Multi-phase Process Mining:Building Instance Graphs

Jason Ree3/31/11

School of Technology ManagementUNIST

Introduction: Instance GraphsInstance Graph

◦Corresponds to a specific class of Petri nets known as marked graphs, T-systems or partially ordered runs

◦An abstraction of the instance onto instance Event-driven Process Chains (EPCs) Instance EPC

Describes the control-flow of a case (i.e. a single process instance)

Provides a graphical representation describing the causal relations

1.1 Process Instance

In other words,◦ Process Instance of length n: σ = t1t2 … tn ∈ T+ , where ti are tasks

◦ W ∈ T+ N denotes a bag (multiset of process instances)◦ W(σ): the number of times a process instance of the form σ appears in the log

T+

case 1 task S

case 1 task A

case 1 task B

σ

T

1.2 Instance Domain Instance Net: a model of one instance

Since events that appear multiple times in a process instance have to be duplicated in an instance net, we define an instance domain to be used as a basis for generating instance nets

In an instance net, the instance σ is extended with some ordering relation to reflect some causal relation.

1.3 Instance Net

Also◦ Since the set of entries is given as a log, and an instance mapping can be inferred for each

instance based on textual properties, only the ordering relation based on the given log needs to be defined.

In other words,◦ An instance net is defined only as a set of entries from the log and an ordering on that set◦ Instance nets require

1. sequence of events σ ∈ T+ as they appear in a specific instance 2. ordering on the domain of σ is required

Instance Net (σ, )

2.1 Causal Ordering

Example

Causal ordering inferred on T◦ S w A

◦ S w B

T = {S, A, B}

2.2 Instance Ordering

Example◦ where case 1 = σ1 and case 2 = σ2

◦ σ1 = SAB and D σ1 = {1,2,3}

◦ Using the causal relation the relation is inferred such that 1 2 and 1 3

Instance Net (σ, )

2.3 Instance Graph

In other words,◦ An instance graph is a graph where each node represents one log entry of a specific

instance and can be used as a basis to generate models in a particular language◦ Also it is a graph that typically describes an execution path of some process model, as well

as causal relations between tasks

3.1 Instance Event-driven Process Chains (Instance EPCs)

Note:◦ An instance EPC doesn’t contain any connectors other than AND-split and AND-joins connectors◦ There is exactly one initial event and one final event

3.2 Generating Instance EPCs from Instance Graphs

3.2 Generating Instance EPCs from Instance Graphs

Thank you!Questions?