Construct chronicles For each fuzzy clusters of step : instances are sorted in the decreasing order...
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Transcript of Construct chronicles For each fuzzy clusters of step : instances are sorted in the decreasing order...
Construct chroniclesFor each fuzzy clusters of step ‚:
instances are sorted in the decreasing order of their membership degree
the T first instances that respect the Q criterion are retained to construct a chronicle.
Goal: extraction of temporal patterns that discriminate event sequences
• Long event sequences• Few event types• Numerical temporal information is of major
importance
Temporal patterns: chronicles Sets of events such that the delay between their occurrences is bounded by a numerical interval
A B[0,3]
A[-1,4]
B[0,3]
A [2,2]
C
B CBC A
Motivation Temporal Inductive Database
A B BC
Queries
Answers
Freq(C,L1) ¸ 5 Æ Freq(C,L2) · 8 Æ C v C1
Freq(C1,L) ¸ 10 Æ L 2 D …
Temporal patterns : Chronicles Data : Event sequences
Event sequences
Chronicles
B B BA B BA B BA B A B A B BA
Chronicle Recognition in Event Sequences
i1
i2
i3
i4
i5
i6
i7
i8
i9
i10
i11
Qe&d - The earliest distinct instances criterion Qe&d (C1,L1) = {i1, i8, i10}• Two instances have no common events • Instances occur as early as possible according to a total order on instances in the
sequence
Qm - The minimal occurrences criterion Qm(C1,L1) ={i1, i6, i8, i9, i10}
• An instance is not contained by another instance
Qd - The distinct instances criterion Qd (C1,L1) ={i2, i7, i8, i10}
• Selects instances that form a maximum clique in the graph of distinctness instances.
An Order Relation on Chronicles
B[-1,3]
[1,5]B[-3,-2]
A
B[-2,5]
A
B[1,2]
A C[1,2]
B[1,2]
[1,5]B[-3,-2]
A C[1,2]
L1:
Instances ofC1 in L1
L : An event sequence W : A maximal time window T : A minimum frequency threshold Q :A recognition criterion
(Application dependent)
Input
Find every frequent parallel episodes
Apriori manner
Format of every temporal constraints : [-W,W]
… AB
CA
BC
Fuzzy cluster instances of chronicles found in step .
Instances of the chronicle C2
C2
Compute the set of the frequent minimal (maximally specific) chronicles FmcQ,W(L,T)
The most specific chronicles are retained
An Inductive Database for Mining Temporal Patterns in Event Sequences
Alexandre Vautier, Marie-Odile Cordier and René Quiniou Irisa - DREAM Project Campus de Beaulieu 35042 RENNES Cedex, FRANCE{Alexandre.Vautier,Marie-Odile.Cordier,Rene.Quiniou}@irisa.fr
More general
More specific
Frequent Minimal Chronicles Search – Fmc SearchFreqW,Q(C,L) ¸ T
Processing a Complex Query
B CBC A
A B BC
L1 :
L2 :
FreqW,Q (C,L1) ¸ T1 Æ FreqW,Q (C,L2) < T2
FmcW,Q(L2,T2)
FmcW,Q(L1,T1)
Chronicle search space
B[-W,W]
A
Fmc SolutionVersion space
Version space computation
Mitchell’s algorithm
Bounds of the version space represent the solution
Only one algorithm is used to compute Fmcs
Frequency of ChroniclesSome Recognition Criteria for Frequency Computation
B CBC A
B CBC
B C
[-2,2]
B 2 instances
Constraints on frequency should satisfy monotonicity or anti-monotonicity properties
3 instances
<Freq(B,L)
¸ Freq(BC,L)
L:
B[-1,3]
[1,5]B[-3,-2]
A
C1
Freq(C,L2) < T2
,: Freq(C,L2) ¸ T2
A
ƒ‚ „Output
Freq(C,L1) ¸ T1
Fmc
A.Vautier