1. Edi Winarko, John F. Roddick
ARMADA – An algorithm for discovering richer relative temporal association rules from interval-based data
Edi Winarko, John F. Roddick
DKE (Data & Knowledge Engineering) 2007

2. OUTLINE 1. Introduction 2. Related work 3. Problem statement
4. ARMADA – mining richer temporal association rules
5. Experiment results
6. Conclusion and future work

3. 1. Introduction Former studies have been focused on time points.
Some applications events are better treated as intervals rather than time points.
ARMADA algorithm.

4. 2. Related work Allen’s interval expression.
Kam and Fu’s model and definition.

5. 3. Problem statement
Given a temporal database D = {t1….tn} ti consists of a client-id, a temporal attribute, a start-time, and an end-time, where start-time < end-time.
S denote the set of all possible states, s is a state in S. A period of time (b, s, f ), where state s ∈ S, b for start-time and f for end-time. EX: (2, A, 7) refers to state A start in 2 and end in 7.
If s is a single state type in S, then s is a temporal pattern, denoted as <s>.

6. 3. Problem statement
Given n state intervals (bi, si, fi ) , 1 ≦ i ≦ n, a temporal pattern of size n > 1 is defined by a pair
maps index i to the corresponding state, and M is an n*n matrix whose elements M[i, j] denotes the relationship between intervals (bi, si, fi ) and (bi, si, fj ).
Seven relations : before (b), meets (m), overlaps (o), is-finished-by (fi), contains (c), equals (=), and starts (s).

7. 3. Problem statement

8. 3. Problem statement
A B C D
A B D
為何呢? 因為把P2的D移除調會得到P1的樣子，但是對於P3，把DC移掉剩下AB的關係跟P1並不同，所以並非snbpattern
p1 is a subpattern of p2, but it is not a subpattern of p3.

9. 3. Problem statement

10. 3. Problem statement
Given a minimum support minsup, a pattern is called frequent if its support is greater than or equal to minsup. Here we set 40% as the minsup.

11. 3. Problem statement

12. 3. Problem statement
A richer temporal association rule is an expression X=>Y, where X and Y are frequent temporal patterns such that X ⊆ Y (X is a subpattern of Y).
EX: is a subpattern of
If A overlaps B occurs, then it is highly likely that A before D and B before D will also occur.

13. 4. ARMADA – mining richer temporal association rules
Step 1 – reading the database into memory

14. 4. ARMADA – mining richer temporal association rules
minsup = 40%
Candidate <A> (σ = 75%), <B> (σ = 75%), <C> (σ = 75%), <D> (σ = 100%), <E> (σ = 50%),
<F> (σ = 25%),
<G> (σ = 25%).
Frequent 1-pattern:
<A>, <B>, <C>, <D>, <E>

15. 4. ARMADA – mining richer temporal association rules
Step 2 – constructing the index set

16. 4. ARMADA – mining richer temporal association rules
前面訂下規則，按照字母順序去做mining，這邊先找出所有開頭為A的組合

17. 4. ARMADA – mining richer temporal association rules
因為是按照字母順序做mining，所以下一個以state B開始

18. 4. ARMADA – mining richer temporal association rules
Step 3 – mining patterns from the index set
計算這個relation的support count 是否有過門檻 將prefix p的pattern去和frequent state s做合併以產生下一個level的pattern

19. 4. ARMADA – mining richer temporal association rules
Continuing example
Prefix = <A> combine with s ∈ {B, C, D, E}
這邊都是以A為主去作範例
Relation <A, E> have 1 overlap relation(25%) and 1before relation(25%), so <A, E> is not considered as frequent.

20. 4. ARMADA – mining richer temporal association rules
Continuing example
Prefix = <A,B> , combine with s ∈ {C, D}
Prefix = <A,C> , combine with s ∈ {D}
Prefix = <A,D> ,combine with none
Prefix = <A,B, D> , combine with s ∈ {C}
2-pattern 的AB AC AD再去跟BCDE做合併 (不重附)

21. 5. Experiment results

22. 5. Experiment results

23. 6. Conclusion and future work
ARMADA algorithm looks promising as a method for discovering patterns and rules from interval-based data.
Future work: consider to use real-world databases for the experiment.