1. Measuring the Precision of
Multi-perspective
Process Models
Felix Mannhardt
joint work with
Massimiliano de Leoni, Hajo A. Reijers,
Wil M.P. van der Aalst

2. Precision
Department of Mathematics and Computer Science PAGE 1 / 8
“Flower Model” lacking any precision
B
C
A

3. Precision of Multi-perspective Process Models
Department of Mathematics and Computer Science PAGE 2 / 8
A 𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 𝐴
B
𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 𝐵
𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 𝐵 > 𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 𝐴
Existing work ignores added precision
by multi-perspective rules / constraints

4. Approach: Multi-perspective Precision
Department of Mathematics and Computer Science PAGE 3 / 8
Multi-perspective
Process Model (P)
Fitting Event
Log (L)
Precision
[0..1]
INPUT OUTPUT
APPROACH
𝒆 ∈𝑳
𝒐𝒃𝒔𝒆𝒓𝒗𝒆𝒅 𝑷 (𝒆)
𝒑𝒓𝒆𝒄𝒊𝒔𝒊𝒐𝒏(𝑷, 𝑳) =
𝒆 ∈𝑳
𝒑𝒐𝒔𝒔𝒊𝒃𝒍𝒆 𝑷(𝒆)

5. Precision: Observed / Possible Behavior
Department of Mathematics and Computer Science PAGE 4 / 8
C Id Event Loan obs pos
1 𝑒1 Handle Request 800
1 𝑒2 Simple Check -
1 𝑒3 Decide -
2 𝑒4 Handle Request 1800
2 𝑒5 Ext. Check -
2 𝑒6 Decide -
𝒐𝒃𝒔 𝑷 𝒆 𝟏 = { Handle Request } = 𝟏
𝒑𝒐𝒔 𝑷 𝒆 𝟏 = Handle Request = 𝟏
𝒔𝒕𝒂𝒕𝒆 𝒆 𝟏 = (< >, { })
C Id Event Loan obs pos
1 𝑒1 Handle Request 800 1 1
1 𝑒2 Simple Check -
1 𝑒3 Decide -
2 𝑒4 Handle Request 1800
2 𝑒5 Ext. Check -
2 𝑒6 Decide -
C Id Event Loan obs pos
1 𝑒1 Handle Request 800 1 1
1 𝑒2 Simple Check - 1 1
1 𝑒3 Decide -
2 𝑒4 Handle Request 1800
2 𝑒5 Ext. Check -
2 𝑒6 Decide -𝒐𝒃𝒔 𝑷 𝒆 𝟐 = { Simple Check } = 𝟏
𝒑𝒐𝒔 𝑷 𝒆 𝟐 = Simple Check = 𝟏
𝒔𝒕𝒂𝒕𝒆 𝒆 𝟐 = (< 𝐻 >, { 𝐿 = 800 })
C Id Event Loan obs pos
1 𝑒1 Handle Request 800 1 1
1 𝑒2 Simple Check - 1 1
1 𝑒3 Decide - 1 1
2 𝑒4 Handle Request 1800
2 𝑒5 Ext. Check -
2 𝑒6 Decide -
𝒐𝒃𝒔 𝑷 𝒆 𝟑 = { Decide } = 𝟏
𝒑𝒐𝒔 𝑷 𝒆 𝟑 = Decide = 𝟏
𝒔𝒕𝒂𝒕𝒆 𝒆 𝟑 = (< 𝐻, 𝑆 >, { 𝐿 = 800 })
C Id Event Loan obs pos
1 𝑒1 Handle Request 800 1 1
1 𝑒2 Simple Check - 1 1
1 𝑒3 Decide - 1 1
2 𝑒4 Handle Request 1800 1 1
2 𝑒5 Ext. Check -
2 𝑒6 Decide -
𝒐𝒃𝒔 𝑷 𝒆 𝟒 = { Handle Request } = 𝟏
𝒑𝒐𝒔 𝑷 𝒆 𝟒 = Handle Request = 𝟏
𝒔𝒕𝒂𝒕𝒆 𝒆 𝟒 = (<>, { })
C Id Event Loan obs pos
1 𝑒1 Handle Request 800 1 1
1 𝑒2 Simple Check - 1 1
1 𝑒3 Decide - 1 1
2 𝑒4 Handle Request 1800 1 1
2 𝑒5 Ext. Check - 1 2
2 𝑒6 Decide -𝒐𝒃𝒔 𝑷 𝒆 𝟓 = { Ext. Check } = 𝟏
𝒑𝒐𝒔 𝑷 𝒆 𝟓 = Ext. Ce𝑐𝑘, 𝑆𝑖𝑚𝑝𝑙𝑒 𝐶ℎ𝑒𝑐𝑘 = 𝟐
𝒔𝒕𝒂𝒕𝒆 𝒆 𝟓 = (< 𝐻 >, { 𝐿 = 1800 })
C Id Event Loan 𝒐𝒃𝒔 𝑷 𝒑𝒐𝒔 𝑷
1 𝑒1 Handle Request 800 1 1
1 𝑒2 Simple Check - 1 1
1 𝑒3 Decide - 1 1
2 𝑒4 Handle Request 1800 1 1
2 𝑒5 Ext. Check - 1 2
2 𝑒6 Decide - 1 1
𝒐𝒃𝒔 𝑷 𝒆 𝟔 = Decide = 𝟏
𝒑𝒐𝒔 𝑷 𝒆 𝟔 = 𝐷𝑒𝑐𝑖𝑑𝑒 = 𝟏
𝒔𝒕𝒂𝒕𝒆 𝒆 𝟔 = (< 𝐻, 𝐸 >, { 𝐿 = 1800 })
C Id Event Loan 𝒐𝒃𝒔 𝑷 𝒑𝒐𝒔 𝑷
1 𝑒1 Handle Request 800 1 1
1 𝑒2 Simple Check - 1 1
1 𝑒3 Decide - 1 1
2 𝑒4 Handle Request 1800 1 1
2 𝑒5 Ext. Check - 1 2
2 𝑒6 Decide - 1 1
6 7
𝒐𝒃𝒔 𝑷 𝒆 = { observed activities at state }
𝒑𝒐𝒔 𝑷 𝒆 = | 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑎𝑐𝑡𝑖𝑣𝑖𝑡𝑖𝑒𝑠 𝑎𝑡 𝑠𝑡𝑎𝑡𝑒 |
𝒔𝒕𝒂𝒕𝒆 𝒆 = 𝑠𝑡𝑎𝑡𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑟𝑜𝑐𝑒𝑠𝑠 𝑚𝑜𝑑𝑒𝑙
𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 𝑃, 𝐿 =
𝑒∈𝐿 𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝑃(𝑒) = 6
𝑒∈𝐿 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑃(𝑒) = 7
≈ 𝟎. 𝟖𝟔

6. Full Example for Model A & Model B
Department of Mathematics and Computer Science PAGE 5 / 8
A
C Id Event Loan 𝒐𝒃𝒔 𝑷 𝒑𝒐𝒔 𝑷
1 𝑒1 Handle Request 800 1 1
1 𝑒2 Simple Check - 1 2
1 𝑒3 Decide - 1 1
2 𝑒4 Handle Request 1800 1 1
2 𝑒5 Extensive Check - 2 2
2 𝑒6 Decide - 1 1
3 𝑒7 Handle Request 1800 1 1
3 𝑒8 Simple Check - 2 2
3 𝑒9 Decide - 1 1
4 𝑒10 Handle Request 2500 1 1
4 𝑒11 Extensive Check - 1 2
4 𝑒12 Decide - 1 1
14 16
Model A
𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 𝑃, 𝐿 =
𝑒∈𝐿 𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝑃(𝑒) = 14
𝑒∈𝐿 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑃(𝑒) = 16
≈ 𝟎. 𝟖𝟕𝟓
B
C Id Event Loan 𝒐𝒃𝒔 𝑷 𝒑𝒐𝒔 𝑷
1 𝑒1 Handle Request 800 1 1
1 𝑒2 Simple Check - 1 1
1 𝑒3 Decide - 1 1
2 𝑒4 Handle Request 1800 1 1
2 𝑒5 Extensive Check - 2 2
2 𝑒6 Decide - 1 1
3 𝑒7 Handle Request 1800 1 1
3 𝑒8 Simple Check - 2 2
3 𝑒9 Decide - 1 1
4 𝑒10 Handle Request 2500 1 1
4 𝑒11 Extensive Check - 1 1
4 𝑒12 Decide - 1 1
14 14
Model B
𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 𝑃, 𝐿 =
𝑒∈𝐿 𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝑃(𝑒) = 14
𝑒∈𝐿 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑃(𝑒) = 14
≈ 𝟏

7. Evaluation on Road Fines Log
0.30
0.36
0.64
0.83
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Inductive Miner Inductive Miner &
Rules
Normative Model Normative Model &
Rules
ETC Precision Precision Fitness

8. Summary
Department of Mathematics and Computer Science PAGE 7 / 8
• 1st precision measure for
multi-perspective process models
− Fast to calculate
− Flexible framework
− Implemented in ProM
• Preliminary Evaluation
− Illustrative examples
− Real-life dataset with > 500,000 events
Handle
750
Simple Decide
Handle
1250
Ext. Decide
Handle
5000
Simple Decide
Handle
750
Simple Decide
Handle
1500
Simple Decide
precision [0..1]

9. Department of Mathematics and Computer Science
Image source: http://commons.wikimedia.org/wiki/File:Pictofigo_-_Idea.png
Questions? Remarks? Ideas?