLFKXӛLWKӡL JLDQĈk\OjÿӝÿRNKRҧQJFiFKÿѫQJLҧQQKҩWYjGӉWtQKWRiQQKҩW
&KRKDLFKXӛLWKӡLJLDQ& ^F F ôF Q `Yj4 ^T T ôT Q `NKRҧQJFiFK
(XFOLGJLӳDKDLFKXӛLWKӡLJLDQ&Yj4ÿѭӧFWtQKEҵQJF{QJWKӭFVDX Ĉӝ ÿR NKRҧQJ FiFK (XFOLG Fy ѭX WKӃ Oj ÿѫQ JLҧQ GӉ KLӋQ WKӵF Yj WKӡL JLDQ WKӵFWKLWKҩS7X\QKLrQÿӝÿR(XFOLGFyQKѭӧFÿLӇPOjQKҥ\FҧPYӟLQKLӉXYjNpP WtQKOLQKKRҥWYuÿӝÿRQj\\rXFҫXKDLFKXӛLWKӡLJLDQFyFKLӅXGjLEҵQJQKDX
2.1.2 Ĉӝ ÿR[Rҳn thӡLJLDQÿӝng (Dynamic Time Warping ± DTW) Ĉӝ ÿR[Rҳn thӡLJLDQÿӝng (Dynamic Time Warping ± DTW) ÿѭӧFÿӅ xuҩt bӣi
%HUQWYj&OLIIRUG>4] FyÿһFÿLӇPFKtQKOjviӋFiQK[ҥ NK{QJWX\ӃQWtQKNKL VRViQKJLӳa hai chuӛi thӡLJLDQ&{QJWKӭFWtQKWRiQQKѭVDX
Giҧ sӱ FyKDLFKXӛi thӡi gian ܳ Yjܥ FyFKLӅXGjLOҫQOѭӧWOj݊ Yj݉vӟi: ܳ ൌ ݍ ଵ ǡ ݍ ଶ ǡ ǥ ǡ ݍ ǡ ǥ ǡ ݍ ܥ ൌ ܿ ଵ ǡ ܿ ଶ ǡ ǥ ǡ ܿ ǡ ǥ ǡ ܿ
8 ĈӇ WtQKWRiQNKRҧQJFiFKDTW giӳa hai chuӛL WUrQ WD [k\ Gӵng mӝt ma trұn ܦ FyNtFKWKѭӟc ݉ ൈ ݊ gӑLOjma tr̵n xo̷n (warping matrix)
7URQJÿySKҫn tӱ ܦ ൌ ݀ሺݍ ǡ ܿ ሻ Oj NKRҧQJ FiFK JLӳD KDL ÿLӇm ݍ Yjܿ (vӟi kho̫QJ FiFK (XFOLG WKu݀ሺݍ ǡ ܿ ሻ ൌ ሺݍ Ȃܿ ሻ ଶ ) Ĉ˱ͥng xo̷n W (warping path)
OjPӝt tұSFiFSKҫn tӱ OLrQWөc cӫa ma trұQÿӏQKQJKƭDPӝWiQK[ҥ giӳa ܳ Yjܥ Phҫn tӱ thӭ ݇ cӫa ܹ ÿѭӧFÿӏQKQJKƭDOjݓ ൌ ሺ݅ǡ ݆ሻ , YuYұ\WDFy ܹ ൌ ݓ ଵ ǡ ݓ ଶ ǡ ǥ ǡ ݓ ଷ ǡ ǥ ǡ ݓ vӟi ݉ܽݔሺ݊ǡ ݉ሻ ܭ ݉ ݊Ȃ ͳ
7KHRÿӏQKQJKƭDÿѭӡng xoҳn tӕLѭXOjÿѭӡng xoҳQFKRJLiWUӏ khoҧQJFiFK xoҳn nhӓ nhҩt: ܦܹܶሺܳǡ ܥሻ ൌ ݉݅݊ ە ۔ ۓ ඩ ݓ ୀଵ
7URQJ ÿyFKLSKt[Rҳn cӫa mӝWÿѭӡng xoҳQOjWәng khoҧQJFiFK FӫD FiF cһSÿLӇPWѭѫQJӭng vӟLFiF{QҵPWUrQÿѭӡng xoҳQÿy
+uQh 2.1&iFKWtQKNKRҧQJFiFKÿӝ ÿR[Rҳn thӡLJLDQÿӝng [6]
(A) Hai chu͟i thͥi gian ࡽ Yj B) Ma tr̵QWtQK'7:&.͇t qu̫ iQK[̩ ÿL͋m trong DTW) Ĉѭӡng xoҳn tӕLѭXQj\FyWKӇ WuPÿѭӧc bҵQJFiFKVӱ dөQJSKѭѫQJSKiS quy ho̩FKÿ͡ng (dynamic programming) &{QJWKӭc truy hӗi cho kho̫QJFiFKWtFKONJ\cumulative distance) ߛሺ݅ǡ ݆ሻ ÿѭӧc ÿӏQKQJKƭDQKѭVDX
7URQJ ÿykho̫QJ FiFK WtFK ONJ\ ߛሺ݅ǡ ݆ሻ tҥL {ሺ݅ǡ ݆ሻ cӫa ma trұQ ÿѭӧF WtQK bҵng khoҧQJFiFK݀ሺ݅ǡ ݆ሻ cӫD{WѭѫQJӭng cӝng vӟLJLiWUӏ nhӓ nhҩt cӫa khoҧQJFiFK WtFK ONJ\ FӫD FiF { OLӅn kӅ WUѭӟF { ÿy KRҧQJ FiFK [Rҳn thӡL JLDQ ÿӝng cӫa hai chuӛi thӡi gian ܳ Yjܥ OjFăQEұc hai cӫa khoҧQJFiFKWtFKONJ\WҥL{FyFKӍ sӕ Oj ሺ݉ǡ ݊ሻ+uQK2.1 minh hӑDFiFKWtQKNKRҧQJFiFKFӫDÿӝ ÿR[Rҳn thӡLJLDQÿӝng ĈӇ hҥn chӃ sӕ OѭӧQJÿѭӡng xoҳQZDUSLQJSDWKWURQJTXiWUuQKWuPWѭѫQJ tӵÿѭӡng xoҳn W phҧLFyÿӫ 3 yӃu tӕ VDXÿk\ x ĈL͉u ki QELrQ ݓ ଵ ൌ ሺͳǡ ͳሻ Yjݓ ൌ ሺ݉ǡ ݊ሻ, UjQJEXӝFQj\\rXFҫXÿѭӡng xoҳn phҧi bҳWÿҫu YjNӃWWK~Fӣ KDLJyFÿӕi diӋn cӫa ma trұn xoҳn x 7tQK OLrQ WͭF cho ݓ ൌ ሺܽǡ ܾሻ WKuݓ ିଵ ൌ ሺܽ ᇱ ǡ ܾ ᇱ ሻ WURQJ ÿyܽȂ ܽ ᇱ ͳ Yj ܾ െ ܾǯ ͳ5jQJEXӝFQj\\rXFҫXÿѭӡQJ[RҳQSKҧLGLFKX\ӇQJLӳDQKӳQJ{ OLӅQNӅNӇFҧQKӳQJ{OLӅQNӅWKHRÿѭӡQJFKpR x 7tQKÿ˯QÿL XWăQJ cho ݓ ൌ ሺܽǡ ܾሻWKuݓ ିଵ ൌ ሺܽ ᇱ ǡ ܾ ᇱ ሻ vӟi ܽȂ ܽ ᇱ Ͳ Yj ܾȂ ܾ ᇱ Ͳ5jQJEXӝFQj\\rXFҫXFiFÿLӇm trong ܹ SKҧLWăQJÿѫQÿLӋXWKHR WKӡLJLDQ
Giҧi thuұWÿѭӧc thӵc hiӋQQKѭVDX:
Input : Q: array [1 ôQ], C: array [1 m], DTW: array [1 ôQ, 1 ôP]
3 DTW [i, j] = (Q [i] ± C [j]) 2 + min (DTW [i - 1, j], DTW [i, j - 1], DTW [i - 1, j - 1])
10 6DXÿk\VӁ OjYtGө cho viӋFWtQKNKRҧQJFiFK'7:JLҧ sӱ WDFyKDLFKXӛi thӡLJLDQQKѭVDX
+uQK2.2 WUuQKEj\ÿѭӡng cong biӇu diӉn hai chuӛi thӡi gian Q YjC
+uQK2.2 Hai chuӛi thӡi gian Q YjC ĈӇ WtQKNKRҧQJFiFK'7:JLӳa hai chuӛi thӡLJLDQWUrQWD[k\Gӵng ma trұn xoҳQOѭXNKRҧQJFiFKWtFKONJ\QKѭKuQK2.3 MӛL{WURQJPDWUұQQj\FKӭa khoҧng FiFKWtFKONJ\Fӫa tӯng cһSÿLӇPWѭѫQJӭng
+uQK2.3 Ma trұn biӇu diӉn FiFKWtQK'7:FKRKDLFKXӛi thӡi gian
11 Trong ma trұQWUrQJLiWUӏ cӫDFiF{ÿѭӧFWtQKQKѭVDX x ߛሺͳǡ ͳሻ ൌ ሺܳ ଵ െ ܥ ଵ ሻ ଶ x ߛሺͳǡ ݅ሻ ൌ ߛሺͳǡ ݅ െ ͳሻ ሺܳ ଵ െ ܥ ሻ ଶ x ߛሺ݅ǡ ͳሻ ൌ ߛሺ݅ െ ͳǡ ͳሻ ሺܳ െ ܥ ଵ ሻ ଶ x ߛሺ݅ǡ ݆ሻ ൌ ݉݅݊ሼߛሺ݅ െ ͳǡ ݆ሻǡ ߛሺ݅ǡ ݆ െ ͳሻǡ ߛሺ݅ െ ͳǡ ݆ െ ͳሻሽ ൫ܳ െ ܥ ൯ ଶ
6DXNKLWtQKÿѭӧc JLiWUӏ cho tҩt cҧ FiF{WDFyÿѭӡng xoҳn bao gӗPFiF{ WKDPJLDWtFKONJ\JLiWUӏ FKR{ሺͳͲǡ ͳͲሻ7URQJYtGө WUrQÿѭӡng xoҳQOjFiF{ÿѭӧc W{ÿӓ Vұy khoҧQJFiFKDTW cӫa hai chuӛi ܳ Yjܥ OjξͳͲ ൎ ͵Ǥͳ ѬXÿLӇPĈӝÿR'7:SKKӧSYӟLFiFGӳOLӋXFKXӛLWKӡLJLDQFyKuQKGҥQJ WѭѫQJWӵQKDXQKѭQJÿӝGjLWKӡLJLDQNKiFQKDXKRһF³OӋFKQKDX´YӅPһWWKӡLJLDQ
1KѭӧFÿLӇP 1KѭӧF ÿLӇP OӟQ QKҩW FӫD NKRҧQJ FiFK '7: Oj ÿӝ SKӭF WҥS WtQKWRiQOӟQ9ӟLKDLFKXӛLQ YjC FyFKLӅXGjLOҫQOѭӧWOjm YjnÿӇWtQK NKRҧQJ FiFK'7:FӫDKDLFKXӛLQj\WDSKҧL[k\GӵQJPDWUұQD FyNtFKWKѭӟFm ợn Yj
WtQKNKRҧQJFiFKWtFKONJ\WѭѫQJӭQJYӟLKjPȖ FKRPӑL{WURQJPDWUұQÿy1KѭYұ\ ÿӝ SKӭF WҥS WtQK WRiQ FӫD JLҧL WKXұW WtQK '7: Vӱ GөQJ SKѭѫQJ SKiS TX\ KRҥFK ÿӝQJOjO(mn)
9LӋFWtQKÿӝÿR[RҳQWKӡLJLDQÿӝQJFyFKLSKtOӟQYuSKҧLWuPÿѭӡQJ[RҳQ ÿҥWJLiWUӏQKӓQKҩWWURQJPDWUұQEҵQJSKѭѫQJSKiSTX\KRҥFKÿӝQJĈӝSKӭFWҥSFӫDJLҧLWKXұWQj\OjO(mn)7X\QKLrQGӵDWUrQêWѭӣQJFѫEҧQOjJLӟLKҥQÿѭӡQJ[RҳQEҵQJFiFKWKrPYjRFiFJLӟLKҥQFөFEӝWUrQWұSKӧSFiFEѭӟFVӁ[HP[pWÿmFyKDLUjQJEXӝFYӅÿѭӡQJ[RҳQSKәELӃQOjUjQJEXӝF6DNRH-&KLEDYjUjQJEXӝFKuQKEuQKKjQK,WDNXUD
Kӻ thuұWUjQJEXӝFWRjQFөc
%rQFҥnh nhӳQJUjQJEXӝFÿӕi vӟLÿѭӡng xoҳn thӡLJLDQÿӝQJÿmÿӅ cұp ӣ phҫQ WUѭӟF ÿӇ ÿҧm bҧR ÿѭӡng xoҳQ NK{QJ ÿL FKӋFK KѭӟQJ TXi [D VR YӟL ÿѭӡng FKpRFӫa ma trұQQJѭӡLWDÿmÿӅ UDWKrPQKӳQJUjQJEXӝFPDQJêQJKƭDWRjQFөc 5jQJEXӝFQj\ÿӏQKQJKƭDPӝt tұp con cӫa ma tr̵n xo̷n ZDUSLQJPDWUL[FKRSKpS ÿѭӡng xoҳn tiӃQ KjQK GL FKX\Ӈn mӣ rӝng gӑL Ojc͵a s͝ xo̷n (warping window)
MөF ÿtFK FKtQK FӫD UjQJ EXӝF WRjQ FөF Oj WăQJ WӕF ÿӝ WtQK WRiQ '7: WK{QJ TXD
12 viӋc giҧPNK{QJJLDQWuPNLӃPÿѭӡng xoҳQÿӗng thӡi nJăQWUѭӡng hӧp mӝt phҫn nhӓ cӫa mӝt chuӛLiQK[ҥ YjRSKҫn lӟQWѭѫQJӭng cӫa mӝt chuӛLNKiF
7URQJFiFNӻ thuұWUjQJEXӝFWRjQFөc, phә biӃn nhҩWOjNӻ thuұWUjQJEXӝc dҧi Sakoe ± &KLEDYjKuQKEuQKKjQK,WDNXUD x 5jQJEXӝc dҧi Sakoe ± ChibaÿѭӧFÿӅ xuҩt bӣLKDL6DNRHYj&KLED[11], UjQJEXӝFQj\ÿѭӧFP{Wҧ QKѭVDX
GӑLÿѭӡng xoҳn tӕLѭXOjWұSFiF{WURQJPDWUұn cӫa hai chuӛi thӡi gian:
7URQJ ÿyw k = (i, j) k 5jQJ EXӝc Sakoe-&KLED \rX Fҫu |i ± j| r, trong ÿyݎOjPӝt sӕ QJX\rQGѭѫQJFKRWUѭӟFÿѭӧc gӑLOjFӱa sә xoҳn (;HPKuQK2.4)
5jQJEXӝFKuQKEuQKKjQK,WDNXUD,WDNXUD3DUDOHORJUDP: ÿѭӧFÿӅ xuҩt bӣi Itakura (1975) [8]5jQJEXӝFQj\FNJQJÿӏnh QJKƭDÿѭӡng xoҳQFNJQJEDRJӗm mӝt tұSFiF {WURQJPDWUұn cӫa hai chuӛi thӡi gian:
7URQJÿyw k = (i, j) k 5jQJEXӝFKuQKEuQKKjQK,WDNXUD\rXFҫu |i ± j| r, WURQJÿyݎOjPӝWKjPELӃQWKLrQWKHRthӡi gian (;HPKuQK2.5)
+uQK2.55jQJEXӝFKuQKEuQKKjQK,WDNXUD 2.2 7ẻ0.,ӂ07ѬѪ1*7Ӵ 75ầ1'Ӳ LIӊU CHUӚI THӠI GIAN
Mӝt chu͟i thͥi gian (time series) OjFKXӛi trӏ sӕ thӵc, mӛi trӏ biӇu diӉn mӝt
JLiWUӏ ÿRWҥi nhӳng thӡLÿLӇPFiFKÿӅu nhau Nhӳng tұp dӳ liӋu chuӛi thӡi gian rҩt lӟn xuҩt hiӋn trong nhiӅu lƭnh vӵF NKiF QKDX QKѭ \ NKRD Nӻ thuұt, kinh tӃ WjL FKtQKYYô7uPNL͇PW˱˯QJW (similarity search) OjF{QJWiFFăQEҧn nhҩWÿӇ khai WKiFQKӳQJFѫVӣ dӳ liӋu chuӛi thӡi gian
7KHREjLEiR>5@ÿӇ thӵc hiӋQWuPNLӃPWѭѫQJWӵ WUrQGӳ liӋu chuӛi thӡi gian, SKѭѫQJSKiSl̵p ch͑ mͭc (indexing) FyNKҧ QăQJKӛ trӧ hiӋu quҧ viӋc lҩ\YjJKpS cһp dӳ liӋu chuӛi thӡL JLDQ ÿѭӧF \rX Fҫu Hҫu hӃW FiF SKѭѫQJ SKiS Oұp chӍ mөc QJj\QD\FKRGӳ liӋXÿDFKLӅXQKѭR-tree YjR* -tree lҥi giҧm dҫn hiӋu suҩt ӣ FiF chiӅu lӟQKѫQWӯ 8-10 chiӅXYjKRҥWÿӝQJQKѭWKXұWWRiQTXpWWXҫn tӵ ӣ bӝ dӳ liӋu lӟQKѫQFKLӅX9uYұ\ÿӇ sӱ dөng kӻ thuұt lұp chӍ mөc dӳ liӋXÿDFKLӅXÿLӅu cҫn thӵc hiӋQÿҫXWLrQOjJLҧm sӕ chiӅXWUrQGӳ liӋu chuӛi thӡLJLDQJL~SFKRFiFGӳ liӋu FiFFKLӅXFDRKѫQiQK[ҥ vӅ NK{QJJLDQFKLӅu thҩSKѫQ6DXÿyGQJPӝt sӕ biӋn SKiSÿRNKRҧQJFiFKQKѭ(XFOLGÿӇ ttQKWRiQNKRҧQJFiFKYjVX\UDVӵ giӕng nhau giӳa hai bӝ dӳ liӋu chuӛi thӡi gian
Hҫu hӃW FiF SKѭѫQJ SKiS WLӃp cұQ SKiW WULӇQ FKR ÿӃQ QD\ ÿӇ thӵc hiӋQ WuP kiӃPWѭѫQJWӵ trong dӳ liӋu chuӛi thӡi gian dӵDWUrQYLӋc giҧm sӕ chiӅu Giҧm sӕ chiӅXFyWKӇ ÿѭӧc thӵc hiӋn bҵng nhiӅXFiFK0ӝt sӕ SKѭѫQJSKiSWKѭӡQJÿѭӧc sӱ dөQJÿӇ thӵc hiӋn viӋc giҧm sӕ chiӅu bao gӗm Discrete Fourier Transform (DFT),
Discrete Wavelet Transform (DWT) [12], Singular Value Decomposition (SVD)
14 3KѭѫQJSKiSWKѭӡQJÿѭӧc sӱ dөng nhҩWÿӇ giҧm sӕ chiӅXOjGӵDWUrQ')7 ')7NKi SKKӧp cho dӳ liӋu tӵ QKLrQWKHRGҥQJKuQKVLQQKѭQJ QyNK{QJWKtFK hӧSÿӇ WtQKWtQKLӋu bӏ JLiQÿRҥn KӃ ÿӃQSKѭѫQJSKiSELӃQÿәi Wavelet dҥng Haar OjSKѭѫQJSKiSSKә biӃn nhҩWÿѭӧc sӱ dөQJÿӇ biӃQÿәLFiFJӧQVyQJWrong dӳ liӋu, tӯ ÿyJLҧPNtFKWKѭӟc cӫa bӝ dӳ liӋX7X\QKLrQYӅ FѫEҧQSKѭѫQJSKiS+DDUKRҥt ÿӝQJNK{QJÿѭӧFWUѫQWUXOҳPGRÿySKѭѫQJSKiS+DDUELӃQÿәi xҩp xӍ tҩt cҧ WtQ hiӋX WK{QJ TXD FҩX WU~F JLӕng mӝW FiL WKDQJ &iF KӋ sӕ cҫQ ÿѭӧF WKrP YjR NKi nhiӅu, viӋFWuPNLӃPFiFJӧQVyQJGүn xuҩWOLrQWөc trong dӳ liӋu vүQFzQOjYҩQÿӅ ÿDQJÿѭӧFQJKLrQFӭu
Kӻ thuұt SKkQUm tr͓ NuG͓ (Singular Value Decomposition ± SVD) OjPӝt kӻ thuұt giҧm sӕ chiӅu dӳ liӋX&iFWK{QJVӕ ÿѭӧc sӱ dөQJÿӇ WtQKWRiQYHFWѫFѫVӣ, Yu vұy bҩt cӭ NKLQjRFiFFѫVӣ dӳ liӋXÿѭӧc cұp nhұWFiFYHFWѫFѫVӣ cҫn phҧLÿѭӧc WtQKWRiQOҥi ThӡLJLDQWtQKWRiQOҥLFyWKӇ trӣ QrQNK{QJNKҧ thi cho mөFÿtFKWKӵc tӃ ÿһc biӋWOjNKLFiFFѫVӣ dӳ liӋXTXiOӟn
7URQJNKLÿySKѭѫQJSKiSx̭p x͑ g͡p tͳQJÿR̩n (PAA) thӵc hiӋn giҧm sӕ chiӅu bҵQJ FiFK FKLD FiF WUuQK Wӵ thӡL JLDQ WKjQK FiF ÿRҥQ GjL EҵQJ QKDX Yj WtQKWRiQFiFJLiWUӏ WUXQJEuQKFӫa tӯQJSKkQNK~F Yjÿѭӧc sӱ dөQJNKiSKә biӃQYuVӵ ÿѫQJLҧn.
CHUҬ1+ẽ$'Ӳ LIӊU (Z-SCORE NORMALIZATION)
3KpSFKXҭQKyDGӳ liӋu Z-6FRUHOjTX\WUuQKÿҧm bҧo rҵng tҩt cҧ FiFSKҫn tӱ cӫD YHFWѫ ÿҫX YjR ÿѭӧc chuyӇQ WKjQK YHFWѫ ÿҫX UD Fy JLi WUӏ WUXQJ EuQK [ҩp xӍ 0 WURQJNKLÿӝ lӋch chuҭn nҵm trong phҥm vi gҫQ&{QJWKӭc biӃQÿәi: ݔ ᇱ ൌ ௫ ିఓ ఙ , ݅ א ܰ 7URQJÿy ݔ ᇱ : ph̯n t͵ thͱ i sau khi chu̱QKyD ݔ : ph̯n t͵ thͱ i cͯa chu͟i dͷ li XEDQÿ̯u ߤJLiWU͓ WUXQJEuQKFͯa chu͟i dͷ li u ߪÿ͡ l ch chu̱n
RӠI RҤ&+ẽ$&+8ӚI THӠI GIAN
Thu giҧm sӕ chiӅu bҵQJSKѭѫQJSKiS[ҩp xӍ gӝp tӯQJÿRҥn (Piecewise
Dӳ liӋu chuӛi thӡLJLDQWKѭӡng rҩt lӟQQrQYLӋFWuPNLӃm trӵc tiӃSWUrQGӳ liӋu chuӛi thӡi gian gӕFWKѭӡng NK{QJKLӋu quҧĈӇ khҳc phөc vҩQÿӅ Qj\FiFKWLӃp cұn FKXQJWKѭӡQJÿѭӧc sӱ dөng bao gӗPFiFEѭӟc sau:
- ÈSGөng mӝt sӕ SKѭѫQJSKiSELӃQÿәi xҩp xӍ ÿӇ thu giҧPÿӝ lӟn cӫa dӳ liӋu sao cho vүn giӳ ÿѭӧF FiF ÿһW WUѭQJ Fӫa dӳ liӋX &iF SKѭѫQJ SKiS ELӃQ ÿәL Qj\ WKѭӡQJÿѭӧc gӑLOjSKѭѫQJSKiSthu gi̫m s͙ chi͉u (demensionality reduction)
- Thӵc hiӋQEjLWRiQWUrQGӳ liӋu xҩp xӍWDWKXÿѭӧc tұp kӃt quҧ xҩp xӍ
- DӵD WUrQ NӃt quҧ xҩp xӍ Qj\ WKӵc hiӋn truy cұS ÿƭD ÿӇ thӵc hiӋn hұu kiӇm WUrQGӳ liӋu gӕc nhҵm loҥi bӓ FiFFKXӛLWuPVDLWURQJWұp kӃt quҧ xҩp xӍ ĈLӅu kiӋn chһQGѭӟi:
Do khi xҩp xӍ dӳ liӋu sӁ Jk\UDPҩWPiWWK{QJWLQQrQNKLWKӵc hiӋQWUrQGӳ liӋu xҩp xӍ FyWKӇ WuPUDl͟i WuP VyW (false dismissal) hoһc l͟i WuPVDL (false alarm) ĈӇ ÿҧm bҧRFyNӃt quҧ FKtQK[iFOӛLWuPVyWNK{QJÿѭӧFSKpS[ҧy ra MһWNKiFOӛi WuPVDLFNJQJQrQWKҩSÿӇ giҧPFKLSKtWURQJTXiWUuQKKұu kiӇm
L͟LWuPVyW xҧy ra khi mӝt chuӛL6WURQJFѫVӣ dӳ liӋXWѭѫQJWӵ vӟi chuӛi cҫn
WuPQKѭQJNӃt quҧ WuPNLӃPNK{QJFyFKXӛi S L͟LWuPVDL xҧy ra khi mӝt chuӛi S WURQJFѫVӣ dӳ liӋXNKiFYӟi chuӛi cҫQWuP QKѭQJNӃt quҧ WuPNLӃm lҥLFyFKXӛi S
H̵u ki͋m OjTXiWUuQKNLӇm tra lҥLWUrQGӳ liӋu gӕFFiFFKXӛLWuPÿѭӧFWURQJNK{QJ gian thu giҧPWѭѫQJWӵ vӟi chuӛi cҫQWuPQKҵm loҥi bӓ FiFFKXӛLWuPVDL
Mӝt kӃt quҧ quan trӑQJ ÿm ÿѭӧF )DORXWVRV Yj FiF Fӝng sӵ chӭnJ PLQK Oj ÿӇ NK{QJ[ҧy ra lӛLWuP[yWWKuÿӝ ÿRNKRҧQJFiFK Vӱ dөQJWURQJNK{QJJLDQ[ҩp xӍ ÿһFWUѭQJSKҧLOjFKһQGѭӟi cӫDÿӝ ÿRNKRҧQJFiFKVӱ dөQJWURQJNK{QJJLDQJӕc [3@1JKƭDOj'feature;ả@Yjb ± a OjVӕ QJX\rQOҩy ra trong tҫm [32,
&iFPүu dӳ liӋXQKkQWҥRÿѭӧFWtQKUDWӯ EDKjPQyLWUrQOjPWKjQKEӝ dӳ liӋu CBF, gӗm 128 mүu cho mӛLKjPYjPӛi mүXFyFKLӅXGjLÿLӇm dӳ liӋu
+uQK4.3 P{Wҧ EDÿѭӡQJFRQJÿҥi diӋn cho ba lӟSKjPF\OLQGHUEHOOYjIXQQHO
+uQK4.3%Dÿѭӡng cong biӇu diӉn ba lӟSKjP&\OLQGHU%HOOYj)XQQHO 4.3.3 Bӝ dӳ liӋu Trace
Bӝ dӳ liӋX Qj\ Oj Pӝt tұp con cӫa bӝ dӳ liӋu Transient Classification Benchmark (dӵ iQ 7UDFH Ĉk\ Oj Pӝt bӝ dӳ liӋu tәng hӧS ÿѭӧc thiӃt kӃ ÿӇ P{
37 phӓng sӵ hӓQJKyFFӫa thiӃt bӏ ÿRWURQJPӝWQKjPi\QăQJOѭӧng hҥWQKkQ%ӝ dӳ liӋXÿѭӧc tҥo ra bӣi Davide Roverso Bӝ dӳ liӋXÿҫ\ÿӫ gӗm 16 lӟp, 50 mүu trong mӛi lӟp Mӛi mүu gӗPÿһFWUѭQJ ĈӇ ÿѫQJLҧn, bӝ dӳ liӋu Trace ӣ ÿk\FKӍ gӗPÿһFWUѭQJWKӭ hai cӫa lӟSYj FQJÿһFWUѭQJWKӭ ba cӫa lӟSYj%ӝ dӳ liӋu Trace ӣ ÿk\Jӗm 200 mүu, 50 mүu cho mӛi lӟp Tҩt cҧ FiFPүXÿѭӧc nӝLVX\ÿӇ ÿѭDYӅ FQJFKLӅXGjLJӗPÿLӇm dӳ liӋu
+uQK4.4 BӕQQKyPÿѭӡng cong biӇu thӏ cho bӕn lӟp trong bӝ dӳ liӋu Trace 4.3.4 Bӝ dӳ liӋu Fish
Bӝ dӳ liӋXQj\OjWӯ nhӳQJKuQKҧnh cӫDFiÿѭӧc chөSWURQJFiFYLGHR7ӯ KuQKWKFӫa tӯQJFRQFiKӋ thӕng xӱ Oêҧnh sӁ chuyӇQKuQKGҥng hai chiӅu cӫDFiWKjQKPӝt chuӛi thӡLJLDQÿѫQELӃQQKѭÿѭӧc minh hӑDWURQJ+uQK4.5
+uQK 4.53KtDWUrQOjKuQKchөp cӫa mӝWFRQFi7ӯ KuQKGҥQJÿѭӡQJELrQFӫa
FiPӝt chuӛi thӡLJLDQÿѫQELӃQÿѭӧc tҥo ra ӣ SKtDGѭӟi
Tӯ mӝt tұp hӧS KuQK ҧnh cӫa nhiӅX FRQ Fi Gѭӟi dҥng thӭc chuӛi thӡi gian ÿѫQELӃQFK~QJWDFҫQSKkQOӟSFK~QJWKjQKUDORҥLFiFyWrQQKѭVDX&KLQook Salmon, Winter Coho, Brown Trout, Bonneville Cutthroat, Colorado River
&XWWKURDW@Yjb ± a OjVӕ QJX\rQOҩy ra trong tҫm [32,
&iFPүu dӳ liӋXQKkQWҥRÿѭӧFWtQKUDWӯ EDKjPQyLWUrQOjPWKjQKEӝ dӳ liӋu CBF, gӗm 128 mүu cho mӛLKjPYjPӛi mүXFyFKLӅXGjLÿLӇm dӳ liӋu
+uQK4.3 P{Wҧ EDÿѭӡQJFRQJÿҥi diӋn cho ba lӟSKjPF\OLQGHUEHOOYjIXQQHO
Bӝ dӳ liӋu Trace
Bӝ dӳ liӋX Qj\ Oj Pӝt tұp con cӫa bӝ dӳ liӋu Transient Classification Benchmark (dӵ iQ 7UDFH Ĉk\ Oj Pӝt bӝ dӳ liӋu tәng hӧS ÿѭӧc thiӃt kӃ ÿӇ P{
37 phӓng sӵ hӓQJKyFFӫa thiӃt bӏ ÿRWURQJPӝWQKjPi\QăQJOѭӧng hҥWQKkQ%ӝ dӳ liӋXÿѭӧc tҥo ra bӣi Davide Roverso Bӝ dӳ liӋXÿҫ\ÿӫ gӗm 16 lӟp, 50 mүu trong mӛi lӟp Mӛi mүu gӗPÿһFWUѭQJ ĈӇ ÿѫQJLҧn, bӝ dӳ liӋu Trace ӣ ÿk\FKӍ gӗPÿһFWUѭQJWKӭ hai cӫa lӟSYj FQJÿһFWUѭQJWKӭ ba cӫa lӟSYj%ӝ dӳ liӋu Trace ӣ ÿk\Jӗm 200 mүu, 50 mүu cho mӛi lӟp Tҩt cҧ FiFPүXÿѭӧc nӝLVX\ÿӇ ÿѭDYӅ FQJFKLӅXGjLJӗPÿLӇm dӳ liӋu.
Bӝ dӳ liӋu Fish
Bӝ dӳ liӋXQj\OjWӯ nhӳQJKuQKҧnh cӫDFiÿѭӧc chөSWURQJFiFYLGHR7ӯ KuQKWKFӫa tӯQJFRQFiKӋ thӕng xӱ Oêҧnh sӁ chuyӇQKuQKGҥng hai chiӅu cӫDFiWKjQKPӝt chuӛi thӡLJLDQÿѫQELӃQQKѭÿѭӧc minh hӑDWURQJ+uQK4.5
+uQK 4.53KtDWUrQOjKuQKchөp cӫa mӝWFRQFi7ӯ KuQKGҥQJÿѭӡQJELrQFӫa
FiPӝt chuӛi thӡLJLDQÿѫQELӃQÿѭӧc tҥo ra ӣ SKtDGѭӟi
Tӯ mӝt tұp hӧS KuQK ҧnh cӫa nhiӅX FRQ Fi Gѭӟi dҥng thӭc chuӛi thӡi gian ÿѫQELӃQFK~QJWDFҫQSKkQOӟSFK~QJWKjQKUDORҥLFiFyWrQQKѭVDX&KLQook Salmon, Winter Coho, Brown Trout, Bonneville Cutthroat, Colorado River
&XWWKURDW