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Mining Serial Episode Rules with Time Lags over Multiple Data Streams

This research discusses the extraction of serial episode rules with time lags (SER) from continuous data streams. It introduces a centralized system for synchronized data collection and describes the structure of n-tuple events and itemsets. The approach emphasizes identifying minimal occurrences of serial episodes while considering user-defined time bounds. The method leverages a prefix tree for efficient rule generation, utilizing Lossy Counting to manage minimal occurrences effectively. Experiments demonstrate the effectiveness and efficiency of the proposed methods in mining SERs while handling time lags.

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Mining Serial Episode Rules with Time Lags over Multiple Data Streams

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  1. Mining Serial Episode Rules with Time Lags over Multiple Data Streams Tung-Ying Lee, En Tzu Wang Dept. of CS, National TsingHua Univ. (Taiwan) Arbee L.P. Chen Dept. of CS, National Chengchi Univ. (Taiwan) DaWaK’08

  2. Outline • Introduction • Related work • Preliminaries • Method • Experiments • Conclusions

  3. Introduction • In many applications, data are generated as a form of continuous data streams. • Continuously detecting flow and occupancy of a road to qualify the congestion condition of a road forms data streams • When roads A and B have heavy traffic, 5 mins later, road C will most likely be congested • Serial episode rules with time lags (SER) : XlagY

  4. Related Work • Finding episodes/episode rules from static time series data has been studied for decades • Episodes Precursor Successor B D A D B A E L C Serial episode rule Episode D B A Serial episode

  5. Preliminaries • Environment: a centralized system collecting n synchronized data streams DS1, DS2, …, DSn • n-tuple event: a set of items coming from all streams at the same time • itemset: a subset of an n-tuple event • serial episode: described as an ordered list of itemsets e.g. serial episode (aA)(bB) Itemset {gA} time: 1, 2, 3, 4, 5, 6, 7, 8 DS1: a, b, b, c, g, a, b, f DS2: A, B, S, G, A, B, A, F DSn: , , , , , , ,  … n-tuple event

  6. Preliminaries (cont.) • Minimal occurrence: given a serial episode S, a time interval [a, b] is a minimal occurrence of S, if • S occurs in [a, b] • S does not occur in any proper subintervals of [a, b] • If (b-a+1)  T, a time bound given by users, [a, b] is valid • MO(S): the set of all minimal occurrences of S • Supp(S): the number of valid minimal occurrences of S Time bound T: 3 DS1 DS2

  7. Preliminaries (cont.) • A SER is R: S1Lag = LS2 • Supp(R): |{[a, b]|[a, b]MO(S1)[a, b]: valid  [c, d] MO(S2)[c, d]: valid s.t. (c-a) = L} • Conf(R) = Supp(R)/Supp(S1) 4 Time bound T: 3 DS1 DS2

  8. Preliminaries (cont.) • Problem Formulation: given 4 parameters • the maximum time lag (Lmax) • the minimum support (minsup) • the minimum confidence (minconf) • the time bound (T) • Find all SERs e.g. R: S1Lag = LS2 satisfying • L  Lmax • Supp(R)  N  minsup, (N: the number of received n-tuple events) • Conf(R)  minconf • Calculating supports for serial episodes and SERs must take T into account Time bound T: 3 DS1 DS2

  9. Preliminaries (cont.) • Using the prefix tree for keeping serial episodes • S: a serial episode, X: an item • S+X: X follows S • S+_X: X and the last itemset in S appear at the same time  Level 0 Root A B Level 1 _B B Serial episode (AB) Level 2 Serial episode (A)(B)

  10. B B [2, 3] [1, 3] LossyDL • The concept of LossyDL: keeping the valid minimal occurrences of a serial episode for generating rules  Processing C can generate (B)(C): [2, 3] and (BC): [3, 3] At time point = 3, a 2-tupe event (BC) arrives, T = 3 Each item in the current 2-tuple event needs to be processed (traversing in a bottom-up order) B A [2, 2] [3, 3] [1, 1] The last two minimal occurrences needs to be checked B [1, 2] [1, 3]: not minimal Using Lossy Counting [VLDB02], whenever N  0 mod 1/, the oldest minimal occurrence is removed

  11. LossyDL (Rule Generation) • Mining SERs • For any two serial episode with supports  (minsup  )  N are checked to see if any minimal occurrences of them can be combined. Then, Supp(R) can be computed • For each R: S1Lag = LS2, it will be returned if • Supp(R)  (minsup  )  N, and • (Supp(R) + N)/Supp(S1) minconf

  12. TLT • A lot of minimal occurrences are kept in LossyDL, but only the last two are used while updating • Observations • XL(AB) and XLA, obviously Supp(XLA)  Supp(XL(AB)): XL(AB) is not significant if XLA does not satisfy one of minsup and minconf • (AB)L(CD) and ALC, obviously Supp(ALC)  Supp((AB)L(CD)): (AB)L(CD) is not significant if Supp(ALC) < Supp(AB)  minconf

  13. TLT (cont.) • Observations (cont.): • Given a SER: (A)(B)5(CD), and T = 3 • A1B or A2B, that is ApB, 0<p< T (T1 types) • A1B4(CD), A2B3(CD), that is ApBLp(CD) • Supp(ApBLp(CD))  min(Supp(ApB), Supp(BLpC)) • (A)(B)5(CD) is not significant, if • pmin(Supp(ApB), Supp(BLpC)) < Supp(A)(B)  minconf • Using the observations to prune insignificant rules • Time lag table (TLT) • ALB is a reduced SER, if A and B are single items • For finding S1LmaxS2, the reduced SERs having a time lag at most Lmax+T1 (from the first itemset of precursor to the last itemset of successor) • Using Lmax+T1 Time Lag Tables to keep the supports of reduced SER

  14. TLT (cont.) • The support and the last two minimal occurrences of an serial episode are kept in the prefix tree • Keeping supports instead of keeping minimal occurrence lists • Keeping the last two minimal occurrences for updating the supports • WheneverN  0 mod 1/, all supports are decreased by 1 • In addition, the last Lmax+T1 n-tuple events are kept for updating the Time Lag Tables

  15. TLT (Rule Generation) • Mining SERs • Any two serial episode with supports  (minsup  )  N form the candidate SERs • A candidate SER will be returned if it can pass the pruning rules from the above observations

  16. Experiments • real dataset • PDOMEI: the dataset contains the dryness and climate indices derived by experts, usually used to predict droughts • Parameter setting •  = 0.1minsup • Lmax = 10

  17. Conclusions • We address the problem of finding significant serial episode rules with time lags over multiple data streams and propose two methods to solve it. TLT is more space-efficient, but LossyDL has high precision

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