Efficient Process Model Discovery Using Maximal Pattern Mining
- 1. Maximal Pattern Mining Veronica Liesaputra1, Sira Yongchareon1 & Shivadon Chaisiri2 1Unitec Institute of Technology & 2University of Waikato New Zealand
- 2. Background Businesses use process models to help them monitor and improve their performance Hand-made High level and understandable Do not align with reality Incorrect decisions Abundance of event data Generates models based on real processes process mining
- 3. Event Log Trace: Sequentially recorded events START Turn on hot & cold water Check whether it is too hot/cold Wait for 2 minutes Check whether it has enough water Wait for 2 minutes Check whether it has enough water Turn Off hot & cold taps END Event name, agent, timestamp, resource, input and output data To simplify, we only consider the event’s name • Represent each event with symbols 𝑎𝑎, 𝑏𝑏, 𝑐𝑐, 𝑒𝑒, 𝑓𝑓, 𝑒𝑒, 𝑓𝑓, 𝑔𝑔, ℎ a b d e g h c f
- 4. Process Discovery Given a set of traces { 𝑎𝑎, 𝑏𝑏, 𝑐𝑐, 𝑒𝑒, 𝑓𝑓, 𝑒𝑒, 𝑓𝑓, 𝑔𝑔, ℎ , 𝑎𝑎, 𝑏𝑏, 𝑐𝑐, 𝑑𝑑, 𝑐𝑐, 𝑑𝑑, 𝑐𝑐, 𝑑𝑑, 𝑒𝑒, 𝑓𝑓, 𝑔𝑔, ℎ } find the actual model Criteria3 Can model complex constructs: Sequence, Optionality, Concurrency, Duplicate tasks, Non-free choice, Self/Nested loops, Hidden tasks Able to handle noise & incomplete logs No over-fitting & under-fitting Simple & Fast a b d e g h c f 3Buijs, J.C.A.M., van Dongen B.F., van der Aalst, W. M. P. (2014) Quality Dimensions in Process Discovery: The importance of fitness, precision, generalization & simplicity
- 5. Existing approaches4 Noise Duplicates tasks Hidden tasks Non-free choice Loops Sound Approach α++ 2 events Heuristics 2 events Genetic Trace AGNEs Trace ILP Trace 4De Weerdt, J., Baesens, B., Vanthienen, J. (2012) Business process discovery: new techniques and applications
- 6. Maximal Pattern Mining Goal: To find maximal patterns that cover most of the traces in the logs Find loops Store frequent patterns and events in vertical format Identify concurrent events Discover events sequential order Check for loops Prune non-maximal patterns Generate graph
- 7. Notations Logs T = {t0 , t1 … tn} T = {〈a,b,c,b,b,c,d,e〉, 〈a,b,c,b,b,c,d,e〉, 〈a,b,b,c,e,d〉} Trace tn = 〈z0 , z1 … zm〉 t2 = 〈a,b,b,c,e,d〉 Maximal Pattern P = {p0 , p1 … pi} P = {〈a, (b*, c)*, {d, e}〉} Pattern pi = 〈e0, e1 … ej〉 Event: a, d, e Parallelization: {d, e} Loops: b*, (b*, c)* Support a.support = 3 p0.support = 3 a b c d e AND AND
- 8. Loops t0 = 〈a, b, d, d, c, b, b, b, d, c, b, d, c, g, g〉 Self loop 〈a, b, d*, c, b*, d, c, b, d, c, g*〉 Nested Loop 〈a, (b, d*, c)*, g*〉 a b cd g
- 9. Vertical Representation Patterns are stored as an IdList in bitset representation5 P = {〈a, (b*, c)*, d, e, a〉,〈a, b*, c, e, d, a〉,〈e, d, a〉} a b c d e $ id pos id pos id pos id pos id pos id pos 0 0, 5 0 1 0 2 0 3 0 4 0 6 1 0, 5 1 1 1 2 1 4 1 3 1 6 2 2 2 1 2 0 2 3 5Ayres, J., Flannick, J., Gehrke, J., Yiu, T. (2002) Sequential pattern mining using a bitmap representation
- 10. Vertical Representation Patterns are stored as an IdList in bitset representation5 Noisy data Keeps only frequent events (vk.support ≥ threshv) and patterns (pi.support ≥ threshp) Validation set for parameter tuning Frequent events/sub-patterns generate frequent super-patterns Joint operations to calculate support Only requires a single scan through the logs Fast and memory efficient 5Ayres, J., Flannick, J., Gehrke, J., Yiu, T. (2002) Sequential pattern mining using a bitmap representation
- 11. Concurrency T = {〈c, a, b, d〉, 〈c, a, d, b〉, 〈c, d, a, b〉, 〈a, c, d, b, a, b, c, d〉} Check for possible cases of parallelization Ignore order within parallelizations for now 〈c, a, b, d〉, 〈c, a, d, b〉 〈c, a, {b, d}〉 〈c, a, {b, d}〉, 〈c, d, a, b〉 〈c, {a, b, d}〉 Handle incomplete logs: Sub-pattern ⊆ super-pattern 〈c, {a, b, d}〉, 〈a, c, d, b, a, b, c, d〉 〈{a, b, c, d}〉, 〈{a, b, c, d}, a, b, c, d〉 a b dc AND AND
- 12. Concurrency T = {〈c, a, b, d〉, 〈c, a, d, b〉, 〈c, d, a, b〉, 〈a, c, d, b, a, b, c, d〉} Check for possible cases of parallelization Store event order for incomplete inclusion 〈c, a, {b, d}〉, 〈c, d, a, b〉 〈c, {a, b, d}〉 𝑎𝑎 → 𝑏𝑏 but 𝑏𝑏 ↛ 𝑎𝑎 : a b 𝑎𝑎 → 𝑑𝑑 and 𝑑𝑑 → 𝑎𝑎 : {a, d} 〈c, a, {b, d}〉, 〈c, d, a, b〉 〈c, {(a, b), d}〉 〈c, {(a, b), d}〉, 〈a, c, d, b, a, b〉 〈{(a, b), (c, d)}〉, 〈{(a, b), (c, d)}, a, b, c, d〉 𝑐𝑐 → 𝑑𝑑 but 𝑑𝑑 ↛ 𝑐𝑐 : c d a b dc AND AND
- 13. Concurrency T = {〈c, a, b, d〉, 〈c, a, d, b〉, 〈c, d, a, b〉, 〈a, c, d, b, a, b, c, d〉} Check for possible cases of parallelization Store event order for incomplete inclusion Solve loops 〈{(a, b), (c, d)}, a, b, c, d〉 〈{(a, b), (c, d)}*〉 a b dc AND AND
- 14. Maximal Patterns P = {〈a, b, c, d, e〉, 〈a, {b, c*}, d, e〉, 〈a, b, c, e〉, 〈a, f, e〉, 〈f, g〉, 〈f, h〉} Pattern pi is maximal ⟺ no other pattern pj in P covers the same or more traces P = {〈a, {b, c*}, d, e〉, 〈a, b, c, e〉, 〈a, f, e〉, 〈f, g〉, 〈f, h〉} a b d c AND XOR XOR XORAND ∅ XOR f eXOR f XOR XOR g h XOR
- 15. Loops {ABCE, ACBE, ABDDCE} α++ MPM
- 16. Duplicates {ADAF, AEAF, AHBAG, AHCAG} Heuristic Miners MPM A H G B F E D C XORA H XOR D E XOR XOR B C XOR A F A G XOR
- 17. Non-free choice {ABC, ABDE, ADBE} AGNEs MPM A C ED B
- 18. Duplicates in Parallel {ACBA, ACAB, CAAB, CABA, ABCA} Genetic Miner MPM AND AND C A A B XOR A B C XORAND AND
- 19. Evaluation Criteria3: Replay fitness: Alignment distance function6 Simplicity3 Precision (no under-fit)7 Generalization (no over-fit): k-fold cross validation Time van der Aalst, W. M. P., Adriansyah, A., van Dongen, B. (2012) Replaying History on Process Models for Conformance Checking & Performance Analysis Adriansyah, A., Munoz-Game, J., Carmona, J., van Dongen, B.F., van der Aalst, W.M.P. (2015) Measuring Precision of Modeled Behaviour 3Buijs, J.C.A.M., van Dongen B.F., van der Aalst, W. M. P. (2014) Quality Dimensions in Process Discovery: The importance of fitness, precision, generalization & simplicity 6 7
- 20. Synthetic data 300 to 350 traces with max. 10 unique events α++: Under-fits & unsound Genetic: Duplicates & very slow ILP: Under-fits & slow MPM: Duplicates Heuristics & AGNEs: Mid-range Fitness Precision Simplicity Time α++ 0.7 0.5 1.0 250 ms Genetic 0.9 0.9 0.7 1 hour Heuristics 0.8 0.7 0.8 10 s AGNEs 0.8 0.8 0.6 5 mins ILP 1.0 0.6 0.9 2 mins MPM 1.0 0.9 0.7 150 ms Fitness Precision Simplicity Time α++ 3 3 1 1 Genetic 1 1 3 4 Heuristics 2 3 2 2 AGNEs 2 2 3 3 ILP 1 3 1 3 MPM 1 1 3 1
- 21. Real-life data Similar results α++ : Under-fits & unsound Genetic: Very slow ILP: Under-fits & slow MPM: Duplicates Heuristics: Unsound & slow AGNEs: Incorrect false negatives Fitness Precision Simplicity Time α++ 0.3 0.4 0.9 10 mins Genetic DNF DNF DNF >5 days Heuristics 0.7 0.8 0.8 1 hour AGNEs 0.5 0.6 0.3 20 hours ILP 1.0 0.5 0.8 2 hours MPM 0.9 0.9 0.7 9 mins Fitness Precision Simplicity Time α++ 4 3 1 1 Genetic - - - - Heuristics 2 1 1 2 AGNEs 3 2 3 3 ILP 1 3 1 2 MPM 1 1 2 1
- 22. Conclusions MPM Can model complex constructs: Sequence, Optionality, Concurrency, Duplicate tasks, Non-free choice, Self/Nested loops, Hidden tasks Cannot handle duplicate tasks in parallel processes Able to handle noise & incomplete logs No over-fitting & under-fitting Fast Capable of stream mining Uses duplicate events Low simplicity score Task abstractions