2002 Journal of Software

Transcription

1 1-9825/22/13(3) Journal of Software Vol13, No3,,,, (, 2326) http//wwwustceducn,,,,, Agrawal,,, ; ; ; TP18 A,,,,, ( ),,, ; Agrawal [1], [2],, 1 Agrawal [1], [1],Agrawal,, Heikki Mannila Agrawal, ; (G ); ( ) (197 ),,,,, ; (197 ),,,, ; (197 ),,,, ; (1968 ),,,, ; (1938 ),,,,,

2 411 [3], Tim Oates (MSDD) [4],, Oates, Oates,, 2,,,,,,, [5] ( 1 ), ;,,, ( ), ( 2, 3 ),,,, a c c d e f e c g d d a c f a c c d e f e c g d d a c f Fig1 Transform time series into discrete symol sequenc Fig2 Linear segment representation of multiple time series 1 2, [4],,, 1,,,,,

3 412 Journal of Software 22,13(3) DJI3 Nikkei225 Fig3 Time series of two stock indexes (left) and their linear segment representations (right) 3 ( ) 3 1 S={S 1,S 2,,S m } C={C 1,C 2,,C n } PM=(S i,c j,t s,t e ), S i S,C j C,T s T e 2 P=(V,,T s,t e V PM V,, x, y V,x y, x y, P ;, x, y V, x y y x, P Ts,T e P V V, P 3 P s (V,,T s,t e ) P (V,,T s,t e ), P s P, V V, ( = ),T s =<T s,t e =<T e 4 P (V,,T s,t e ) [t,t ], [t,t ] V =V,, t=<t s,t >=T e 5 P [t,t ], [u,u ] [t,t ], P Si(P) P Si(P)={[t,t ] [t,t ] P } P S, Si(P) Si(P), f min (t t) T 4 C k k,l k k, 1 Find_Freq_Pattern(S,T, f min ) S, T, f min T L k {Si(P) P L k } (1) C 1 = 1 = ; //,C (2) For all P C 1, Si(P); //,Si(P) (3) L 1 ={P C 1 length(si(p))>= f min }; (4) k =1; (5) while L k >=2 (a) k =k +1;

4 413 () C k =C_generator(L k 1 ); // L k 1 k C k, L k 1 (c) For all P C k do // Si(P), 2 ; (d) P 1 P 2, Si(P 1 ) Si(P 2 ) Si(P); (e) L k ={P C k length(si(p))>= f min }; (6) L k (k=1,2,) Si(P) C k ( C_generator ) [1], ( ),, (k 2), Agrawal, k (k 2) (k 1),, k 1 Si(P), k c k, Si(p k 1 ) 2 join(l k 1,Si,C k ) k 1 L k 1 {Si(P) P L k 1 }, C k {Si(P) P C k } (1) for all P C k do (a) find P 1 L k 1,where P 1 (1)=P(1), P 1 (2)=P(2),,and P 1 (k 1)=P(k 1); //P(i) P i () find P 2 L k 1,where P 2 (1)=P(2),P 2 (2)=P(3),,and P 2 (k 1)=P(k); (c) Si(P)={[t,t ] [t,t1] Si(P 1 ) [t2,t ] Si(P 2 ), t<t2,t1<t,t t=<t, [t,t ] }; (2) end, P 1 L k 1 P 2 L k 1, P C k, Si(P) }; Si(P)={[t,t ] 1 1 ] Si(P 1 ) [t 2,t 2 ] Si(P 2 ), t=min{t 1,t 2 },t =max{t 1,t 2 },t t=<t, Si(P 1 ) + Si(P 2 ) Si(P 1 ) + Si(P 2 ), Si(P 1 ) + Si(P 2 ), Si(P 1 ) + Si(P 2 ) P 1 P 2 P C k [t,t ], P 1, P 1 [t 1,t 1 ](t 1 >=t t 1 =<t ), [t 1,t 1 ] Si(P 1 ), [t 11,t 11 ] Si(P 1 ), t 11 >=t 1 t 11 =<t 1, P 2 [t 2,t 2 ] Si(P 2 )(t 2 >=t t 2 =<t ), Si(P 1 ) + Si(P 2 ), 1 f min T L k ( f min,t),k=1,2,,m, Si(P),P L k 1 f min =f min 1 T=T 1 F 1, f min 2 =<f min 1 T 2 >=T 1 F 2, T 2 =T 1, ; T 2 >=T 1,, F A (f min A,T A ) F B (f min B,T B ), f min A <f min B T A <T B F A F B =L A B (f min B, T A )={P P F A &P F B }, P L A B (f min B,T A ),Si(P)=Si A (P),,Si A (P) F A P

5 414 Journal of Software 22,13(3),,, 5 DJI3 Nikkei ~ ( ) ( ),, f min T, 1 f min =3 T 2 T=4 f min,,, Tale 1 Numer of candidate patterns and frequent patterns of different lengths (K) discovered when different spans of time (T ) are adopted 1 (T ) (K) f min =3 K=1 K=2 K=3 K=4 K=5 K=6 T=1 Candidate pattern set Frequent pattern set T=2 Candidate pattern set Frequent pattern set T=3 Candidate pattern set Frequent pattern set T=4 Candidate pattern set Frequent pattern set , Tale 2 Numer of candidate patterns and frequent patterns of different lengths (K) discovered when different frequency thresholds (f min ) are adopted 2 ( f min ) (K) T=4 K=1 K=2 K=3 K=4 K=5 K=6 f min =3 Candidate pattern set Frequent pattern set f min =5 Candidate pattern set Frequent pattern set f min =7 Candidate pattern set Frequent pattern set f min =9 Candidate pattern set Frequent pattern set , 4 f min T, T, f min ns Num er of patter Candidat set Frequent set Numer of patterns Candidate set Frequent set Span of time Frequency threshold,,,, Fig4 Relationship of the numer of patterns with the span of time (left) and frequency threshold (right) 4 T( ) f min ( )

6 415 5 ( ) DJI3 1 5 Nikkei DJI3 Nikkei Fig5 Some discovered frequent patterns of different lengths represented in linear segments 5, (1),,, (2),, References [1] Agrawal, R, Imielinski, T, Swami, A Mining association rules etween sets of items in large dataases In Buneman, P, Jajodia, S, eds Proceedings of the ACM SIGMOD Conference on Management of Data (SIGMOD 93) Washington, DC ACM, ~216 [2] Mannila, H, Toivonen, H Discovering generalized episodes using minimal occurrences In Proceedings of the 2nd International Conference on Knowledge Discovery and Data Mining (KDD 96) Portland, Oregon AAAI Press, ~151 http//wwwcs helsinkifi/~mannila/postscripts/genepisodesps [3] Mannila, H, Toivonen, H, Verkamo, AI Discovery of frequent episodes in event sequences Data Mining and Knowledge Discovery, 1997,1(3)259~289 [4] Oates, T, Cohen, PR Searching for structure in multiple streams of data In Proceedings of the 13th International Conference on Machine Learning Morgan Kaufmann Pulishers, Inc, ~354 http//www-ekslcsumassedu/papers/oates96cps [5] Li, Bin, Tan, Li-xiang, Zhang, Jin-song, et al The study of the data mining oriented method for the symolization of time series Journal of Circuits and Systems, 2,5(2)9~14 (in Chinese)

7 416 Journal of Software 22,13(3) [5],,,,,2,5(2)9~14 An Algorithm for Discovering Frequent Patterns in Non-Synchronous Multiple Time Series LI Bin, TAN Li-xiang, XIE Guang-jun, LI Hai-ying, ZHUANG Zhen-quan (Department of Electronic Science and Technology, University of Science and Technology of China, Hefei 2326, China) http//wwwustceducn Astract Discovering frequent patterns in multiple time series is important in practices Methods appeared in literatures assume that the multiple time series are synchronous, ut in the real world, that is not always satisfied, in most cases they are non-synchronous In this paper, an algorithm for discovering frequent patterns in nonsynchronous multiple time series is proposed In this algorithm, first, the time series is segmented and symolized with the linear segment representation and the vector shape clustering method, so that each symol can represent a primitive and independent pattern Then, the minimal occurrence representation of time series and the association rule discovery algorithm proposed y Agrawal is comined to extract frequent patterns of various structures from non-synchronous multiple time series Compared with the previous methods, the algorithm is more simple and flexile, and does not require time series to e synchronous Experimental results show the efficiency of the algorithm Key words data mining; time series; frequent pattern; minimal occurrence; symolization Received June 15, 2; accepted Septemer 26, 2 Supported y the National Grand Fundamental Research 973 Program of China under Grant NoG ; the National Research Foundation for the Doctoral Program of Higher Education of China under Grant No