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CONFORMANCE CHECKING IN THE LARGE: PARTITIONING AND TOPOLOGY Jorge Munoz-Gama, Josep Carmona and Wil M.P. van der Aalst

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Motivation 2 THEORYREALITY REALITY REFLECTION LOGS

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BPM 2013 (Tuesday) BPI Workshop 2013 Community Motivates Itself 3 Process Mining Conformance Checking Conformance Dimensions Alignment based Conformance Big Data Conformance Checking Applications Decomposition RPST BPM 2013 (Wednesday)

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Conformance General Idea 4 model Log trace mismatches

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Conformance in a Nutshell 5 Log Model A B C D E A B B C Alignment E FitnessPrecision How much behavior of the log is captured by the model? How accurate is the model describing the log? Conformance mismatch on the Log Conformance mismatch on the Model

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Conformance in the Large How easy is to diagnose a conformance problem here? How much time it takes? 6

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General Idea: Decomposition 7

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The 4 Challenges Comprehensible Guaranties Fast Diagnosis 8 ?

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SESE and RPST for decomposing 9 SESERPST Single Entry Single Exit components Refined Process Structure Tree * Artem Polyvyanyy: Structuring Process Models. PhD Thesis. University of Potsdam (Germany), January 2012 * Hopcroft, J., Tarjan, R.E.: Dividing a graph into triconnected components. SIAM J. Com- put. 2(3), 1973 Based on graph decomposition

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Interior, Boundary, Entry, and Exit nodes Given a subgraph and a node of it: Interior node: connected only to nodes of the subgraph. Boundary node: not interior Entry node: boundary where no incoming edge in subgraph or all outgoing edges in Exit node: boundary where no outgoing edge in subgraph or all incoming edges in 10

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Nodes examples 11

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Structural Decomposition 12 transition place token A B D E F C

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Example of SESE and RPST 13 SESE: set of edges which graph has a Single Entry node and a Single Exit node Refined Process Structure Tree (RPST) containing non overlapping SESEs Unique Modular Linear Time

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Why SESE and RPST? Why SESE? Only one entry; only one exit Represent subprocesses within the process Intuitive for conformance diagnosis Why RPST? Partitioning over the RPST Any cut is a partitioning Algorithm to partitioning by size (k) 14

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Why SESE and RPST? Why SESE? Only one entry; only one exit Represent subprocesses within the process Intuitive for conformance diagnosis Why RPST? Partitioning over the RPST Any cut is a partitioning Algorithm to partitioning by size (k) 15 K<

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The 4 Challenges Comprehensible Guaranties Fast Diagnosis 16 ?

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Properties of the Partitioning What about the guaranties in conformance checking? Decomposed Perfectly Fitting Checking: A model/log is perfectly fitting if and only if all the components are perfectly fitting 17 * W.M.P. van der Aalst : Decomposing Petri nets for process mining: A generic approach. Distributed and Parallel Databases, 2013

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SESE and Decomposed Perfectly Fitting SESEs (per se) do not satisfy the Decomposed Perfectly Fitting Checking property 18 1 token in p => abcdef fits S but not S2 2 tokens in p => abdecf fits S1 and S2 but not S

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Valid Decomposition The problem is in the boundary places No reflection on the log A partition with only transitions shared among components (no places neither arcs) Transitions have reflect on the log Use that reflection to sync the components This is known as a valid decomposition Details in: 19 * W.M.P. van der Aalst : Decomposing Petri nets for process mining: A generic approach. Distributed and Parallel Databases, 2013 * J. Munoz-Gama, J. Carmona, and W.M.P. van der Aalst : Conformance checking in the large: partitioning and topology. BPM 2013

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SESE to Valid Decomposition Create a ‘bridge’ for each shared place 20

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Results 21 SESEs and Bridges Few with non negligible size

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SESE + Bridging Theorem Theorem: SESE decomposition with Bridging post- processing satisfies the Decomposed Perfectly Fitting Checking 22

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The 4 Challenges Comprehensible Guaranties Fast Diagnosis 23 ?

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Results 1 Net – 1h 15min 7 Subnets – 2min 24

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Results 25 Better performance with large, concurrency, long traces and concentrated conformance problems Not always faster: short traces, fitting. Overhead of the decomposition Results even in cases that the original approach can handle

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The 4 Challenges Comprehensible Guaranties Fast Diagnosis 26 ?

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Results 27 Conformance problems spread Conformance problems concentrated

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Topology 28 S1 S4 S2 S3 B1 B2 S7S8 S5 S6

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Topology Enhancement 29 S1 S4 S2 S3 B1 B2 S7S8 S5 S6 t1,t3,t4,t5,t7,t7,t9

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Topological Diagnosis Algorithms Non-Fitting (Weakly) Connected Components 30 S1 S4 S2 S3 B1 B2 S7S8 S5 S6 Non-Fitting Subnet

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Topological Diagnosis in Large 31

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Topological Results 32 From almost 700 nodes … … to 70

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The 4 Challenges Comprehensible Guaranties Fast Diagnosis 33

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Future Work Estimate fitness Not decisional but metric Divide-and-Conquer Alignment Algorithms Reconstruct the alignment New decompositions Less trivial components New conformance dimensions Precision, generalization, … 34

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Conclusions Partitioning Technique for Conformance Checking Based on SESE and RPST May be faster, distributed, and help on the diagnosis Topology for diagnosis Implemented in ProM framework. 35

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Thank You

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Process Mining in a Nutshell 37 THEORYREALITY

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Process Mining in a Nutshell 38 THEORYREALITY REALITY REFLECTION LOGS

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