In Section 3.4 we explain how we determine which log traces are or obtaining predictive information of an enabled activity. In Section 3.5 we describe how we calculate the weighting of log traces 3.4 Support The relevance of log traces for a recommendation is determined on basis of su port. Typically, traces that are relevant are those that support the enabled ac- tivity for which the recommendation is computed. What support exactly means here, depends on the trace abstraction used For the prefix abstraction, we say that a log trace o supports enabled activity e, if and only if e occurs in g at the same index as in the partial trace p, when this activity is executed For set abstraction, we consider a log trace o to support the enabled activity e whenever activity e has been observed at least once in the log race. To support an enabled activity e in multi-set abstraction of trace o, the the frequency of activity e in the partial trace p must be less than the frequency in the log trace o, i.e., by executing e after p, the total number of e's does not exceed the number of es in a Definition 7(Activity support functions ). Let A be a set of activities g E A' and enabled activity e E A. We use the predicate s(p, o, e) to state that log trace a supports the execution of e after partial trace p. The predicate is defined for the three abstractions b sp(p, o,e) op(l4+1) ss(p, o, e) sm(P,a,e)←→pm(e)<om(e) The support predicate is used to filter the event log by removing all traces that do not support an enabled activity Definition 8(Support filtering). Let A be a set of activities and L E B(A' an event log over A. Furthermore, let (p, e)be a recommendation request with E A and e c A. we define the log filtered on support of enabled activity e∈ E and partial trace p as Lie.el)=l∈L|s(po,e) Log traces from L(p,e) support enabled activity e and are used for the recom- mendation of e. Next, we define a weighing function() to express the relative importance of each of these log traces for the recommendation of an activity e. Note that a ranges over a multi-set traces
In Section 3.4 we explain how we determine which log traces are relevant for obtaining predictive information of an enabled activity. In Section 3.5 we describe how we calculate the weighting of log traces. 3.4 Support The relevance of log traces for a recommendation is determined on basis of support. Typically, traces that are relevant are those that support the enabled activity for which the recommendation is computed. What support exactly means here, depends on the trace abstraction used. For the prefix abstraction, we say that a log trace σ supports enabled activity e, if and only if e occurs in σ at the same index as in the partial trace ρ, when this activity is executed. For set abstraction, we consider a log trace σ to support the enabled activity e whenever activity e has been observed at least once in the log trace. To support an enabled activity e in multi-set abstraction of trace σ, the the frequency of activity e in the partial trace ρ must be less than the frequency in the log trace σ, i.e., by executing e after ρ, the total number of e’s does not exceed the number of e’s in σ. Definition 7 (Activity support functions). Let A be a set of activities, ρ, σ ∈ A∗ and enabled activity e ∈ A. We use the predicate s(ρ, σ, e) to state that log trace σ supports the execution of e after partial trace ρ. The predicate is defined for the three abstractions by: sp(ρ, σ, e) ⇐⇒ σp(|ρ| + 1) = e ss (ρ, σ, e) ⇐⇒ e ∈ σs sm(ρ, σ, e) ⇐⇒ ρm(e) < σm(e) The support predicate is used to filter the event log by removing all traces that do not support an enabled activity. Definition 8 (Support filtering). Let A be a set of activities and L ∈ B(A∗ ) an event log over A. Furthermore, let (ρ, E) be a recommendation request with ρ ∈ A∗ and E ⊆ A. We define the log filtered on support of enabled activity e ∈ E and partial trace ρ as L s (ρ,e) = Jσ ∈ L | s(ρ, σ, e)K 1 Log traces from L s (ρ,e) support enabled activity e and are used for the recommendation of e. Next, we define a weighing function (ω) to express the relative importance of each of these log traces for the recommendation of an enabled activity e. 1 Note that σ ranges over a multi-set traces
3.5 Trace Weight The support of an enabled activity determines the part of the log that serves as a basis for a recommendation. However, from the traces supporting an enabled activity, not every one is equally important, i.e., some log traces match the partial trace better than others. Hence, we define weighing functions that assign a weight to each log trace. The weight of a trace can be between l and 0, where a value of 1 indicates that two traces fully match and 0 that they do not match at all. The calculation of the degree of matching depends on the trace abstraction For prefixes, the weight of a log trace is 1 if the partial trace is a prefix of the log trace, otherwise, the weight is 0. For the set abstraction, the weight of the log trace is defined as the fraction of distinct partial trace activities that the partial trace abstraction and log trace abstraction have in common. The weight of a trace for the multi-set abstraction is similar to the set-weight, however, the frequency of a Definition 9(Weight functions). Let A be a set of activities and o,PE A* We define w(p, a),i.e, the relative importance of a log trace o when considerin the partial trace p as follows 4()={n.m≤ ws (p, a)= Ips I 3.6 Expected Outcome Definition 5 states that a recommendation for enabled activity e contains pre- dictive information about the target value. We define the expected outcome of the target value( do value), when e is executed in the next step, as a weighted average over target values of log traces from L(e,e), the log filtered on support of e. The target value of each trace from Lie, e) is weighted(w)on basis of the degree of matching with the partial trace. Definition 10(do calculation). Let A be a set of activities, T a target func- tion,p,∈A·,L∈B(A*)ande∈ E C A an enabled activity. The expected target value when p is completed by the user after performing activity e next is defined u(p,a)·T() Similarly, we define the expected target value of not doing an enabled activit e2. The dont function determines the weighted average over all alternatives of e, i.e., all traces that do not support the execution of e after p, but do support any of the alternatives e after Note that in both do and dont 2 ranges over a multi-set of traces
3.5 Trace Weight The support of an enabled activity determines the part of the log that serves as a basis for a recommendation. However, from the traces supporting an enabled activity, not every one is equally important, i.e., some log traces match the partial trace better than others. Hence, we define weighing functions that assign a weight to each log trace. The weight of a trace can be between 1 and 0, where a value of 1 indicates that two traces fully match and 0 that they do not match at all. The calculation of the degree of matching depends on the trace abstraction. For prefixes, the weight of a log trace is 1 if the partial trace is a prefix of the log trace, otherwise, the weight is 0. For the set abstraction, the weight of the log trace is defined as the fraction of distinct partial trace activities that the partial trace abstraction and log trace abstraction have in common. The weight of a trace for the multi-set abstraction is similar to the set-weight, however, the frequency of activities is also considered. Definition 9 (Weight functions). Let A be a set of activities and σ, ρ ∈ A∗ . We define ω(ρ, σ),i.e., the relative importance of a log trace σ when considering the partial trace ρ as follows: ωp(ρ, σ) = 1 , if ρp ≤ σp 0 , otherwise , ωs (ρ, σ) = |ρs ∩ σs | |ρs | , ωm (ρ, σ) = |ρm C σm | |ρm | 3.6 Expected Outcome Definition 5 states that a recommendation for enabled activity e contains predictive information about the target value. We define the expected outcome of the target value (do value), when e is executed in the next step, as a weighted average over target values of log traces from L s (ρ,e) , the log filtered on support of e. The target value of each trace from L s (ρ,e) is weighted (ω) on basis of the degree of matching with the partial trace. Definition 10 (do calculation). Let A be a set of activities, τ a target function, ρ, σ ∈ A∗ , L ∈ B(A∗ ) and e ∈ E ⊆ A an enabled activity. The expected target value when ρ is completed by the user after performing activity e next is defined as: do(e, ρ, L) = P σ∈Ls (ρ,e) ω(ρ, σ) · τ (σ) P σ∈Ls (ρ,e) ω(ρ, σ) Similarly, we define the expected target value of not doing an enabled activity e 2 . The dont function determines the weighted average over all alternatives of e, i.e., all traces that do not support the execution of e after ρ, but do support any of the alternatives e 0 after ρ. 2 Note that in both do and dont Σ ranges over a multi-set of traces