DECOMPOSED CONFORMANCE

Jorge Munoz-Gama, Josep Carmona and W.M.P van der Aalst

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About Myself• Jorge Munoz-Gama

• Barcelona• Universitat Politecnica de Catalunya (UPC)• Advisor: Josep Carmona

• Studies• Bachelor in Computer Science (2009)• Master in Computation (2010)• PhD in Computation ( expected Oct. 2014)

• TUE (2012 and 2013) and NII (2012)• Conformance Checking and Diagnosis in Process Mining

• Topics• Precision within Conformance

• Arya, Wil and Boudewijn

• Decomposed Conformance• Wil and Eric

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Abstract Wordle

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Outline• Diagnosis using SESE + RPST

• SESE / RPST• Benefits and limitations

• Valid Decomposition using SESE + RPST• Valid Decomposition• Transform SESE into Valid Decomposition

• Alignments and Fitness from Valid Decomposition• Stitching Check• Divide and Conquer Algorithm

Diagnosis using SESE+RPST

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Conformance Diagnosis in the Large

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Process Diagnosis like a Map

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Process Diagnosis like a Map

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Decomposition Goals

• Intuitive structural decomposition• Low decoupling• Sub-processes within the main process• SESE

• Hierarchy between components• Nested components• RPST

* Artem Polyvyanyy: Structuring Process Models. PhD Thesis. University of Potsdam (Germany), January 2012

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Structure instead of Behavior

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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

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SESE, Canonical SESE and RPST

• SESE : set of edges which subgraph has a Single Entry node and a Single Exit node

• Canonical SESE: not overlap with any other SESE

• Refined Process Structure Tree (RPST) containing the Canonical SESEs• Unique• Modular

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Example of SESE and RPST

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Conformance and Markings• The analysis is strongly depended on the markings

A

B

C

A

B

C

D

E

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Best Effort Analysis• Best Effort Analysis oriented to understanding, diagnosis

and testing

• Include artificial place when the entry (or exit) is a transition• Short-circuited the component to allow repetitions

• Heuristic based on invariants of the whole net

• Use of the particularities of the net• Safe, Sound, Bounded, …

• But at this point there are not guarantees for the general case

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Implementation

Package JorgeMunozGama

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Implementation

Package JorgeMunozGama

Process Conformance and Refinement 18

Published Work

9 Sep 2010

Hierarchical Conformance Checking of Process Models Based on Event Logs

J. Munoz-Gama, J. Carmona and W. van der AalstPetri Nets 2013

Valid Decomposition using SESE+RPST

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Hierarchy is not Decomposition• Hierarchy aids in the diagnosis• But does not make conformance computation faster• Actually, the conformance is computed much more times

• Possible to limit to some range of levels or to focus on particular part

• Not guarantees for the general case

• Can we achieve a decomposition of the conformance problem?• That reduces the time?• With guarantees on the fitness result?

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Partitioning the RPST• Any cut in the RPST is partitioning on the edges

• Algorithm to cut by the size of the component (k-partitioning)

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Properties of the Partitioning• It is faster …

• … but what about the guarantees?

• Decomposed Perfectly Fitting Checking: A model/log is perfectly fitting if and only if all the components are perfectly fitting

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SESE and Decomposed Perfectly Fitting

• SESEs (per se) do not satisfy the Decomposed Perfectly Fitting Checking property

• 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• Each place appears in precisely one of the subnets• Each edge appears in precisely one of the subnets• Transitions may appear in multiple subnets

• Invisible transitions must appear in precisely one subnet • Duplicate transitions must appear in precisely one subnet

* Wil M.P. van der Aalst: Decomposing Petri Nets for Process Mining: A Generic Approach. BPMCenter.org, 2012

Valid Decompositions satisfy Decomposed Perfectly Fitting Checking property !

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

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Results (1)

• 1 Net – 1h 15min• 7 Subnets – 2min

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Results (2)

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Topology

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Topology and NFCC and NFN

• Non Fitting Connected Components (NFCC)

• Non Fitting Net (NFN)

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Topology Algorithms on Large

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DivideAndConquer Package

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DecomposedConformance Package

Process Conformance and Refinement 33

Published Work

9 Sep 2010

Conformance Checking in the Large: Partitioning and Topology

J. Munoz-Gama, J. Carmona and W. van der AalstBusiness Process Management (BPM) 2013

Alignments and Fitnesson Valid Decompositions

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Adapted Cost Function

• Adapted Cost Function

Cost involving the task

# subnets having the task

• Theorem: The sum of the costs of all the subnets using the adapted cost function is a lower bound of the cost in overall alignment• Upper bound on the fitness

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Lower bound on the costs - Idea

AA

SN

SN1 SN2 SN3

BB

C-

DD

EE

FF

GG

-H

II

JJ

KK

LL

AA

BB

DD

EE

KK

LL

C-

AA

C-

FF

GG

-H

II

JJ

A-

CC

FF

GG

HH

II

JJ

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Stitching Check

SN1-SN2 SN2-SN3 SN1-SN3

AA

SN

BB

C-

DD

EE

FF

GG

-H

II

JJ

KK

LL

SN1AA

BB

DD

EE

AA

C-

FF

GG

-H

II

JJ

SN2

SN3KK

LL

C-

AA

AA

C-

C-

SN1

SN2

SN2

SN3The order of the

tasks matters

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Stitching Check Theorem

• Theorem: Given a trace, if it agrees on the stitching check, the sum of the costs using the adapted cost function is not a bound but the exact result.

• An optimal alignment for the whole trace can be constructed straightforward from the alignments of the subnets

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Stitching Check Corollary• Corollary: if all the shared transitions are synchronous

moves, is not a bound but exact.

• Interesting from a Diagnosis point of view

• Two optimal alignments: one with synchronous moves in the shared transitions, and the other no.

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Two possible optimal alignments

B-

AA

-B

CC

DD

EE

FF

-A

BB

A-

CC

DD

EE

FF

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Two possible optimal alignments

B-

AA

-B

-A

BB

A-

BB

DD

EE

BB

CC

EE

EE

FF

BB

DD

EE

BB

CC

EE

EE

FF

They do not agree on B (not even in the # occurrences

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Modified Alignment Algorithm• Modify the alignment algorithm to prioritize solutions with

synchronous moves for a given set of tasks (if exists)

Priority queue

10 10 10 11 11 12

12

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Estimating Fitness• If all traces in the log satisfy the stitching check the fitness

is exact (unlikely)• Just that one trace does not satisfy, the fitness is not

formally guaranteed• However, it must be experimentally accurate

10000 traces satisfy stitching check

1 trace not satisfy stitching check

fitness

The error is negligible

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Fitness Interval• Give the percentage of traces with exact value• But also a confidence interval on the fitness

Lower Bound of trace

Upper Bound of trace

fitness

fitness (if satisfy stitching check)

0 (if not satisfy stitching check)

• The bounds for the log are the average of the bounds per trace

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Merging Subnets• If they don’t agree, merge them

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Stitching Matrix• Stitching problems between subnets• Blueprint for merging

SN1 SN2 SN3

SN1

0 0 0

SN2

0 0 0

SN3

0 0 0

L

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Stitching Matrix• Stitching problems between subnets• Blueprint for merging

SN1 SN2 SN3

SN1

0 0 1

SN2

0 0 0

SN3

1 0 0

L

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Decomposed Conformance Algorithmdc (L,SN)

L[ ], SN[ ] = decompose (L, SN)

A[ ] = align (L[ ], SN[ ])

Lp, Ap[ ] = pass_stitching_check (L, A[ ])

Lf, Af[ ] = fail_stitching_check (L, A[ ])

while (not_final_condition)

Ms = stitching_matrix (Af[ ])

L[ ] = project_log (Lf, SN[ ])

A[ ] = align (L[ ], SN[ ])

Lp, Ap[ ] = Lp, Ap[ ] + pass_stitching_check (L, A[ ])

Lf, Af[ ] = fail_stitching_check (L, A[ ])

SN[ ] = merge_subnets (Ms)

compute_fitness (Ap[ ], Af[ ])

compute_alignments (Ap[ ])

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Conclusions• How SESE and RPST may help for diagnosis

• How to create Valid Decompositions from SESE• Partitioning the Problem• Bridging• Topology and Topological Algorithms

• Estimating fitness from Valid Decompositions• Stitching Check• Fitness Interval• Decomposed Conformance Algorithm

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Future Work• New approaches for creating Valid Decompositions

• Based on Transition-Separation Pairs• SESE+Passages

• Study on the decomposed fitness• When it’s more effective and when to stop• More complex merging strategies• Real-case scenarios

• Conformance Checking in Hierarchy

Thank You