Download Mining Nonambiguous Temporal Patterns for Interval

Discovering multi-label
temporal patterns in
sequence databases
Yen-Liang Chen , Shin-Yi Wu, Yu-Cheng Wang
IS (Information Sciences) 2011
1
OUTLINE
•
•
•
•
•
1. Introduction
2. Related works
3. Problem definition
4. The algorithm
5. Performance evaluation and
real case experiments
• 6. Conclusions and future work
2
1. Introduction
• Multi-label event
3
1. Introduction
• Multi-label temporal pattern representation
• MLTPM (Multi-label temporal pattern mining)
for discovering multi-label temporal patterns from
multi-label sequence data.
4
2. Related works
• Allen-based representation
“Maintaining knowledge about temporal intervals”
• Kam and Fu’s method
• TPrefixSpan
• HTPM
5
3. Problem definition
• Let event types 1, 2, . . ., and u be all the event types in
temporal database D .
• Let Li = {li1, li2, …, lit } be the set of all labels for event type i.
• A multi-label item has three related attributes:
1. event type
2. occurrence number of the event type
3. label index
6
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.
7
3. Problem definition
EXAMPLE
The first occurrence of event type a
with three statuses : (a11 , a13 , a12) length = 3
The second occurrence of event type a
with two statuses : (a22 , a23) length = 2
The first occurrence of event type b
with two statuses : (b12 , b14) length = 2
The second occurrence of event type b
with two statuses : (b22 , b23) length = 2
The first occurrence of event type c
with two statuses : (c12 ) length = 1
8
3. Problem definition
EXAMPLE
(a11 , a13 , a12) is the first occurrence of event type a in the sequence.
(a22 , a23) is the second occurrence.
a11 .oNum = 1
a11 .lNum = 1
a11 .eType = a
a23 .oNum = 2
a23 .lNum = 3
a23 .eType = a
9
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 , b12) = “<” ,
because time (a11) = 4 < time (b12) = 6
10
3. Problem definition
• A multi-label temporal sequence or pattern is a sequence
of multi-label items interweaved with temporal
relationships.
11
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:
12
3. Problem definition
EXAMPLE
a11 < a12 , b11 < b12
12 =
21 1
1
a
a
2
a a = a= 2b
2 3
3 1
13
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 = (a11 < b12 < a12 < a13 = b13 = c11),
then Rel (a12 , c11 ) = Small (< , = , =) = “<“,
and Rel (a13 , c11 ) = Small (= , =) = “=“,
14
3. Problem definition
EXAMPLE
mltp = (a11 < a12 < a13 < b13 < b14 )
mlts = (a11 < a12 < b12 < a13 < b13 < c11 < a22 < b23 < b24 )
we show that mltp ⊆ mlts because we can find s1,s2, s4, s8,and
s9 in mlts.
15
3. Problem definition
(Cont.)
1
2
3
4
5
6
7
8 9
mltp = (a11 < a12 < a13 < b13 < b14 )
mlts = (a11 < a12 < b12 < a13 < b13 < c11 < a22 < b23 < b24 )
• (1) Type equivalence
p1.eType = s1.eType = a
p2.eType = s2.eType = a
p3.eType = s4.eType = a
p4.eType = s8.eType = b
p5.eType = s9.eType = b
(2) Label equivalence:
p1.lNum = s1.lNum = 1
p2.lNum = s2.lNum = 2
p3.lNum = s4.lNum = 3
p4.lNum = s8.lNum = 3
p5.lNum = s9.lNum = 4
16
3. Problem definition
(Cont.)
1
2
3
4
5
6
7
8 9
mltp = (a11 < a12 < a13 < b13 < b14 )
mlts = (a11 < a12 < b12 < a13 < b13 < c11 < a22 < b23 < b24 )
• (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.
17
3. Problem definition
(Cont.)
1
2
3
4
5
6
7
8
mltp = (a11 < a12 < a13 < b13 < b14 )
mlts = (a11 < a12 < b12 < a13 < b13 < c11 < a22 < b23 < b24 )
• (4) Same label ordering:
¤1 = Small (⊕1) = Small (<) = “<”
¤2 = Small (⊕2 , ⊕3) = Small (< , <) = “<”
¤3 = Small (⊕4 , ⊕5 , ⊕6 , ⊕7 ) = Small (< , < , < , <) = “<”
¤4 = Small (⊕8) = Small (<) = “<”
18
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 interLk is the set of frequent inter-event patterns with length
k, where k is the number of event occurrences
19
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 < a12 < a13 < a22 <
a24 is treated as an inter-event pattern because event
type a occurs twice.
20
4. The algorithm
•
Phase 1
21
4. The algorithm
EXAMPLE
1
<(1,4)>
and <(2,13)>
JoinBut
(a1occurrence
we obtain
the pattern
(a11 < a12)
1) and (a 2) ,records
cannot be joined in this phase.
22
4. The algorithm
EXAMPLE
Generate intra- Lk from intra- L(k-1)
23
4. The algorithm
•
Phase 2
24
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.
25
4. The algorithm
EXAMPLE
The two inter-L1 patterns (a11 < a12 ) and (b12 < b13 )
have different event types, so they are joinable.
26
4. The algorithm
EXAMPLE
Although the two inter-L1 patterns (b12 ) and (b12 < b13 ) have the
same event type, their occurrence records have different
occurrence numbers.
27
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.
28
EXAMPLE
The two inter-L2 patterns are joinable because
(1) They have the same first 1 event, a11 < 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.
29
5. Performance evaluation and
real case experiments
30
5. Performance evaluation and
real case experiments
31
6. Conclusions and future work
• MLTPM
32