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 )

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 2

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 3

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 4

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 5 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. 6 Transaction

3. Problem definition A customer C is a sequence of transactions. C =, where ts(T i ) < ts(T j ) if i < j. ts(T i ) : the time-point at which T i has been issued. 7 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, where e i = (E, t i ), e i ∈ T i, t i ∈ TS, and t i ≦ t i+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 [t 1, t n ]. 8 Sequence of events

3. Problem definition A time interval between the first event e 1 and the last event e n of ES is expressed as [t 1, t n ]. 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. 9

3. Problem definition A sequence ES’ of events with a time interval is denoted by,Where e j ’ = (E x,[vs j, ve j ]) and ve j ≦ vs j+1 for each j = 1,...,n-1. ES’ is a sequence of events for an event type E x. 10 Sequence of events with a time interval

3. Problem definition Suppose that a database of transactions DB is as follows: 11 EXAMPLE SS(Cid = 101) = {,,,, } SS means a set of sequences DB = { T 1 = (101, {D,B}, 1), T 2 = (101, {D,A,E}, 2), T 3 = (101, {A,E,B}, 3), T 4 = (101, {C}, 5, T 5 = (101, {E,C}, 7)} ES(Cid = 101,E) = 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) : 12 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 13

3. Problem definition 14

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)/ N cust ≧ Supp min (the minimum support assigned by a user), then E is a large event type and an event e having E is a large event. N cust is the number of customers in DB 15 For instance, assume that there are 500 customers and Supp min is 40%. If Supp(E) is 200, E is a large event type since Supp(E)/ N cust = 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 E i. WFreq min is 50%, WFreq(E i ) is 6, E i is a uniform event type since WFreq(E 1 )/ W num = 6/10 = Window size

3. Problem definition 17 Candidate temporal interval relations

3. Problem definition A temporal interval relation rule TR is defined as TR(e 1 ’,e 2 ’,e 3 ’) = (R 1 (e 1 ’,e 2 ’)|Supp(R 1 )) Λ (R 2 (e 2 ’,e 3 ’)|Supp(R 2 )) Λ (R 3 (e 1 ’,e 3 ’)|Supp(R 3 )) 18

4. Technique for mining temporal Interval relation rules (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 20 Window size = 2 Window length = 12/2 = 6

4. Technique for mining temporal Interval relation rules 21

4. Technique for mining temporal Interval relation rules 22

4. Technique for mining temporal Interval relation rules DAG TR (B, C, E) for TR(B, C, E) is defined as (Vertex, Edge), where Vertex = {B, C, E} Edge = {,,. 23 Event type Events relation Relation support

4. Technique for mining temporal Interval relation rules 24

5. Experimental results 25

5. Experimental results 26

6. Conclusions and future research 27