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Mining temporal interval relational rules from temporal data. Yong Joon Lee , Jun Wook Lee , Duck Jin Chai , Bu Hyun Hwang , Keun Ho Ryu. JSS ( The Journal of Systems and Software ) 2009. OUTLINE. 1. Introduction 2. Related works 3. Problem definition
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Mining temporal interval relational rules from temporal data Yong Joon Lee , Jun Wook Lee , Duck Jin Chai , Bu Hyun Hwang , Keun Ho Ryu JSS (The Journal of Systems and Software ) 2009
OUTLINE • 1. Introduction • 2. Related works • 3. Problem definition • 4. Technique for mining temporal Interval relation rules • 5. Experimental results • 6. Conclusions and future research
1. Introduction • Lots of studies did not consider temporal interval data and used only data stamped with time points. • The preprocessing algorithm • The temporal interval relation discovery algorithm
2. Related works • Sequential patterns • Similar time sequences • Temporal rules • These studies are limited to data stamped with time points and do not consider temporal interval data. • Allen’s interval algebra
3. Problem definition • TS : a set of primitive time points. • An event e , e = (E,t) • E : event type • t : a time-point at which an event e has occurred. t ∈ TS Event
3. Problem definition • A transaction is a set of events such as e = (Cid,E,t), • Cid : a customer identifier • E : an event type • t : a time-point that the event has occurred. Transaction
3. Problem definition • A customer C is a sequence of transactions. • C = <T1,T2,. . .,Tn >, where ts(Ti) < ts(Tj) if i < j. • ts(Ti) : the time-point at which Ti has been issued. Customer
3. Problem definition • A sequence of events for a customer Cid and an event type E. • Event sequence , ES(Cid,E), is represented by <e1,e2,. . .,en >, where ei = (E, ti), ei ∈ Ti , ti ∈ TS, and ti≦ ti+1 for each i=1,…,n-1 • A time interval between the first event e1 and the last event en of ES is expressed as [t1, tn]. Sequence of events
3. Problem definition • A time interval between the first event e1 and the last event en of ES is expressed as [t1, tn]. • An event e’ with a temporal interval is denoted as e’= (E,[vs,ve]), • e’.vs = event e’ start time-point • e’.ve = event e’ end time-point • A sequence of events with the same event type can be converted into one generalized event with a time interval.
3. Problem definition • A sequence ES’ of events with a time interval is denoted by <e1’,e2’,. . .,en’ >,Where ej’ = (Ex ,[vsj, vej]) and vej≦vsj+1 for each j = 1,. . .,n-1. • ES’ is a sequence of events for an event type Ex. Sequence of events with a time interval
3. Problem definition • Suppose that a database of transactions DB is as follows: EXAMPLE SS(Cid = 101) = { <(D,1)(D,2)> , <(B,1)(B,3)> , <(A,2)(A,3)> , <(E,2)(E,3)(E,7)> , <(C,5)(C,7)> } SS means a set of sequences DB = { T1 = (101 , {D,B}, 1) , T2 = (101 , {D,A,E}, 2) , T3 = (101 , {A,E,B}, 3) , T4 = (101 , {C}, 5 , T5 = (101 , {E,C}, 7)} ES(Cid = 101,E) = <(E,2)(E,3)(E,7)> can be converted into a generalized event (E, [2, 7]). Similary , (D,[1,2]) (B,[1,3]) (A,[2,3]) (C,[5,7])
3. Problem definition • A temporal interval relation is defined as R(x,y) = {P(x,y)|(x,y)∈Ω ,P∈IO} • The set of temporal interval operators is IO = {before, equals, meets, overlaps, during} • R(x,y) : Temporal interval relation Let IE be {(D, [1,2]), (B, [1,3]), (A, [2,3]). There are three temporal interval relations such as meets(D,A), during(D,B), and during(A,B).
3. Problem definition • The support of E is denoted by Supp(E) and it is the number of customers supporting E in DB. • If Supp(E)/ Ncust≧Suppmin(the minimum support assigned by a user), then E is a large event type and an event e having E is a large event. • Ncust is the number of customers in DB For instance, assume that there are 500 customers and Suppmin is 40%. If Supp(E) is 200, E is a large event type since Supp(E)/Ncust = 200/500 = 0.4.
3. Problem definition • For instance, suppose that 10 windows with a window size five exist in the lifespan [1, 50] of Ei. • WFreqmin is 50% ,WFreq(Ei) is 6, Ei is a uniform event type since WFreq(E1)/ Wnum = 6/10 = 0.6. Window size
3. Problem definition Candidate temporal interval relations
3. Problem definition • A temporal interval relation rule TR is defined as TR(e1’,e2’,e3’) = (R1(e1’,e2’)|Supp(R1)) Λ (R2(e2’,e3’)|Supp(R2)) Λ (R3(e1’,e3’)|Supp(R3))
4. Technique for mining temporal Interval relation rules 101 (D,1)(D,2) (B,1)(B,3) (A,2)(A,3) (E,2)(E,3)(E,7) (C,5) [D(1,2)] [B(1,3)] [A(2,3)] [E(2,7)] [C(5)] 101 A B C D E 102 B C E G 103 B C D E F 104 A C D E F
4. Technique for mining temporal Interval relation rules Window size = 2 Window length = 12/2 = 6
4. Technique for mining temporal Interval relation rules • DAGTR(B, C, E) for TR(B, C, E) is defined as (Vertex, Edge), where Vertex = {B, C, E} Edge = {<B, C,before>, <C, E,during>, <B, E, overlapsi>. Event type Events relation Relation support
