Chapter 4 PROCESS DISCOVERY TECHNIQUES RECOMMENDATION
4.2. Process Discovery Recommendation Framework
4.2.3. Knowledge data base construction
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Definition 4.19 (Improved reachable dependency related to invisible tasks)
Let A be a set of activities, L be an event log over A, me be an activity from A, x,y be two invisible tasks, the improved reachable dependencies related to invisible tasks in a non- free choice are defined as follows:
𝑥 ⊱𝐿 𝑚 ⇔ ∃(𝑎=⊥ ∨ 𝑎∈𝐿) ∧ 𝑏∈𝐿 (𝑎 →𝐿 𝑥) ∧ (𝑥 →𝐿 𝑏) ∧ 𝑏 ⊱𝐿,𝑝𝑟𝑒=𝑎 𝑚 ∧
∄𝒏∈𝝈 𝒃 ⊱𝑳,𝒑𝒓𝒆=𝒂𝒏 ,
𝑚 ⊱𝐿 𝑥 ⇔ ∃ 𝑎∈𝐿 ∧(𝑏∈𝐿 ∨ 𝑏=⊤) (𝑎 →𝐿 𝑥) ∧ (𝑥 →𝐿 𝑏) ∧ 𝑚 ⊱𝐿,𝑝𝑟𝑒=𝑏𝑎 ∧
∄𝒏∈𝝈 𝒎 ⊱𝑳,𝒑𝒓𝒆=𝒏 𝒂 ,
𝑥 ⊱𝐿 𝑦 ⇔ ∃(𝑎1=⊥ ∨ 𝑎1∈𝐿) ∧ 𝑏1∈𝐿 ∧ 𝑎2∈𝐿 ∧ (𝑏2∈𝐿 ∨ 𝑏2=⊤) (𝑎1 →𝐿 𝑥) ∧ (𝑥 →𝐿 𝑏1)
∧ (𝑎2 →𝐿 𝑦) ∧ (𝑦 →𝐿 𝑏2) ∧ 𝑏1 ⊱𝐿,𝑝𝑟𝑒=𝑎1,𝑝𝑜𝑠𝑡=𝑏2 𝑎2 ∧ ∄𝒏∈𝑳 𝒃𝟏⊱𝑳,𝒑𝒓𝒆=𝒂𝟏,𝒑𝒐𝒔𝒕=𝒃𝒏 𝒂𝟐.
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Skip in parallel (IvT − LS𝑝𝑎𝑟), invisible tasks of type Long-Redo in sequence (IvT − LR𝑠𝑒𝑞), invisible tasks of type Long-Redo in parallel (IvT − LR𝑝𝑎𝑟), non-free choice construct (NFC), and invisible tasks involved in a non-free choice construct (IvT-NFC).
(a) Algorithms classification based on their ability in mining complex constructs There are plenty of empirical studies on the capability of process discovery techniques in mining complex constructs. However, most of studies focus on a small number of algorithms or on the most frequently used ones. Moreover, they do not evaluate the ability of algorithms in discovering all types of complex constructs. Therefore, we generated event logs containing all types of aforementioned complex constructs. We imported the event logs with the ProM tool and ran the plugin of each of the aforementioned algorithms.
𝛼 algorithm and 𝛼+algorithm were not evaluated because we know before that 𝛼 algorithm cannot discover the complex constructs and 𝛼+algorithm can discover from complex constructs only the two types of short loops (𝐿1𝑝 and 𝐿2𝑝 ). We ran the experiments on the rest of algorithms. The results shows that 𝛼++algorithm can correctly discover the two types of short loops and the three types of non-free choice constructs while it is incapable of discovering all types of invisible tasks and IvT-NFC. 𝛼#algorithm is able of mining 𝐿1𝑝, 𝐿2𝑝, IvT − SS𝑠𝑒𝑞, IvT − SR𝑠𝑒𝑞, IvT − LS𝑠𝑒𝑞, IvT − LR𝑠𝑒𝑞 whereas it is unable of discovering IvT − SS𝑝𝑎𝑟, IvT − SR𝑝𝑎𝑟, IvT − LS𝑝𝑎𝑟, IvT − LR𝑝𝑎𝑟, IvT − SW, NFC, and IvT − NFC. Inductive miner can discover correctly the two types of short loops, seven types of invisible tasks. However, this latter cannot detect one type of invisible tasks which are of type Switch and of type Short Redo in parallel, non-free choice constructs and invisible tasks involved in a non-free choice construct. Heuristic miner is capable of mining invisible tasks of types IvT − LR𝑠𝑒𝑞, IvT − SS𝑠𝑒𝑞, IvT − LS𝑠𝑒𝑞, IvT − LS𝑝𝑎𝑟, IvT − SW, a similar behaviour to short loops of type 𝐿2𝑝, but it cannot discover short loops of type 𝐿1𝑝, invisible tasks of types IvT − SR𝑠𝑒𝑞, IvT − SR𝑝𝑎𝑟, IvT − SS𝑝𝑎𝑟, non-free choice constructs, and invisible tasks involved in a non-free choice construct. Integer linear programming miner (ILP) can mine the two types of short loops, whereas it cannot discover all types of invisible tasks, non-free choice constructs, and invisible tasks involved in a non-free choice construct. Evolutionary Tree Mine (ETM) is capable of discovering short loops of types 𝐿1𝑝, invisible tasks of types IvT − SS𝑠𝑒𝑞, IvT − LS𝑠𝑒𝑞 while it is incapable of mining short loops of type 𝐿2𝑝, invisible tasks of types IvT − SR𝑠𝑒𝑞, IvT − SR𝑝𝑎𝑟, IvT − LR𝑠𝑒𝑞, IvT − LR𝑝𝑎𝑟, IvT − SS𝑝𝑎𝑟, IvT −
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LS𝑝𝑎𝑟, IvT − SW, non-free choice constructs, and invisible tasks involved in a non-free choice construct. Region miner (RM) is able of deriving short loops of type 𝐿2𝑝, invisible tasks of type similar behaviour to IvT − LR𝑠𝑒𝑞, while it cannot discover short loops of types 𝐿1𝑝, the rest of invisible tasks, non-free choice constructs, and IvT − NFC. Transition system (TS) can derive short loops of types 𝐿2𝑝 and similar behaviour to 𝐿1𝑝, invisible tasks of types IvT − SS𝑠𝑒𝑞, similar behaviour to IvT − SR𝑠𝑒𝑞, similar behaviour to IvT − SS𝑝𝑎𝑟. However, this technique cannot discover IvT − LR𝑠𝑒𝑞, IvT − LR𝑝𝑎𝑟, IvT − LS𝑠𝑒𝑞, IvT − LS𝑝𝑎𝑟, non- free choice constructs, and invisible tasks involved in a non-free choice structure. Disjunctive Workflow Schema (DWS) algorithm can mine short loops of type, invisible tasks of types IvT − SS𝑠𝑒𝑞, IvT − SR𝑠𝑒𝑞, IvT − LS𝑠𝑒𝑞, IvT − LR𝑠𝑒𝑞, IvT − SW. Nevertheless, it cannot derive short loops of types 𝐿1𝑝, all invisible tasks that are involved in a parallel construct, non-free choice constructs, and invisible tasks involved in a non-free choice construct. Finally, genetic miner (GM) can discover all constructs except invisible tasks of type IvT − SS𝑝𝑎𝑟, non-free choice constructs, and IvT − NFC. The abilities of these algorithms in mining the complex constructs are summarized in Table 4.1.
Table 4.1. Comparison of the ability of current algorithms in mining standard and complex constructs
𝜶++ 𝜶# IM HM ILP ETM RM TS DWS GM
𝐋𝟏𝐩 Yes Yes Sb No Yes Yes No Sb No Yes
𝐋𝟐𝐩 Yes Yes Yes Sb Yes No Yes Yes Yes Yes
𝐈𝐯𝐓𝐒𝐑𝐬𝐞𝐪 Sb Yes Yes No No No No Sb Yes No
𝐈𝐯𝐓𝐋𝐑𝐬𝐞𝐪 No Yes Yes Yes No No Sb No Yes Yes
IvTSRpar No No No No No No No No No No
IvTLRpar No No Yes No No No No No No Yes
𝐈𝐯𝐓𝐒𝐒𝐬𝐞𝐪 No Yes Yes Yes No Yes No Yes Yes Yes
𝐈𝐯𝐓𝐒𝐒𝐩𝐚𝐫 No No Yes No No No No Sb No No
𝐈𝐯𝐓𝐋𝐒𝐬𝐞𝐪 No Yes Yes Yes No Yes No No Yes Yes
𝐈𝐯𝐓𝐋𝐒𝐩𝐚𝐫 No No Yes Yes No No No No No Yes
𝐈𝐯𝐓𝐒𝐖 No Yes No Yes No No No No Yes Yes
NFC Yes No No No No No No No No Yes
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𝑰𝒗𝑻𝒊𝒏−𝑵𝑭𝑪 No No No No No No No No No No
There is no discovery algorithm capable of discovering invisible tasks of type Short Redo in parallel and invisible tasks involved in a non-free choice constructs. Only 𝛼$ algorithm can discover these two types of invisible tasks. However, this algorithm is not implemented in ProM. Therefore, we exclude the detection of invisible tasks of types IvT − SRpar and IvT − NFC.
(b) Mining time based classification of discovery algorithms
Process model discovery time may differentiate from algorithm to algorithm. Most of existing algorithms may take milliseconds to few minutes based on the size of the event logs to discover a process model. However, there are some algorithms which can take a long time to derive a process model such as genetic miner. This latter takes a long time in mining a process model even with a small event log and for big event log, it may run forever. Therefore, genetic algorithm might be the last candidate process discovery algorithm to recommend. The Evolutionary tree miner and Integer linear programing algorithms also take two much time to discover a model. Genetic miner takes time more than ETM and ETM takes time more than the ILP algorithm, and these three algorithms take time compared to the rest of algorithms.
(c) Algorithms classification based on their ability in discovering sound models.
There are process discovery algorithms that are not guaranteed to discover sound models. 𝛼 algorithm series and heuristic miner might produce process models that are not sound. They may contain problems such as deadlocks, livelocks, etc. The inductive miner and ILP miner can guarantee soundness of discovered models (Jouck et al., 2018). A process model that is not sound cannot replay traces until the end.
Conclusion
In this chapter, we proposed a framework for recommending the suitable process discovery algorithm to a given event log. The proposed methodology consists of detecting the complex control flow constructs existing in event log without discovering any model. Then recommending the best algorithm to a given event log based on a knowledge database containing information of the ability of existing algorithms on mining complex constructs, based on computation time, and based on the ability of model on discovering sounds models.
The complex control-flow constructs detection is based on the relations introduced in Alpha
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algorithms (𝛼++, 𝛼#, 𝛼$), but in this work, the relations are used and improved to detect complex constructs from event logs without discovering any process model.
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Chapter 5 RECOMMENDATION FRAMEWORK IMPLEMENTATION AND