Discovering multi-label temporal patterns in sequence databases Yen-Liang Chen, Shin-Yi Wu, Yu-Cheng Wang IS (Information Sciences)

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 L i = {l i 1, l i 2, …, l i t } 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 8 EXAMPLE The first occurrence of event type a with three statuses : (a 1 1, a 1 3, a 1 2 ) length = 3 The second occurrence of event type a with two statuses : (a 2 2, a 2 3 ) length = 2 The first occurrence of event type b with two statuses : (b 1 2, b 1 4 ) length = 2 The second occurrence of event type b with two statuses : (b 2 2, b 2 3 ) length = 2 The first occurrence of event type c with two statuses : (c 1 2 ) length = 1

3. Problem definition 9 EXAMPLE (a 1 1, a 1 3, a 1 2 ) is the first occurrence of event type a in the sequence. (a 2 2, a 2 3 ) is the second occurrence. a 1 1.oNum = 1 a 1 1.lNum = 1 a 1 1.eType = a a 2 3.oNum = 2 a 2 3.lNum = 3 a 2 3.eType = a

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: 10 Rel(a 1 1, b 1 2 ) = “<”, because time (a 1 1 ) = 4 < time (b 1 2 ) = 6

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 13 EXAMPLE a 1 1 < a 1 2, b 1 1 < b 1 2 a 1 2 = a 2 2 a 1 3 = b 1 1 a 2 2 = a 1 3

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 = (a 1 1 < b 1 2 < a 1 2 < a 1 3 = b 1 3 = c 1 1 ), then Rel (a 1 2, c 1 1 ) = Small (<, =, =) = “<“, and Rel (a 1 3, c 1 1 ) = Small (=, =) = “=“, 14

3. Problem definition 15 EXAMPLE mltp = (a 1 1 < a 1 2 < a 1 3 < b 1 3 < b 1 4 ) mlts = (a 1 1 < a 1 2 < b 1 2 < a 1 3 < b 1 3 < c 1 1 < a 2 2 < b 2 3 < b 2 4 ) we show that mltp ⊆ mlts because we can find s 1,s 2, s 4, s 8,and s 9 in mlts.

3. Problem definition (Cont.) (1) Type equivalence(2) Label equivalence: p 1.eType = s 1.eType = ap 1.lNum = s 1.lNum = 1 p 2.eType = s 2.eType = ap 2.lNum = s 2.lNum = 2 p 3.eType = s 4.eType = ap 3.lNum = s 4.lNum = 3 p 4.eType = s 8.eType = bp 4.lNum = s 8.lNum = 3 p 5.eType = s 9.eType = bp 5.lNum = s 9.lNum = mltp = (a 1 1 < a 1 2 < a 1 3 < b 1 3 < b 1 4 ) mlts = (a 1 1 < a 1 2 < b 1 2 < a 1 3 < b 1 3 < c 1 1 < a 2 2 < b 2 3 < b 2 4 )

3. Problem definition (Cont.) (3) Occurrence number agreement: p 1, p 2, p 3,have the same event type and occurrence number, so do s 1, s 2, s 4. p 4, p 5 have the same event type and occurrence number, so do s 8, s mltp = (a 1 1 < a 1 2 < a 1 3 < b 1 3 < b 1 4 ) mlts = (a 1 1 < a 1 2 < b 1 2 < a 1 3 < b 1 3 < c 1 1 < a 2 2 < b 2 3 < b 2 4 )

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 (<) = “<” mltp = (a 1 1 < a 1 2 < a 1 3 < b 1 3 < b 1 4 ) mlts = (a 1 1 < a 1 2 < b 1 2 < a 1 3 < b 1 3 < c 1 1 < a 2 2 < b 2 3 < b 2 4 )

4. The algorithm There are two kinds of multi-label temporal patterns. Intra-event pattern It consists of only one event occurrence and intra-L k 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- L k 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 a 1 1 < a 1 2 < a 1 3 < a 2 2 < a 2 4 is treated as an inter-event pattern because event type a occurs twice. 20

4. The algorithm Phase 1 21

4. The algorithm 22 EXAMPLE But occurrence records and cannot be joined in this phase. Join (a 1 1 ) and (a 1 2 ), we obtain the pattern (a 1 1 < a 1 2 )

4. The algorithm 23 EXAMPLE Generate intra- L k from intra- L (k-1)

4. The algorithm Phase 2 24

4. The algorithm After phase 1, we combine all intra-event patterns to obtain inter-L 1. When generating inter-L 2, GenInterLk joins all pairs of inter-event patterns (including self-join) in inter-L 1. The occurrence records for two patterns in inter-L 1 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 26 EXAMPLE The two inter-L 1 patterns (a 1 1 < a 1 2 ) and (b 1 2 < b 1 3 ) have different event types, so they are joinable.

4. The algorithm 27 EXAMPLE Although the two inter-L 1 patterns (b 1 2 ) and (b 1 2 < b 1 3 ) have the same event type, their occurrence records have different occurrence numbers.

4. The algorithm When generating inter-L k (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

29 EXAMPLE The two inter-L 2 patterns are joinable because (1) They have the same first 1 event, a 1 1. (2) Although they have the same last event type b, they have different occurrence numbers.

5. Performance evaluation and real case experiments 30

5. Performance evaluation and real case experiments 31

6. Conclusions and future work MLTPM 32