Discovering hybrid temporal patterns from sequences consisting of point- and interval-based events

Discovering hybrid temporal patterns from sequences consisting of point- and interval-based events Shin-Yi Wu & Yen-Liang Chen DKE 2009

OUTLINE • 1. Introduction • 2. Related works • 3. Problem definition • 4. Mining hybrid temporal patterns • 5. Experiments • 6. Conclusion

1. Introduction • Event sequences contain both point-based and interval-based events are called hybrid event sequences. • Hybrid temporal pattern • HTPM(Hybrid temporal pattern mining )

2. Related works • Allen-based representation“Maintaining knowledge about temporal intervals” • Kam and Fu’s method • TPrefixSpan

3. Problem definition • Let E be the {ty1; ty2; . . . ; tyu} of all event types that may occur in the point-based and interval-based events. • Point-based event (poE), stored in the form (et, Tp). • Interval-based event (inE), stored in the form (et, [Ts,Te])

3. Problem definition EXAMPLE

3. Problem definition • A hybrid event sequence can be represented as • where SIDi is the sequence id of • In a hybrid event sequence with ID = sj ,the occurrence of event ei is recorded asoccur(ei, sj) = {TP1 , TP2 ,…..} • If ei is a poE; occur(ei, sj) = {[Te1, Ts1], [Te2, Ts2],…..} • if ei is an inE. The operation occur outputs all occurrence time .

3. Problem definition EXAMPLE occur(c,1) = {6,8} occur(a,2) = {[8,11]} occur(a,3) = {4,10], [9,12]}

3. Problem definition • A hybrid temporal pattern (htp) is represented as htp = (N0⊕0 N1⊕1 N2⊕2….⊕(k-1) Nn) • Ni ∈ {poE, inE+ , inE-} (0 ≦i ≦ n)⊕i∈ {< , =} (0 ≦i≦ (n-1)) • An event node Nx is arranged before event node Ny in a hybrid temporal pattern if the following conditions are satisfied:

3. Problem definition EXAMPLE ( a+ <a-) [3,8] ( b+ <b-) [3,5] (b) 3 ( a+ <a-) [3,9] ( a+ <a-) [4,9] The length of a hybrid temporal pattern is the number of event occurrences in a pattern. A hybrid temporal pattern with length l is called an l-events hybrid temporal pattern. rule 1(Timing).  b< a+2 < b- < a-0 < a-1 rule 2(Alphabet).  a+1 = b+ rule 3(Event node type).  b+ = b rule 4(Occurrence mark).  a+0 = a+1 , a-1 = a-2 • htp1 = (a+0 = a+1 = b+ = b< a+2 < b- < a-0 < a-1 = a-2 )

3. Problem definition • occur(htpi, sj) = {ot1 ,ot2, …..}The occurrence of a hybrid temporal pattern htpi with k event nodes in a sequence sj . • Each ota is a sequence of k time values, which are the occurrence times of the k event nodes of htpi in sj. • occur(htpi, sj) returns all occurrences of htpi in sj.

3. Problem definition EXAMPLE s1 Given four htps: htp2 = (c) htp3 = (a+ <a-) htp4 = (a+ <b+ <a- <b- ) htp5 = (a+ =b+ <a- <b- ) occur(htp2, s1) = {(6),(8)} occur(htp3, s1) = {(5,10),(8,12)} occur(htp4, s1) = {(5,6,10,12)} occur(htp5, s1) = Ø htp2INs1 , htp3INs1 , htp4Ns1 htp5 ~ INs1

3. Problem definition

4. Mining hybrid temporal patterns • HTPM (Hybrid Temporal Pattern Mining) • Let Lk be the set of frequent k-events hybrid temporal patterns. The process starts by scanningthe hybrid event sequence database D to generate L1.

4. Mining hybrid temporal patterns • Event set E = {a, b, c}. • When min_sup is set to 50%, GenL1() scans database D once, and obtains L1 = { ( a+ <a-), ( b+ <b-), ( c)}

4. Mining hybrid temporal patterns • After generating L1, GenLk joins the ORs of two (k-1)-events hybrid temporal patterns to obtain one or more patterns with length k. • When generating L2; GenLk joins all pairs of patterns (including self-join) in L1 • For example, we have to join the following pairs:(( a+ <a-) ,( a+ <a-))(( a+ <a-), ( b+ <b-))(( a+ <a-),(c))(( b+ <b-) ,( b+ <b-))(( b+ <b-),(c))((c),(c))

4. Mining hybrid temporal patterns

4. Mining hybrid temporal patterns EXAMPLE Join ( a+ <a-) and (c), we can obtain the following patterns:( a+ < c <a-) ( c < a+ <a-) ( a+ = c <a-) frequent

4. Mining hybrid temporal patterns EXAMPLE GenLk joins only the pair ( b+ = c < a+ < a- =b-) and ( b+ = c < c < b-), because the first two events in both patterns are ( b+ <b-) and (c), and the prefix 2-events subpattern of these patterns is ( b+ < c <b-)

4. Mining hybrid temporal patterns EXAMPLE Have common prefix (k-2)-subpattern Three occurrence records of ( a+ <a-) and (c) Taking the first tuple as an example, we have to join set {(5, 10), (8,12)} with set {(6), (8)}, which results in set {(5, 6, 10), (5, 8, 10), (6, 8, 12), (8, 8, 12)}. Then use algoORAlignto realignment sets

5. Experiments Compare with PrefixSpan

5. Experiments Compare with TPrefixSpan

6. Conclusion

Discovering hybrid temporal patterns from sequences consisting of point- and interval-based events