discovering multi-label temporal patterns in sequence databases yen-liang chen, shin-yi wu, yu-cheng...
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Discovering multi-label temporal patterns in sequence databases
Yen-Liang Chen , Shin-Yi Wu, Yu-Cheng Wang
IS (Information Sciences) 2011
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OUTLINE• 1. Introduction• 2. Related works• 3. Problem definition• 4. The algorithm• 5. Performance evaluation and
real case experiments• 6. Conclusions and future work
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1. Introduction• Multi-label event
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1. Introduction• Multi-label temporal pattern representation
• MLTPM (Multi-label temporal pattern mining)for discovering multi-label temporal patterns from multi-label sequence data.
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2. Related works• Allen-based representation
“Maintaining knowledge about temporal intervals”
• Kam and Fu’s method
• TPrefixSpan
• HTPM
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3. Problem definition
• Let event types 1, 2, . . ., and u be all the event types in temporal database D .
• Let Li = {li1, li
2, …, lit } be the set of all labels for
event type i.
• A multi-label item has three related attributes:1. event type2. occurrence number of the event type3. label index
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3. Problem definition
• We define the following notations for a multi-label item it:
• A multi-label sequence is a sequence of multi-label items.
• The total number of items in a multi-label sequence is the length of the sequence.
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3. Problem definition
EXAMPLE
The first occurrence of event type a with three statuses : (a1
1 , a13 , a1
2) length = 3The second occurrence of event type a with two statuses : (a2
2 , a23) length =
2The first occurrence of event type b with two statuses : (b1
2 , b14) length = 2
The second occurrence of event type b with two statuses : (b2
2 , b23) length = 2
The first occurrence of event type c with two statuses : (c1
2 ) length = 1
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3. Problem definition
EXAMPLE
(a11 , a1
3 , a12) is the first occurrence of event type a in the sequence.
(a22 , a2
3) is the second occurrence.
a11 .oNum = 1
a11 .lNum = 1
a11 .eType = a
a23 .oNum = 2
a23 .lNum = 3
a23 .eType = a
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3. Problem definition
• Let time(u) be the occurrence time of item u. Then, the order relation Rel(u,v) of two items u and v can be defined as ‘‘<” if time(u) < time(v), and as ‘‘=” if time(u) = time(v).
• EX:
Rel(a11 , b1
2) = “<” , because time (a1
1) = 4 < time (b12) = 6
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3. Problem definition
• A multi-label temporal sequence or pattern is a sequence of multi-label items interweaved with temporal relationships.
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3. Problem definition
• In a multi-label sequence or a multi-label temporal pattern, item u must be placed before item v based on the following conditions:
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3. Problem definition
EXAMPLE
a11 < a1
2 , b11 < b1
2
a12 =
a22
a13 =
b11
a22 = a1
3
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3. Problem definition
• Function Small (⊕r , ⊕r+1 ,…, ⊕q), where ⊕i ∈ {<, =}, will output “<“ if any ⊕i , r ≤ i ≤ q , is “<”. Otherwise, the output of Small is “=”.
• EX:mltp = (a1
1 < b12 < a1
2 < a13 = b1
3 = c11),
then Rel (a12 , c1
1 ) = Small (< , = , =) = “<“,and Rel (a1
3 , c11 ) = Small (= , =) = “=“,
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3. Problem definition
EXAMPLE
mltp = (a11 < a1
2 < a13 < b1
3 < b14 )
mlts = (a11 < a1
2 < b12 < a1
3 < b13 < c1
1 < a22 < b2
3 < b2
4 )
we show that mltp ⊆ mlts because we can find s1,s2, s4, s8,and s9 in mlts.
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3. Problem definition
(Cont.)
• (1) Type equivalence (2) Label equivalence:p1.eType = s1.eType = a p1.lNum = s1.lNum = 1p2.eType = s2.eType = a p2.lNum = s2.lNum = 2p3.eType = s4.eType = a p3.lNum = s4.lNum = 3p4.eType = s8.eType = b p4.lNum = s8.lNum = 3p5.eType = s9.eType = b p5.lNum = s9.lNum = 4
1 2 3 4 5 6 7 8 9mltp = (a1
1 < a12 < a1
3 < b13 < b1
4 )mlts = (a1
1 < a12 < b1
2 < a13 < b1
3 < c11 < a2
2
< b23 < b2
4 )
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3. Problem definition
(Cont.)
• (3) Occurrence number agreement:p1, p2, p3,have the same event type and occurrence number, so do s1, s2, s4.
p4, p5 have the same event type and occurrence number, so do s8, s9.
1 2 3 4 5 6 7 8 9mltp = (a1
1 < a12 < a1
3 < b13 < b1
4 )mlts = (a1
1 < a12 < b1
2 < a13 < b1
3 < c11 < a2
2
< b23 < b2
4 )
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3. Problem definition
(Cont.)
• (4) Same label ordering:¤1 = Small (⊕1) = Small (<) = “<”¤2 = Small (⊕2 , ⊕3) = Small (< , <) = “<”¤3 = Small (⊕4 , ⊕5 , ⊕6 , ⊕7 ) = Small (< , < , < , <) = “<”¤4 = Small (⊕8) = Small (<) = “<”
1 2 3 4 5 6 7 8 mltp = (a1
1 < a12 < a1
3 < b13 < b1
4 )mlts = (a1
1 < a12 < b1
2 < a13 < b1
3 < c11 < a2
2
< b23 < b2
4 )
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4. The algorithm• There are two kinds of multi-label temporal
patterns.• Intra-event pattern
It consists of only one event occurrence and intra-Lk is the set of frequent intra-event patterns with length k, where k is the number of items
• Inter-event pattern It consists of more than one event occurrence and inter-Lk is the set of frequent inter-event patterns with length k, where k is the number of event occurrences
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4. The algorithm• MLTPM(Multi-label temporal pattern mining)
• Phase 1 : intra-event pattern mining, discovering patterns with only one event occurrence.
• Phase 2 : inter-event pattern mining, discovering patterns with more than one event occurrence.
• EX: A multi-label temporal pattern a11 < a1
2 < a13
< a22 < a2
4 is treated as an inter-event pattern because event type a occurs twice.
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4. The algorithm• Phase 1
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4. The algorithmEXAMPLE
But occurrence records <(1,4)> and <(2,13)> cannot be joined in this phase.
Join (a11) and (a1
2) , we obtain the pattern (a1
1 < a12)
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4. The algorithmEXAMPLE
Generate intra- Lk from intra- L(k-1)
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4. The algorithm• Phase 2
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4. The algorithm• After phase 1, we combine all intra-event
patterns to obtain inter-L1.
• When generating inter-L2, GenInterLk joins all pairs of inter-event patterns (including self-join) in inter-L1 .
• The occurrence records for two patterns in inter-L1 are joinable(1) If the patterns have different event types.(2) If the patterns have the same event type, they have different occurrence numbers.
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4. The algorithmEXAMPLE
The two inter-L1 patterns (a11 < a1
2 ) and (b12 < b1
3 ) have different event types, so they are joinable.
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4. The algorithmEXAMPLE
Although the two inter-L1 patterns (b12 ) and (b1
2 < b13 )
have the same event type, their occurrence records have different occurrence numbers.
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4. The algorithm• When generating inter-Lk (k > 2), GenInterLk
only joins pairs of inter-event patterns in inter-L(k-1) that have the same first (k-2) events.
• They must have the same occurrence number and the same occurrence time.
• Two occurrence records for patterns in inter-L(k-1) are joinable.(1) If they have different last event types.(2) If they have the same last event type, they have different occurrence numbers.
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EXAMPLE
The two inter-L2 patterns are joinable because(1) They have the same first 1 event, a1
1 < a12 , and the
same occurrence record, <(1, 4), (1,11)> .(2) Although they have the same last event type b, they have different occurrence numbers.
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5. Performance evaluation and
real case experiments
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5. Performance evaluation and
real case experiments
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6. Conclusions and future work
• MLTPM