Jorge Muñoz-Gama Universitat Politècnica de Catalunya (Barcelona, Spain) Algorithms for Process Conformance and Process Refinement.

Jorge Muñoz-Gama

Universitat Politècnica de Catalunya

(Barcelona, Spain)

Algorithms for Process Conformance and

Process Refinement

Process Conformance and Refinement

2

Outline

9 Sep 2010

Process Mining , Conformance and Refinement

Process Conformance Related Work and Motivation Approach Implementation and Results Extensions

Process Refinement Breaking Concurrencies Supervisory Control Refinement

Future Work and Conclusions


3

Process Mining

9 Sep 2010

* www.processmining.org


4

Refinement


9 Sep 2010

Petri Net

A B DA C D

Event Log

MDT

ETC Precision

Metric

Conformance

(Precision)

A D

C

B

AC

BD

Refined Model

Locate the inconsistencies

Measure the inconsistencies

More accurate model


5

Conformance Dimensions

9 Sep 2010

Fitness

Precision

Generalization

Structure

How much of the observed behavior is

captured by the model

Minimal structure which clearly reflect the

behavior

Models with minimal behavior to represent

accurately the log

Overly precise models which overfit the log


6

Outline

9 Sep 2010






7

Related Work

9 Sep 2010

Precision in the literature Most related work Rozinat et al. Information System 33 (2008) Metric for Precision in Petri Nets Computation of Follows and Precedes relations (Always,

Never, Sometimes) of Model and Log.

Measurement based on discrepancies in Sometimes relations Model relations require a model space state exploration

Coverability

Graph


8

Other Approaches and Motivation

9 Sep 2010

Other approaches as language equivalence or bisimilarity are not suitable for Process Conformance The complete models behavior is required

Goals and Requirements Precision Dimension Petri Nets Avoid the complete state space exploration Effort needed to obtain an accurate model Fine-level precision Locate the precision inconsistencies


9

Outline

9 Sep 2010






10

General Idea: Escaping Edges

9 Sep 2010

ModelBehavior

LogBehavior

ModelBehaviorEscaping

Edges


11

Conformance Route Map

9 Sep 2010

ModelStates

LogStates

Traversal

MDT

Metric

AC

BD

A B DA C D

Petri Net

Event Log


12

Log and Model States

9 Sep 2010

Log Incorporate state information in the log

(Aalst et al. Software and Systems Modeling, 2009) Past, Unlimited and Sequence

Model Markings of the Petri Net


13

Model States and Mapping

9 Sep 2010

Not all the reachable markings (could be infinite)

Only Markings with a Log State mapped on

Log and Model States Mapping i.e., reached marking after replay state prefix

A E

D

C

Bp1 p2 p3

A B Ep4 s1

p1

s2

p2

s3

p3

s4

p4p5

0 1 0 0 1…

0 1 0 0 n

p1 p2 p3 p4 p5

Markings not explored


14

Traversal

9 Sep 2010

Log-guided Traversal of Model Behavior Allowed Tasks :

i.e., actions enabled in that moment

Reflected Tasks : i.e., actions really executed (thus, annotated in the

log)

A E

D

C

Bp1 p2 p3 p4

A E

D

C

Bp1 p2 p3 p4

A B EA C E

<p2>BCD

A B EA C E

BC


15

Traversal (2)

9 Sep 2010

Escaping Edges : i.e., enabled actions not executed Precision discrepancies

A E

D

C

Bp1 p2 p3 p4

A B EA C E

BCD

BC

D


16

Precision Metric

9 Sep 2010

Take into account the Escaping Edges

Between 0 (imprecise) and 1 (precise) More frequent traces, more weight in the metric Independent of Structural dimension Globally precision Localizability

AP

HZ

Q

IA H I ZA P Q Z


17

Minimal Disconformant Traces (MDT)

9 Sep 2010

Localizability of precision inconsistencies

i.e., Minimal traces indicating where the model starts to deviate from the log

Algorithm to compute all MDT using Escaping Edges

Refinement

AnalysisPrecisionMDT

A EA B E

C D P Q

A D

C

B

Refined Petri Net


18

Outline

9 Sep 2010






19

Implementation

9 Sep 2010

ProM 6 Framework

ETConformance Plug-In


20

Results

9 Sep 2010


21

Results (2)

9 Sep 2010


22

Outline

9 Sep 2010






23

Invisible Tasks

9 Sep 2010

Enabled Tasks? C ? B and C ?A

A

A

C

Bp3

p4

... A C ...

Which Marking? <p4> ? <p3,p4> ?

INDETERMINISM

(Transitions associated with no event)


24

Invisible Tasks (2)

9 Sep 2010

Invisible Coverability Graph

Solutions Union of

Enabled Lazy Invisibles * One path only Shortest

Invisible Path *

<1, ω, 0>

<0, ω, 1>

<1, 0, 0>

<0, 0, 1>

Inv1

Inv3

Inv2

A,B

A,DC

A,C

A

D

B

X

XC

X

*Rozinat et al. Information System 33 (2008)


25

Duplicate Tasks

9 Sep 2010

Which Task? B ? B ?

INDETERMINISM

Solutions e.g. Look-ahead

AB

B

D

C

... A B C ...

(Several Transitions associated with the same event)


26

Variant: States as Markings

9 Sep 2010

States as Prefix

States as Markings

A

B

CA B C

A

B

CA B C

<p1><p2><p3>

C B

p1 p2 p3

2Escaping Edges

NO Escaping Edges


27

Variant: Non fitting models

9 Sep 2010

Symmetric to the Escaping Edges (Ee) Log Escaping Edges (LEe): The points where

the log deviates from the model

Fitness instead of Precision

ModelBehavio

r

LogBehavio

r

ModelBehavio

r

Escaping

Edges

LogEscapingBehavior


28

Outline

9 Sep 2010






29

Future Work: Refinement

9 Sep 2010

Refinement can be performed by a Domain Expert

Refinement

Breaking Concurrencie

s

Supervisory Control

AC

BD

Petri Net

Refined Petri Net

A D

C

BEvent Log

A EA B E

MDT

A EA B E

B H J G


30

Many causes for precision inconsistencies

Common one is Concurrency Concurrency in the model allowing several

possibilities But not in the log

Idea is to break the concurrency introducing a new place

We need concurrency relations of the Petri net, the log, and check the results of the new model

Breaking Concurrencies

9 Sep 2010


31

Concurrency: it exists a reachable marking that enables both transitions, and firing one does not disable the other.

Problematic for large nets Structural Concurrency

Best effort overapproximation for general Petri Nets Exact for live and bounded Free Choice systems Polynomial Algorithm

Kovalyov and Esparza , Proc. Intl. Workshop on Discrete Event Sytems, 1996

Breaking Concurrencies: Petri net

9 Sep 2010

A D

C

B


32

Not concurrencies but the absence of them Firing Causality Matrix:

Firing Causality:

Breaking Concurrencies: Log

9 Sep 2010

A B C D

0


33

Break the model concurrency with a place

Breaking Concurrencies

9 Sep 2010

A B C DA D

C

B


34

Supervisory Control

9 Sep 2010

Supervisory Control in Process Mining Santos et al. Supervisory Control Service (2010)

Supervisor

Model

MDT MDT Abstraction

Refined Model


35

Conclusions and Future Work

9 Sep 2010

New technique for precision between Petri nets and Log.

Avoids models state space exploration.

MDT, indicating the points where the model starts to deviates from the log.

Approach implemented as plug-in of ProM 6.

Breaking concurrencies to improve the precision.

Supervisory Control for precision refinement.


36

Thank You

9 Sep 2010

Thank You for Your Attention

Papers:

A fresh look at Precision in Process Conformance

Jorge Muñoz-Gama and Josep Carmona Business Process Management (BPM) 2010

Jorge Muñoz-Gama Universitat Politècnica de Catalunya (Barcelona, Spain) Algorithms for Process Conformance and Process Refinement.

Documents

process refinement1outline9

log state

state information

model states9

log aalst

state prefix aedcbp1p

refinement9process mining

refinement6process mining