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

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mining serial episode rules with time lags over multiple data streams

Mining Serial Episode Rules with Time Lags over Multiple Data Streams

Tung-Ying Lee, En Tzu Wang

Dept. of CS, National Tsing Hua Univ. (Taiwan)

Arbee L.P. Chen

Dept. of CS, National Chengchi Univ. (Taiwan)


  • Introduction
  • Related work
  • Preliminaries
    • Support of a serial episode
    • Support/ confidence of a serial episode rule
    • Data structure used in the algorithms
  • Algorithms
    • LossyDL
    • TLT
  • Experiments
  • Conclusions
  • 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
    • Regarding the values of flows and occupancies coming from roads as an environment of multi-streams and finding serial episode rules from it
    • Serial episode rules with time lags (SER) : XlagY
related work
Related Work
  • Finding episodes/episode rules from static time series data has been studied for decades
  • Finding episodes over data streams
    • Serial episodes [SSDBM04]
    • Episodes [KDD07]












Serial episode rule





Serial episode

  • 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

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



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)


Time bound T: 3



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
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




Level 1



Serial episode (AB)

Level 2

Serial episode (A)(B)



[2, 3]

[1, 3]


  • 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)



[2, 2]

[3, 3]

[1, 1]

The last two minimal occurrences needs to be checked


[1, 2]

[1, 3]: not minimal

Using Lossy Counting [VLDB02], whenever N  0 mod 1/, the oldest minimal occurrence is removed

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
  • A lot of minimal occurrences are kept in LossyDL, but only the last two are used while updating
    • Keeping supports instead of the minimal occurrence lists
    • How to generate rules without the minimal occurrence lists?
    • Re: using the following observations to prune the insignificant rules
  • 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
TLT (cont.)
  • Observations (cont.):
    • Given a SER: (A)(B)5(CD), and T = 3
      • A1B or A2B, that is ApB, 0
      • 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
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
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
  • Two real dataset
    • PDOMEI: the dataset contains the dryness and climate indices derived by experts, usually used to predict droughts
      • Four streams with distinct items # = 28
    • Traffic: the dataset is “Twin Cities’ Traffic data near the 50th St. during the first week of Feb, 2006
      • Three streams with distinct items # = 55
  • Parameter setting
    •  = 0.1minsup
    • Lmax = 10
  • 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
  • In the near future, we will combine these two methods into a hybrid method to investigate the balance between memory space and precision
  • Moreover, we will try to extend the problem of finding serial episode rules to that of finding general episode rules