# Characterizing Situations of Dock Overload in Bicycle Sharing Stations
## 3 Methodology
### Mining Occupancy Monitoring Patterns
#### 3.2.2 Proposed Approach for OMP Mining
These o-itemsets combine the stations having all the same occupancy level in a given time period. As discussed below, these two o-itemset types will be useful at the next step to compute the OMP intermittence value. Condition (ii) allows us to filter out the combinations of o-items related to faraway stations. This will allow us to generate only OMPs including nearby stations in Step 2. _Step 2. OMPs generation._ The output of Step 1 is processed at Step 2 to generate the set of OMPs. An OMP \(P\) is generated from a pair of critical and normal o-itemsets that include (i) the same stations \begin{table}
\begin{tabular}{c c} \hline \hline
**Transaction IDentifier (TID)** & **Transaction** \\ \hline \(\mathrm{TID}_{1}\) & \(\langle s_{1},\mathit{Overloaded},\mathit{TP}_{1}\rangle\), \(\langle s_{2},\mathit{Overloaded},\mathit{TP}_{1}\rangle\), \(\langle s_{3},\mathit{Overloaded},\mathit{TP}_{1}\rangle\) \\ \(\mathrm{TID}_{2}\) & \(\langle s_{1},\mathit{Overloaded},\mathit{TP}_{1}\rangle\), \(\langle s_{2},\mathit{Normal},\mathit{TP}_{1}\rangle\), \(\langle s_{3},\mathit{Overloaded},\mathit{TP}_{1}\rangle\) \\ \(\mathrm{TID}_{3}\) & \(\langle s_{1},\mathit{Overloaded},\mathit{TP}_{1}\rangle\), \(\langle s_{2},\mathit{Overloaded},\mathit{TP}_{1}\rangle\), \(\langle s_{3},\mathit{Normal},\mathit{TP}_{1}\rangle\) \\ \(\mathrm{TID}_{4}\) & \(\langle s_{1},\mathit{Overloaded},\mathit{TP}_{1}\rangle\), \(\langle s_{2},\mathit{Normal},\mathit{TP}_{1}\rangle\), \(\langle s_{3},\mathit{Normal},\mathit{TP}_{1}\rangle\) \\ \(\mathrm{TID}_{5}\) & \(\langle s_{1},\mathit{Normal},\mathit{TP}_{2}\rangle\), \(\langle s_{2},\mathit{Overloaded},\mathit{TP}_{2}\rangle\), \(\langle s_{3},\mathit{Normal},\mathit{TP}_{2}\rangle\) \\ \(\mathrm{TID}_{6}\) & \(\langle s_{1},\mathit{Normal},\mathit{TP}_{2}\rangle\), \(\langle s_{2},\mathit{Overloaded},\mathit{TP}_{2}\rangle\), \(\langle s_{3},\mathit{Normal},\mathit{TP}_{2}\rangle\) \\ \(\mathrm{TID}_{7}\) & \(\langle s_{1},\mathit{Normal},\mathit{TP}_{3}\rangle\), \(\langle s_{2},\mathit{Normal},\mathit{TP}_{3}\rangle\), \(\langle s_{3},\mathit{Normal},\mathit{TP}_{3}\rangle\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Example of Occupancy level dataset in transactional format. and (ii) the same time period. The frequency values of these two o-itemsets are used to compute the criticality and intermittence values of \(P\). The OMP generation process is detailed here using an example case. Let us consider a pair of critical (denoted \(I_{C}\)) and normal (denoted \(I_{N}\)) o-itemsets, having both the same stations and the same time period. Consider for instance the critical o-itemset \(I_{C}=\{\langle s_{i},Overloaded,TP_{k}\rangle,\)\(\langle s_{j},Overloaded,TP_{k}\rangle\}\) and the normal o-itemset \(I_{N}=\{\langle s_{i},Normal,TP_{k}\rangle,\langle s_{j},Normal,TP_{k}\rangle\}\). Let denote as \(freq\_value(critical)\) and \(freq\_value(normal)\) their respective frequency in time period \(TP_{k}\) in the analyzed dataset. Let \(P\) be the OMP generated from these two o-itemsets. The following statements hold:  
1. Pattern \(P\) contains all the stations appearing in the critical o-itemset \(I_{C}\) (or equivalently in the normal o-itemset \(I_{N}\)), i.e., \(P\)=\(\{s_{i},s_{j}\}\). 2. According to Definition 5, the criticality of pattern \(P\) in time period \(TP_{k}\) is the number of times all the stations in \(P\) are overloaded in \(TP_{K}\). It follows that that criticality of \(P\) in period \(TP_{k}\) is equal to the number of transactions in \(TP_{k}\) including the o-itemset \(I_{C}\). Thus, \[criticality=freq\_value(critical).\] (1)
3. According to Definition 5, the intermittence of pattern \(P\) in a time period \(TP_{k}\) is the number of times at least one station in \(P\) (but not all stations at the same time) is overloaded in \(TP_{k}\).