# Understanding Contrail Business Processes through Hierarchical Clustering: A Multi-Stage Framework
## 5 Results and Discussion
### Comparison with Other Trace Clustering Techniques  
We compared the results of the proposed NoHiC technique (Algorithm 1) with two hierarchical clustering techniques from the literature, Agglomerative Hierarchical Clustering (AHC) proposed by [PERSON] et al. (2018) and Trace clustering (ActiTraC) proposed by [PERSON] et al. (2019). For ActiTraC we kept the default settings in the ProM 6.3 plugin _ActiTra_ except for the minimal and maximal cluster size. The maximum number of clusters is selected as 11 as NoHiC identified 11 clusters (as presented earlier in Section 5) and the minimum cluster size is kept to at least 20% of the log in order to avoid clusters with less than around 250 cases per cluster. For the AHC technique, we used several available settings in the ProM plugin Guide Tree Miner for features selection and distance metrics ([PERSON] et al., 2019). In our experiments, the Distance metric used is kept constant as a Euclidian distance and standard feature selection methods of trace clustering are used, such as MR (Maximal Repeat), TR (Tandem Repeat), SMR (Super Maximal Repeat), NSMR (Near Super Maximal Repeat) and K-Gram (\(\mathrm{k}=5\)). We refer to these variations in our results as MR_AHC, TR_AHC, SMR_AHC, NSMR_AHC and K-Gram_AHC. Figure 16: Prediction accuracy with five classification algorithms. Figure 17: Impact of model fitness at each stage of the framework. To analyse the impact of our proposed technique we implemented ActiTraC and the five variations of AHC on two logs; the first is the CDP log as discussed throughout this paper and the other is a public process dataset available as BPI challenge 2012(BPI). A comparison of the CDP and BPI based on the characteristics of the logs is shown in Table 8. The difference in event classes and mean events per case is due to the nature of the process under consideration. In Table 9, a summary of the results is presented showing the total number of clusters generated as a result of running these experiments using both process logs. The NoHiC technique produced the highest number of clusters using CDP and only 2 less clusters using BPI, but the vital characteristic in this research is the business perspective of these clusters. As only NoHiC used business related features (presented in Section 4) none of the other technique produced the clusters which are widely meaningful and understandable for the business users. The clusters produced by AHC and ActiTraC are based on the statistical features such as MR, SMR and event sequence-based features. Values in bold show the best performance of clustering techniques against each metric for a respective dataset. In addition to business relevance, the quality of a clustering technique is considered good if it generates clusters which are less complex and have higher fitness. Such clusters indicate that the clustering technique has discovered meaningful clusters which contain cases with similar characteristics. Fitness comparison of NoHiC with the other clustering techniques is shown in Figure 18. For both logs, NoHiC produced clusters with highest fitness average. The lowest fitness corresponds to the worst quality cluster and highest fitness represents the best quality cluster. Quality of the generated clusters should ideally remain consistent for a given technique. We also extended our comparison by measuring the complexity of the identified clusters, through NoHiC, AHC and ActiTraC using various complexity metrics [33], such as:  
* Nodes per discovered cluster (\(N\))
* Arcs per discovered cluster (\(A\))
* Average connection degree (\(Avg_{CD}\))
* Density (\(D\)): \(\dfrac{|A|}{|N|(|N|-1)}\)
* Cyclomatic number (\(CN\)): Number of the linearly independent cycles: \(|A|-|N|+1\)
* Coefficient of connectivity (\(CNC\)): \(\dfrac{|A|}{|N|}\)
* Coefficient of network complexity (\(CNC_{k}\)): \(\dfrac{|A|^{2}}{|N|}\)