decomposing data-aware conformance checking massimiliano de leoni, jorge munoz-gama, josep carmona,...

Decomposing Data-aware Conformance Checking

Massimiliano de Leoni, Jorge Munoz-Gama, Josep Carmona, Wil van der Aalst

PAGE 1

(a; {A = 3000;R = Michael; E = Pete}); (b; {V = OK;E = Sue});(c; {I = 530;D = OK;E = Sue});(f; {E = Pete});

Example: A Credit Institute

PAGE 2

For such a credit amount, should be interest <450

«Sue» not authorized to

perform b: is not Assistant

Activity h hasn’t been executed: D

cannot be OK

(a; {A = 3000;R = Michael; E = Pete}); (b; {V = OK;E = Pete});(c; {I = 530;D = OK;E = Sue}); (d, {I = 599; D = NOK; E = Sue});(f; {E = Pete});

(a; {A = 5001;R = Michael; E = Pete}); (b; {V = OK;E = Pete});(c; {I = 530;D = NOK;E = Sue}); (f; {E = Pete});

Activity d should have occurred, since amount<5000

Petri Net with Data : Variables and Read/Write Operations

PAGE 3

n1 n2

n3 n5 n6

Credit Request(a)

Register Negative Verification (d)

Inform Customers(e)

Renegotiate (f)

Open Credit Loan (h)

Assessment (c)Interests

Amount

Verification

Decision

Register Loan Rejection (g)


n4n4

Verify (b)Verify (b)

VariablesWrite Operations

Read Operations

Binding

• A binding is a triplet (t,r,w) where• t is the transition that fires• r: V U is the variables that are read along with the

values− dom(r) is the set of read variables− r(v) is the value read for variable v

• w: V U is the variables that are written along with the values− dom(w) is the set of read variables− w(v) is the value read for variable v

PAGE 4

A Sequence of bindings

PAGE 5

n1 n2

n3 n5 n6

Credit Request(a)


Inform Customers(e)

Renegotiate (f)



Amount

Verification

Decision



n4n4


Necessary condition for a binding (t,r,w): dom(r) and dom(w) coincides with the expected read and write operations.

Each transition is associated with all valid bindings

PAGE 6

n1 n2

n3 n5 n6

Credit Request(a)


Inform Customers(e)

Renegotiate (f)



Amount

Verification

Decision



n4n4


Transition Guard

Credit Request --

Verify 0.1 * r(A) < w(I) < 0.2 * r(A)

Assessment r(V) = true

Register Negative Verification r(V) = false AND w(D) = false

Inform Requester --

Register Loan Rejection r(D) = false

Open Credit r(D) = true

Alignments

PAGE 7

Move in both without incorrect write operations

Move in both withincorrect write operations

Move in log

Move in process

n1 n2

n3 n5 n6

Credit Request(a)


Inform Customers(e)

Renegotiate (f)



Amount

Verification

Decision



n4n4


Cost of alignments

• Each move is associated with a cost• Cost of alignment is the sum of the costs of its moves

: Cost of reading/writing a wrong value

<w> <z>

3 2 3 2

3 2 3 2

3 3

<x> <y>

1 2 1 2

2 2

2 2

3 2

3 2

3 2

: Cost of “move on log”

: Cost of not writing or reading a variable

: Cost of “move on model”

Cost of alignments: some examples

8 10

An optimal alignment: an

alignment with the lowest cost

Process: S – A – C – E – A – B - F Process: S {z=1, y=0} – A{x=10} – C{y=11} – E – A{x=3} – B{y=13} - F

Finding optimal alignments: Approach 1

1. Computing the control-flow alignment using existing techniques (the «Arya» technique)

PAGE 10

Log: S {z=10,y=0} – A{x=1} – C{y=11} – E – A{x=3} – B{y=13} -

2. Enriching the alignment with the data operations.

• The alignment is enriched, thus minimizing the cost of the alignment

• Naturally formulated as an Mixed Integer Linear Program

M. de Leoni, W.M.P. van der Aalst: Aligning event logs and process modelsfor multi-perspective conformance checking: An approach based on integer linearprogramming. Proceedings of BPM 2013

Finding optimal alignments: Approach 2

PAGE 11

Process: a b

Log: (a; {A = 3000;R = Michael; E = Pete}); – (b; {V = NOK; E = Sue});

Process: (a; {A = 3000;R = Michael; E = Pete}); – (b; {V = NOK; E = Sue});

F. Mannhardt, M. de Leoni, H. Reijers, W.M.P. van der Aalst: Balanced Multi-Perspective Checking of Process Conformance. Computing Journal, Springer (under review)

Finding an optimal alignments: complexity• Finding an optimal alignments is exponential on the size

of the model, i.e. the number of activities and data variables.

• IDEA: Divide-and-conquer approach • Petri Net with Data is decomposed into smaller fragments

that are checked separetely. • If the decomposition is valid

− Any trace is fitting the entire model if and only if it fits all smaller fragments.

PAGE 12

t1 t2 t3 t4 t6t5

t1 t2 t3

t3 t4

t6t5

Valid decomposition without data

• The following can only appear in precisely one fragment:1. Places

2. Invisible transitions

3. Visible transitions with the same label (name)

4. Arcs • Visible transitions with unique label may appear in

multiple fragments• Each variable appears in precisely one fragment• Each transition shared among fragments may read/write

different variables• The union of the fragments is the entire model

PAGE 13W.M.P. van der Aalst: Decomposing petri nets for process mining: A genericapproach. Distributed and Parallel Databases 31(4) (2013)

Valid decomposition with data

• The following can only appear in precisely one fragment:1. Places

2. Invisible transitions

3. Visible transitions with the same label (name)

4. Arcs • Visible transitions with unique label may appear in

multiple fragments• Each variable appears in precisely one fragment• Each transition shared among fragments may read/write

different variables• The union of the fragments is the entire model

PAGE 14

Instantation of Valid Decompositions

• Different strategies are possible.• We propose two strategies extending what exists for the

data-unaware case:• Maximal Decomposition• SESE-based decomposition

PAGE 15

n1 n2

n3 n5 n6

Credit RequestRegister Negative

Verification

Inform Customers

Renegotiate

Open Credit Loan

AssessmentInterests

Amount

Verification

Decision

Register Loan Rejection Register Loan Rejection

n4n4

VerifyVerify

Maximal Decomposition

• Construction the smallest components that satisfy the Valid Decomposition Definition

• Variables and Places are mutually exclusive

n3Verify

Register Negative Verification

Assessment

n2Credit Request

Verify

Renegotiate

n1Credit Request


Inform Customers

Assessment

n4n4n5

Inform Customers

Renegotiate

Open Credit Loan


n6

Open Credit Loan


Verify

Register Negative Verification Open Credit Loan

Assessment

Verification Decision


Credit Request

Verify

Renegotiate

Interests

Amount

SESE-based Algorithm

PAGE 17

n1 n2 n3 n5 n6Credit Request Verify


Inform Customers

Renegotiate

Open Credit Loan

AssessmentRegister Loan Rejection Register Loan Rejection

n4n4

a bc

de

g

f

h

i

j

lk

m n

po

S1S2

S8S3

S4

S9

S5

S10

S7

S6

S1

S8 S2

S9 S10 S4 S3

S5

S6 S7

a b

m n o p k l

c d i j

e f g h

a) Petri Net

b) Workflow graph and SESEs

c) RPST

Example of the SESE-based Algorithm(k = 2)

PAGE 18

n3Verify


Assessment

n2Credit Request

Verify

Renegotiate

n1Credit Request


Inform Customers

Assessment

n4n4

n5

Renegotiate

Open Credit Loan


n6

Open Credit Loan


Verify

Register Negative Verification Open Credit Loan

Assessment

Verification Decision


Credit Request

Verify

Renegotiate

Interests

Amount

Implementation

Available in the package DataConformanceChecker

PAGE 19

Experiments

• Generating different event logs with 5000 traces with a different average trace length • This ensured by enforcing a larger number of credit renegotiations

• 20% of the transition firings are so as to not satisfy the guards

PAGE 20

n1 n2

n3 n5 n6

Credit RequestRegister Negative

Verification

Inform Customers

Renegotiate

Open Credit Loan

AssessmentInterests

Amount

Verification

Decision


n4n4

VerifyVerify

Results: an exponential reduction of the computation time

PAGE 21

5 10 15 20 25 3010000

100000

1000000

10000000

No Decomposition

SESE-based decomposition (k=2)

Average number of events per event-log trace

Com

puta

tion

Tim

e (in

sec

onds

)

Projection on the model

• For each transition t:• n = number of fragments in which t occurs• is the i-th fragment in which t occurs.

PAGE 22

𝑓𝑖𝑡𝑇𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑜𝑛 (𝑡 )=1−∑𝑖=1

𝑛 ¿ 𝑐𝑜𝑟𝑟𝑒𝑐𝑡(𝑡 ,𝐷𝑃𝑁 (𝑡 )𝑖)¿ 𝑡𝑜𝑡𝑎𝑙(𝑡 ,𝐷𝑃𝑁 (𝑡 )𝑖)

𝑛

#correct(t,DPN) = number of moves in both without

incorrect write operations for t in the alignments between each log trace and DPN

#total(t,DPN) = number of moves for t in the alignments of each log trace and DPN

Projection on the model based on decomposition is an approximation!

PAGE 23

t1 t2 t3 t4 t6t5

t1 t2 t3

t3 t4

t6t5

No decomposition Decomposition

Move in both without incorrect write operations for t

Move in both without incorrect write operations for t in all fragments containing t

• Move in both with incorrect write operations for t

• Move in log• Move in move

The same move for t in at least one of fragments containing t

Projection on the model (without decomposition)

PAGE 24

With decomposition

Without decomposition

Conclusion

• Finding an alignment is exponential in the model size • To speed the computation:

1. Decompose the model in submodels

2. Alignment each trace with each submodel• The decomposition needs to be valid:

Any trace is fitting the entire model if and only if it fits all smaller fragments.

• A more extensive evaluation is needed • Using real processes• Synthetic data referring to models with dozens of

transitions

PAGE 25

decomposing data-aware conformance checking massimiliano de leoni, jorge munoz-gama, josep carmona,...

Documents

michael e

credit institutepage

jorge munozgama

josep carmona