I HC QUC GIA TP H CH MINH TRNG I HC BCH KHOA NGUYN THNH SN KHAI PH D LIU CHUI THI GIAN DA VO RT TRCH C TRNG BNG PHNG PHP IM GIA V K THUT XẫN (TIME SERIES DATA MINING BASED ON FEATURE EXTRACTION WITH MIDDLE POINTS AND CLIPPING METHOD) LUN N TIN S KHOA HC MY TNH TP H CH MINH NM 2014 I HC QUC GIA TP HCM TRNG I HC BCH KHOA NGUYN THNH SN KHAI PH D LIU CHUI THI GIAN DA VO RT TRCH C TRNG BNG PHNG PHP IM GIA V K THUT XẫN (TIME SERIES DATA MINING BASED ON FEATURE EXTRACTION WITH MIDDLE POINTS AND CLIPPING METHOD) Chuyờn ngnh: Khoa hc mỏy tớnh Mó s chuyờn ngnh: 62.48.01.01 Phn bin c lp 1: TS Nguyn c Dng Phn bin c lp 2: TS V Tuyt Trinh Phn bin 1: PGS TS Nguyn Th Kim Anh Phn bin 2: PGS TS Phỳc Phn bin 3: PGS TS Qun Thnh Th NGI HNG DN KHOA HC PGS TS Dng Tun Anh LI CAM OAN Tỏc gi xin cam oan õy l cụng trỡnh nghiờn cu ca bn thõn tỏc gi Cỏc kt qu nghiờn cu v cỏc kt lun lun ỏn ny l trung thc, v khụng chộp t bt k mt ngun no v di bt k hỡnh thc no Vic tham kho cỏc ngun ti liu (nu cú) ó c thc hin trớch dn v ghi ngun ti liu tham kho ỳng theo yờu cu Tỏc gi lun ỏn Nguyn Thnh Sn i TểM TT khc phc c im lng ln ca d liu chui thi gian, nhiu phng phỏp thu gim s chiu da vo rỳt trớch c trng ó c xut v s dng Tuy nhiờn cú khụng ớt phng phỏp thu gim s chiu mc phi hai nhc im quan trng: mt s phng phỏp thu gim s chiu khụng chng minh c bng toỏn hc tha iu kin chn di v mt s phng phỏp khỏc khụng xut c cu trỳc ch mc thớch hp i kốm h tr vic tỡm kim tng t hu hiu úng gúp th nht ca lun ỏn ny l xut mt phng phỏp thu gim s chiu mi da vo im gia v k thut xộn, cú tờn l MP_C (Middle points and Clipping), v kt hp phng phỏp ny vi ch mc ng chõn tri h tr vic tỡm kim tng t mt cỏch hu hiu Qua lý thuyt v thc nghim, chỳng tụi chng minh c phng phỏp MP_C tha iu kin chn di, l iu kin nhm m bo khụng xy li tỡm sút tỡm kim tng t Thc nghim cũn cho thy phng phỏp MP_C hiu qu hn mt phng phỏp c a chung, phng phỏp xp x gp tng on (PAA- Piecewise Aggregate Approximation), v phng phỏp xộn d liu (Clipping) v c ba tiờu chớ: cht chn di, t l thu gim truy xut v thi gian thc thi Lun ỏn cũn cho thy phng phỏp MP_C cú th s dng hiu qu cho bi toỏn tỡm kim tng t trờn d liu chui thi gian dng lung, mt bi toỏn rt thi s, ó v ang c quan tõm nghiờn cu thi gian gn õy, da vo cỏch tớnh toỏn gia tng phng phỏp MP_C v chớnh sỏch cp nht ch mc trỡ hoón (deferred update policy) úng gúp th hai ca lun ỏn ny l vic ng dng thnh cụng phng phỏp thu gim s chiu MP_C v cu trỳc ch mc ng chõn tri vo ba bi toỏn quan trng khai phỏ d liu chui thi gian: gom cm, phỏt hin motif v d bỏo trờn d liu chui thi gian Vi bi toỏn gom cm, chỳng tụi dng tớnh cht a mc phõn gii ca phng phỏp MP_C cú th s dng gii thut I-k-Means gom cm d liu chui thi gian v xut thờm cỏch s dng kd-tree xỏc nh cỏc trung tõm cm ban u cho gii thut I-k-Means nhm khc phc nhc im ca gii thut ny chn cỏc trung tõm cm mc ng mt cỏch ngu nhiờn Vi bi toỏn phỏt hin motif, chỳng tụi xut hai gii thut phỏt hin motif xp x trờn d liu chui thi gian: (1) gii thut s dng R*-tree kt hp vi ý tng t b sm tớnh toỏn ii khong cỏch Euclid v (2) gii thut dng phng phỏp thu gim s chiu MP_C kt hp vi cu trỳc ch mc ng chõn tri Trong hai gii thut ny, gii thut th hai t cú hiu qu cao hn Vi bi toỏn d bỏo d liu chui thi gian, chỳng tụi dng phng phỏp thu gim s chiu MP_C kt hp vi cu trỳc ch mc ng chõn tri vo phng phỏp d bỏo tỡm kim k lõn cn gn nht (k-NN) v thc nghim cho thy phng phỏp ny cho kt qu d bỏo chớnh xỏc cao hn v thi gian d bỏo nhanh hn so vi mụ hỡnh mng n ron nhõn to (ANN) d bỏo vi d liu cú tớnh hay xu hng iii ABSTRACT To overcome high dimensionality of time series data, several dimensionality reduction methods, which is based on feature extraction, have been proposed and used However, a number of these methods did not provide any formal proof that they satisfy the lower bounding condition while many of them did not go with any multidimensional index structure which helps in fast retrieval The first contribution of this thesis is a new dimensionality reduction method based on Middle points and Clipping, called MP_C, which performs effectively with the support of Skyline index Through formal proof and experiments on benchmark datasets, we show that MP_C satisfies the lower bounding condition which guarantees no false dismissals Experimental results also reveal that MP_C is more effective than the popular dimensionality reduction method, Piecewise Aggregate Approximation (PAA) and the Clipping method in terms of tightness of lower bound, pruning ratio and running time We also proposed the extension of MP_C in Kontaki framework which can be applied effectively for similarity search in streaming time series The second contribution of this thesis is the application of MP_C method to the three important time series data mining tasks: clustering, motif detection and time series prediction As for clustering, we exploit the multi-resolution property of MP_C in using I-k-Means algorithm for time series clustering and propose the use of kd-tree in choosing initial centroids for I-k-Means algorithm in order to overcome the drawback of randomly determining the initial centroids in the first level of I-k-Means As for motif discovery, we propose two algorithms for finding approximate motif in time series data: (1) the algorithm that uses R*-tree combined with the idea of early abandoning in Euclidean distance computation and (2) the algorithm using MP_C associated with Skyline index; and between the two algorithms, the latter is more effective than the former As for time series prediction, we propose the use of MP_C with Skyline index in a prediction approach based on a k-nearest-neighbors algorithm and experiments show that the proposed method performs better than artificial neural network model in terms of prediction accuracy and computation time, especially for seasonal and trend time series iv LI CM N Xin by t lũng bit n sõu sc n Thy PGS TS Dng Tun Anh ó tn tỡnh hng dn, ng viờn, ch bo v úng gúp ý kin cho vic nghiờn cu v hon thnh Lun ỏn Tin s ny Tụi xin gi li cm n n cỏc Thy, Cụ khoa Khoa hc v K thut Mỏy tớnh trng i hc Bỏch khoa Tp H Chớ Minh, cỏc bn nhúm nghiờn cu v khai phỏ d liu chui thi gian ó úng gúp nhiu ý kin quớ bỏu cho vic nghiờn cu lun ỏn Tụi cng xin cm n cỏc ng nghip v bn bố khoa Cụng ngh Thụng tin trng i hc S phm K thut Tp H Chớ Minh ó luụn ng viờn, khớch l v to iu kin thun li giỳp tụi hon thnh lun ỏn ỳng hn Cm n ụng Nguyn Quang Chõu, Vit kiu M, ó h tr mt phn kinh phớ tụi cú th cụng b v thuyt trỡnh cụng trỡnh ca mỡnh ti hi ngh ACIIDS 2012 Cm n Giỏo s Tin s H Tỳ Bo (Vin Nghiờn cu Cao Cp Khoa hc v Cụng ngh Nht Bn) ó h tr kinh phớ tụi cú th d hi ngh ComManTel 2013 Tp H Chớ Minh, thỏng nm 2013 Tỏc gi Nguyn Thnh Sn v MC LC DANH MC CC HèNH NH ix DANH MC BNG BIU xiv DANH MC CC T VIT TT xvi CHNG GII THIU 1.1 D liu chui thi gian v cỏc bi toỏn khai phỏ d liu liờn quan 1.2 Mc tiờu, i tng v phm vi nghiờn cu 1.3 Nhim v v hng tip cn ca lun ỏn 1.4 Túm tt kt qu t c .7 1.5 Cu trỳc ca lun ỏn CHNG C S Lí THUYT V CC CễNG TRèNH LIấN QUAN 10 2.1 Cỏc o tng t 10 2.1.1 o Euclid 10 2.1.2 o xon thi gian ng 11 2.2 Thu gim s chiu chui thi gian 12 2.2.1 iu kin chn di 12 2.2.2 Cỏc phng phỏp thu gim s chiu da vo rỳt trớch c trng 13 2.2.3 V tớnh ỳng n v tớnh kh ch mc ca cỏc phng phỏp thu gim s chiu 21 2.3 Ri rc húa chui thi gian 22 2.4 Cu trỳc ch mc 23 2.4.1 R-tree .23 2.4.2 Ch mc ng chõn tri 25 2.5 Tỡm kim tng t trờn d liu chui thi gian 27 2.5.1 í tng tng quỏt 27 2.5.2 So trựng ton chui v so trựng chui 27 2.5.3 o khong cỏch nhúm v iu kin chn di nhúm 28 2.5.4 Cỏc phng phỏp tỡm kim tng t liờn quan 28 2.6 Tỡm kim tng t trờn chui thi gian dng lung 29 2.7 Phỏt hin motif trờn chui thi gian 32 2.7.1 Cỏc khỏi nim c bn v motif .32 2.7.2 Tng quan v mt s phng phỏp phỏt hin motif tiờu biu 36 2.8 Gom cm d liu chui thi gian 41 2.8.1 Gii thiu 41 2.8.2 Gii thut K-Means 42 vi 2.8.3 Gom cm bng thut toỏn I-k-Means 43 CHNG THU GIM S CHIU CHUI THI GIAN BNG PHNG PHP MP_C 46 3.1 Phng phỏp thu gim s chiu MP_C (Middle Points_Clipping) 46 3.2 o tng t khụng gian c trng MP_C 49 3.3 phc ca gii thut thu gim s chiu theo phng phỏp MP_C 52 3.4 Cu trỳc ch mc ng chõn tri cho cỏc chui thi gian c biu din bng MP_C 53 3.4.1 Vựng bao MP_C (MP_C_BR) 53 3.4.2 Hm tớnh khong cỏch gia chui truy Q v MP_C_BR 54 3.4.3 Ch mc ng chõn tri cho phng phỏp biu din MP_C 56 3.4.4 X lý cỏc cõu truy cú chiu di khỏc .58 3.5 Tỡm kim tng t trờn d liu chui thi gian dng lung da vo phng phỏp MP_C v ch mc ng chõn tri 60 3.6 Kt qu thc nghim 61 3.6.1 Thc nghim v bi toỏn tỡm kim tng t trờn d liu chui thi gian 62 3.6.2 Thc nghim v tỡm kim tng t trờn d liu chui thi gian dng lung 74 CHNG PHT HIN MOTIF DA VO CU TRC CH MC A CHIU HOC CH MC NG CHN TRI 78 4.1 Phng phỏp phỏt hin motif da vo cu trỳc ch mc a chiu v k thut t b sm 78 4.2 Phỏt hin motif xp x da trờn phng phỏp MP_C vi s h tr ca ch mc ng chõn tri 84 4.3 Thc nghim v bi toỏn phỏt hin motif 87 4.3.1 Thc nghim 1: So sỏnh ba gii thut dựng R*-tree, RP v R*-tree kt hp vi t b sm 88 4.3.2 Thc nghim 2: So sỏnh ba gii thut dựng R*-tree, RP v MP_C kt hp vi ch mc ng chõn tri 91 CHNG GOM CM CHUI THI GIAN C THU GIM THEO PHNG PHP MP_C BNG GII THUT I-K-MEANS 97 5.1 Túm tt mt s k thut chn trung tõm cm ng thut toỏn k-Means 97 5.2 Biu din chui thi gian nhiu mc xp x theo phng phỏp MP_C 99 5.3 Kd-tree 99 5.4 Dựng kd-tree to cỏc trung tõm cm ng cho thut toỏn I-k-Means 100 5.5 Dựng CF-tree to cỏc trung tõm cm ng cho thut toỏn I-k-Means 103 vii 5.5.1 c trng cm v CF-tree (Cluster Feature tree) 103 5.5.2 Dựng CF-tree to cỏc trung tõm cm cho thut toỏn I-k-Means 105 5.6 Thc nghim v bi toỏn gom cm 106 5.6.1 Cỏc tiờu chun ỏnh giỏ cht lng ca gii thut gom cm .106 5.6.2 D liu dựng thc nghim 108 5.6.3 Kt qu thc nghim v bi toỏn gom cm 109 CHNG D BO D LIU CHUI THI GIAN Cể TNH XU HNG HOC MA BNG PHNG PHP SO TRNG MU 115 6.1 Cỏc cụng trỡnh liờn quan 115 6.2 Xu hng v tớnh d liu chui thi gian 117 6.3 Hai phng phỏp d bỏo d liu chui thi gian 118 6.3.1 D bỏo chui thi gian bng mng n ron nhõn to .118 6.3.2 Phng phỏp xut: k-lõn cn gn nht .121 6.4 ỏnh giỏ bng thc nghim .123 CHNG KT LUN V HNG 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chui Q, C, S khụng gian c trng MP_C tng ng vi cỏc chui thi gian gc Q, C v S - u tiờn, chỳng tụi chng minh: D2(Q, C) D2(Q, S) + D2(S, C) N l Ta cú D2 (Q' , S ' ) D2 ( S ' , C ' ) (d j (q ji , b sji ) (d j ( s ji , b cji )) vi j i q' d j (q ji , b sji ) ji nu (qji > bsji = 0) (qji bsji = 1) s ' d j ( s ji , b cji ) ji nu (sji > bcji = 0) (sji bcji = 1) cỏc trng hp khỏc cỏc trng hp khỏc qji = qji - àqj , ú qji l giỏ tr c chn th i on th j ca chui thi gian Q sji = sji - àsj , ú sji l giỏ tr c chn th i on th j ca chui thi gian S àqj v àsj l giỏ tr trung bỡnh ca on j tng ng chui Q v S bcj v bsj l biu din nh phõn cỏc im c chn on j tng ng hai chui C v S Nh vy q'2ji s'2ji d j (q' ji , b sji ) d j ( s' ji , b cji ) nu (qji > bsji = 0) (qji bsji = 1) (sji > bcji = 0) (sji bcji = 1) cỏc trng hp khỏc p dng tớnh cht phõn phi ca hai phộp toỏn: , Ngoi ra, nu bsji = thỡ sji = sji - àsj Ngc li, nu bsji = thỡ sji > 0, ta c 148 q'2ji s'2ji s c d j (q ji , b ji ) d j ( s ji , b ji ) nu [(qji > bcji = 0) (bsji = bcji = ) (qji > sji > 0)] [(qji bcji = 1) (bsji = bcji = ) (qji sji 0)] cỏc trng hp khỏc (do sji2 > v tớnh cht ca hai phộp toỏn v ) nu [(qji > bcji = 0) [(qji bcji = 1) q '2ji cỏc trng hp khỏc = dj(qji ,bcji) Kt lun D2(Q, C) D2(Q, S) + D2(S, C) - Chng minh DMP_C(Q, C) DMP_C(Q, S) + DMP_C(S, C) N N i i ( w ( qi ci ) ) D2 (Q' , C ' ) ( w ( qi si ) ) D2 (Q' , S ' ) N ( w ( si ci ) ) D2 ( S ' , C ' ) i t Ai = àqi - àsi v Bi = àsi - àci Bt ng thc trờn tng ng vi: N N N i i i w ( qi ci ) D2 (Q' , C ' ) w Ai2 D2 (Q' , S ' ) w Bi2 D2 ( S ' , C ' ) (1) N N i i w Ai2 D2 (Q' , S ' ) w Bi2 D2 ( S ' , C ' ) Ta cú, N N w ( qi ci ) D2 (Q' , C ' ) w ( qi si si ci ) D2 (Q' , C ' ) i i N N w ( Ai Bi ) D2 (Q' , C ' ) w ( Ai2 Bi2 Ai Bi ) D2 (Q' , C ' ) i N i N N i i N w Ai2 w Bi2 2w Ai Bi D2 (Q' , C ' ) i N N w Ai2 D2 (Q' , S ' ) w Bi2 D2 ( S ' , C ' ) 2w Ai Bi i i i (do D2(Q,C) D2(Q,S)+ D2(S,C)) Mt khỏc, N N i i w Ai2 D2 (Q' , S ' ) w Bi2 D2 ( S ' , C ' ) 149 (2) N N i i ( w Ai2 D2 (Q' , S ' )).(w Bi2 D2 ( S ' , C ' )) N N N N i i i i w2 Ai2 Bi2 D2 (Q' , S ' ).w Bi2 D2 ( S ' , C ' ).w Ai2 D2 (Q' , S ' ).D2 ( S ' , C ' ) 2w N N A B i i i i N N i i (do w 0, Bi2 0, Ai2 0, D2 (Q' , S ' ) 0, D2 (S ' , C ' ) 0) N 2w ( Ai Bi ) i (p dng bt ng thc Bunhiacopski-Cauchy-Schwarts) N 2w Ai Bi (3) T (1), (2) v (3) suy DMP_C(Q, C) DMP_C(Q, S) + DMP_C(S, C) i 150 [...]... trong khai phá dữ liệu chuỗi thời gian là thực hiện chúng trong không gian đặc trưng (feature space) của dữ liệu Nhƣ vậy điều đầu tiên và cơ bản nhất trƣớc khi thực hiện các bài toán trong khai phá dữ liệu chuỗi thời gian là các chuỗi thời gian cần đƣợc biểu diễn trong không gian đặc trƣng bằng một kỹ thuật thu giảm số chiều nào đó Sau đó thực hiện các bài toán khai phá dữ liệu trong không gian đặc. .. khai phá dữ liệu chuỗi thời gian đƣợc xếp thứ 3 trong 10 hƣớng nghiên cứu sẽ là quan trọng và thách thức nhất [21] Khi nghiên cứu các bài toán khai phá dữ liệu chuỗi thời gian, ngƣời ta thƣờng vận dụng những kỹ thuật trong các lĩnh vực nhƣ khai phá dữ liệu, học máy, cơ sở dữ liệu, nhận dạng, xử lý tín hiệu, sinh tin học, v.v… Tuy nhiên, vì dữ liệu chuỗi thời gian thƣờng rất lớn, những giải thuật khai. .. Trong chƣơng này, chúng tôi sẽ trình bày tổng quan về chuỗi thời gian và các bài toán quan trọng trong khai phá dữ liệu chuỗi thời gian Tiếp theo là mục tiêu, đối tƣợng, phạm vi nghiên cứu của luận án và tóm tắt kết quả nghiên cứu đạt đƣợc Cuối cùng là cấu trúc của luận án này 1.1 Dữ liệu chuỗi thời gian và các bài toán khai phá dữ liệu liên quan Một chuỗi thời gian (time series) là một chuỗi các điểm. .. thời gian dạng luồng dựa vào ý tƣởng tính toán thu giảm số chiều gia tăng và cập nhật chỉ mục trì hoãn 1.4 Tóm tắt kết quả đạt đƣợc Với nhiệm vụ đầu tiên của luận án, chúng tôi đã đề xuất đƣợc một kỹ thuật thu giảm số chiều dữ liệu chuỗi thời gian dựa trên phƣơng pháp điểm giữa kết hợp với kỹ thuật xén, gọi là MP_C (Middle Points and Clipping) Kỹ thuật này đƣợc thực hiện bằng cách chia chuỗi thời gian. .. nhƣ các điểm cực trị toàn cục Hình 2.8 là ví dụ minh họa phƣơng pháp này (a) (b) (c) Hình 2.8 (a) Tập dữ liệu ban đầu, (b) tập dữ liệu được biểu diễn bằng các điểm mốc và (c) Biểu diễn tập dữ liệu bằng các điểm mốc sau giai đoạn làm trơn [22] - Phương pháp điểm cực trị Năm 2003, Fink and Pratt đã đề xuất một kỹ thuật thu giảm số chiều dựa trên việc trích các điểm quan trọng trong chuỗi thời gian [25]... nền tảng của nhiều bài toán khác trong khai phá dữ liệu chuỗi thời gian Đây là bài toán khó vì kích thƣớc dữ liệu chuỗi thời gian thƣờng lớn và vì chúng ta không thể lập chỉ mục dữ liệu chuỗi thời gian một cách dễ dàng nhƣ trong hệ thống cơ sở dữ liệu truyền thống Một vài thí dụ về ứng dụng của tìm kiếm tƣơng tự trên chuỗi thời gian có thể nêu ra nhƣ sau: - Tìm trong quá khứ, những giai đoạn mà số lƣợng... không thể làm việc một cách hữu hiệu với dữ liệu chuỗi thời gian Motif trong chuỗi thời gian là mẫu xuất hiện với tần suất cao nhất Hình 1.2 minh họa ví dụ về motif là chuỗi con xuất hiện ba lần trong chuỗi thời gian dài hơn Từ khi đƣợc hình thức hóa vào năm 2002, phát hiện motif trong dữ liệu chuỗi thời gian đã và đang đƣợc dùng để giải quyết các bài toán trong nhiều lĩnh vực ứng dụng khác nhau ví... theo số chuỗi trong cơ sở dữ liệu chuỗi thời gian hay chiều dài 3 của chuỗi thời gian mà từ đó các chuỗi con đƣợc trích ra Vì lý do đó, có nhiều thuật toán phát hiện motif xấp xỉ đã đƣợc giới thiệu ( [13], [14], [12], [15], [16], [17]) Các cách tiếp cận này thƣờng có độ phức tạp tính toán là O(n) hay O(nlogn), với n là số chuỗi trong cơ sở dữ liệu chuỗi thời gian hay chiều dài của chuỗi thời gian mà... cách liên tục và đƣợc nối vào cuối chuỗi C theo thứ tự thời gian Vì một chuỗi thời gian dạng luồng bao gồm một số lớn các giá trị, sự tƣơng tự giữa hai chuỗi thƣờng đƣợc tính dựa trên W giá trị cuối cùng (W là chiều dài cửa sổ trƣợt) Cho nên, nếu W = 1024 thì mỗi chuỗi đƣợc coi nhƣ một điểm trong không gian 1024 chiều Các bài toán thƣờng đƣợc nghiên cứu trong khai phá dữ liệu chuỗi thời gian gồm tìm... trọng trong khai phá dữ liệu chuỗi thời gian có chiều dài bằng nhau, đó là: tìm kiếm tƣơng tự, gom cụm, phát hiện motif và dự báo trên dữ liệu chuỗi thời gian, trong đó tìm kiếm tƣơng tự là bài toán nền tảng Do sự thông dụng và dễ hiện thực của độ đo Euclid, trong luận án này, chúng tôi sẽ chỉ nghiên cứu các bài toán khai phá dữ liệu chuỗi thời gian nêu trên với độ đo Euclid 5 1.3 Nhiệm vụ và hƣớng ... SƠN KHAI PHÁ DỮ LIỆU CHUỖI THỜI GIAN DỰA VÀO RÚT TRÍCH ĐẶC TRƢNG BẰNG PHƢƠNG PHÁP ĐIỂM GIỮA VÀ KỸ THUẬT XÉN (TIME SERIES DATA MINING BASED ON FEATURE EXTRACTION WITH MIDDLE POINTS AND CLIPPING METHOD) ... diễn chuỗi thời gian ( [1]) Một chuỗi thời gian dạng luồng (streaming time series) C chuỗi thời gian giá trị tới cách liên tục đƣợc nối vào cuối chuỗi C theo thứ tự thời gian Vì chuỗi thời gian. .. thời gian toán khai phá liệu liên quan Một chuỗi thời gian (time series) chuỗi điểm liệu đƣợc đo theo khoảng thời gian liền theo tần suất thời gian thống Hình 1.1 minh họa ví dụ chuỗi thời gian