# Understanding Contrail Business Processes through Hierarchical Clustering: A Multi-Stage Framework
## 3 Proposed Methodology
### Multi-Stage Framework for Process Log Simplification  
The framework proposed in this paper for understanding the contrail process, i.e., a complex, unlabelled real-world business process, is composed of two independent stages. Stage-1 is to identify the high-level business classes within the business process log through exploring the broad characteristics of process instances, with rule-based mining used to verify the correctness of the classification. Stage-2 is composed of a novel technique of hierarchical clustering of cases for each of the identified high-level business classes. Clustering is performed, based on business characteristics of the cases, through features extraction for each individual case. The feature set is the representation of the features extracted and their underlying attributes for each case. Figure 5 presents the proposed multi-stage framework for clustering of the business process log. Figure 2: Example of contrails in the sky–forming mixture of structured and unstructured patterns [24]. Our aim in stage-1 is to decompose the larger process log into manageable subsets which represent a specific business class. This decomposition allows high level segregation of the contrail processes consisting of events collected from heterogeneous sources. In the first step, high-level business classes are identified from the process log, the next step is to verify the accuracy of the identified business classes, for which all cases in the log are presented in the form of a task-list. Finally, rule-based mining is performed using CBA algorithm [19] to measure the accuracy of the classification. Figure 4: Fuzzy miner model of the BT’s Customer Diagnostic Process. Figure 3: Heuristic miner model for customer diagnostic process. In stage 2, the following are the steps involved in performing hierarchical clustering with identified high-level business classes:  
1. _Case level feature extraction:_ Attributes of each individual case of the process log represented as a feature set. 2. _Feature selection:_ Feature selection in the unsupervised environment is a trade-off between several selected features and accuracy of the performed clustering [20]. We used selective set of features which can reveal the natural grouping of the cases among the process log. Approaches such as wrapper [28] and Multi-objective Feature Selection [20] resulted in the selection of most discriminating features for clustering but the focus of this work is to consider all those features which present a business perspective of grouping within the data. We concluded our feature selection based on several quality level parameters as proposed in [20], implemented through RapidMiner tool. These quality metrics are: * _Correlation:_ It is a Pearson correlation coefficient between the attributes and the labels of the feature set. * _ID-ness:_ It measures the unique attributes in the data. Higher the ID-ness, lower the quality of attribute for clustering. * _Stability:_ It is a measure of constant values in attributes. It is calculated as (2): \[S=\left(N_{n}freq\right)/\left(N_{n}\right)\] (2) where \(N_{n}freq\) is the number of rows with the most frequent non-missing values divided by \(N_{n}\), the total number of data rows with non-missing values. Higher the stability, lower the  
Figure 5: Multi-stage framework for business process log clustering. quality of attribute for clustering. * _Missing values_: It measure the percentage of attributes with missing values. 3. _Defining a distance matrix_: The event log of the real-world business process may contain different data types, including logical, nominal, ordinal and numerical data. It is vital to identify the difference between selected features of the cases using a distance matrix. A Distance matrix helps to identify the centroid distance between selected features. In this paper we used Gower distance measure [29] which was introduced in 1971 and it is a measure of distances between pairs of variables and combining those distances to a single value for each of the pair. 4.