1. Construct chronicles For 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 BCBC A MotivationTemporal Inductive Database AB B C Queries Answers Freq(C,L 1 ) ¸ 5 Æ Freq(C,L 2 ) · 8 Æ C v C 1 Freq(C 1,L) ¸ 10 Æ L 2 D … Temporal patterns : Chronicles Data : Event sequences Event sequences Chronicles B B BABBABBAB A BABBA Chronicle Recognition in Event Sequences i1i1 i2i2 i3i3 i4i4 i5i5 i6i6 i7i7 i8i8 i9i9 i 10 i 11 Q e&d - The earliest distinct instances criterion Q e&d (C 1,L 1 ) = {i 1, i 8, i 10 } Two instances have no common events Instances occur as early as possible according to a total order on instances in the sequence Q m - The minimal occurrences criterion Q m (C 1,L 1 ) ={i 1, i 6, i 8, i 9, i 10 } An instance is not contained by another instance Q d - The distinct instances criterion Q d (C 1,L 1 ) ={i 2, i 7, i 8, i 10 } 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 B [1,5] B [-3,-2] A C [1,2] L1:L1: Instances of C 1 in L 1 L : An event sequenceW : 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 C 2 C2C2 Compute the set of the frequent minimal (maximally specific) chronicles Fmc Q,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 Search Freq W,Q (C,L) ¸ T Processing a Complex Query BCBC A AB B C L 1 : L 2 : Freq W,Q (C,L 1 ) ¸ T 1 Æ Freq W,Q (C,L 2 ) < T 2 Fmc W,Q (L 2,T 2 ) Fmc W,Q (L 1,T 1 ) Chronicle search space B [-W,W] A Fmc Solution Version space Version space computation Mitchells algorithm Bounds of the version space represent the solution Only one algorithm is used to compute Fmcs Frequency of Chronicles Some Recognition Criteria for Frequency Computation BCBC A BCBC 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 C1C1 Freq(C,L 2 ) < T 2, : Freq(C,L 2 ) ¸ T 2 A Output Freq(C,L 1 ) ¸ T 1 Fmc A.Vautier