Download Mining Nonambiguous Temporal Patterns for Interval

ARMADA – An algorithm for discovering richer
relative temporal association rules from
interval-based data
Edi Winarko, John F. Roddick
DKE (Data & Knowledge Engineering) 2007
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OUTLINE
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1. Introduction
2. Related work
3. Problem statement
4. ARMADA – mining richer temporal
association rules
• 5. Experiment results
• 6. Conclusion and future work
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1. Introduction
• Former studies have been focused on time points.
• Some applications events are better treated as intervals
rather than time points.
• ARMADA algorithm.
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2. Related work
• Allen’s interval expression.
• Kam and Fu’s model and definition.
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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>.
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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
.
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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-finishedby (fi), contains (c), equals (=), and starts (s).
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3. Problem statement
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3. Problem statement
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A
B
D
A
B
C
D
p1 is a subpattern of p2, but it is not a subpattern of p3.
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3. Problem statement
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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.
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3. Problem statement
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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.
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4. ARMADA – mining richer
temporal association rules
Step 1 – reading the database into memory
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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>
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4. ARMADA – mining richer
temporal association rules
Step 2 – constructing the index set
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4. ARMADA – mining richer
temporal association rules
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4. ARMADA – mining richer
temporal association rules
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4. ARMADA – mining richer
temporal association rules
Step 3 – mining patterns from the index set
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4. ARMADA – mining richer
temporal association rules
Continuing example
Prefix = <A> combine with s ∈ {B, C, D, E}
Relation <A, E> have 1 overlap relation(25%) and 1before relation(25%),
so <A, E> is not considered as frequent.
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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}
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5. Experiment results
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5. Experiment results
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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.
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