Towards mining the organizational structure of a dynamic event scenario

Abstract

The increasing volume and value of data is an important enabler for data science. In this study, we consider the event data, i.e. information on things that happen in organizations, machines, systems and people’s lives. Each event refers to a well-defined activity in a certain business process execution, the resource (i.e. person or device) executing or initiating the activity, the timestamp of the event, as well as to various data elements recorded with the event (e.g. the geo-location of an activity). Process mining aims to analyze event data, in order to mine knowledge that can contribute to improving a business process behavior. In particular, the focus of this study is on organizational mining, that is a sub-field of process mining that aims at understanding the life cycle of a dynamic organizational structure (i.e. a configuration of organization units) and the interactions among co-workers (resources) arising from the analysis of real-world event logs. The innovative contribution of this study is that the organizational mining goal is here achieved by combining concepts from process mining, stream mining and social network analysis. This combination is an original contribution of this study, not still explored in organizational mining field. In an assessment, benchmark event data are explored, in order to understand how the presented solution allows us to identify the life cycle a dynamic organizational structure.

Appendix A

Let us start from the formulation of Reichardt-Bornholdt measure $\mathcal {RB}(\mathcal {C_{L}})=\frac {1}{2m} \sum \nolimits _{i,j\in \mathcal {N_{L}}}{\left [(A_{ij}-\gamma \frac {deg^{in}(i)deg^{out}(j)}{2m})\delta (C_{\mathcal {L}}^{i},C_{\mathcal {L}}^{j})\right ]}$ as reported in Formula 5. Let us consider that the Kronecker function $\delta (C_{\mathcal {L}}^{i},C_{\mathcal {L}}^{j})$ can also be written as $\delta \left (C_{\mathcal {L}}^{i},C_{\mathcal {L}}^{j}\right )= \sum \limits _{C_{\mathcal {L}}^{h} \in \mathcal {C_{L}}}{\delta \left (C_{\mathcal {L}}^{i}, C_{\mathcal {L}}^{h}\right )\delta \left (C_{\mathcal {L}}^{j}, C_{\mathcal {L}}^{h}\right )}$, where δ(X,Y)=1 1 iff X = Y, 0 otherwise. Therefore, $\mathcal {RB}(\mathcal {C_{L}})$ can be rewritten as follows:

$$\begin{array}{@{}rcl@{}} \mathcal{RB}&=&\frac{1}{2m} \sum\limits_{i,j\in \mathcal{N_{L}}}{\left[(A_{ij}-\gamma \frac{deg^{in}(i)deg^{out}(j)}{2m})\sum\limits_{C_{\mathcal{L}}^{h} \in \mathcal{C_{L}}}{\delta\left( C_{\mathcal{L}}^{i}, C_{\mathcal{L}}^{h}\right)\delta\left( C_{\mathcal{L}}^{j}, C_{\mathcal{L}}^{h}\right)}\right]}\\ &=&\frac{1}{2m} \displaystyle \sum\limits_{\scriptscriptstyle i,j\in \mathcal{N_{L}}}\scriptscriptstyle{\left[ A_{ij} \displaystyle\sum\limits_{\scriptscriptstyle C_{\mathcal{L}}^{h} \in \mathcal{C_{L}}}{\scriptscriptstyle \delta\left( C_{\mathcal{L}}^{i}, C_{\mathcal{L}}^{h}\right)\delta\left( C_{\mathcal{L}}^{j}, C_{\mathcal{L}}^{h}\right)} -\scriptscriptstyle \gamma \frac{deg^{in}(i)deg^{out}(j)}{2m} \displaystyle\sum\limits_{\scriptscriptstyle C_{\mathcal{L}}^{h} \in \mathcal{C_{L}}}{\scriptscriptstyle \delta\left( C_{\mathcal{L}}^{i}, C_{\mathcal{L}}^{h}\right)\delta\left( C_{\mathcal{L}}^{j}, C_{\mathcal{L}}^{h}\right)} \right]}\\ &=&\scriptscriptstyle \displaystyle \sum\limits_{\scriptscriptstyle C_{\mathcal{L}}^{h} \in \mathcal{C_{L}}}{\scriptscriptstyle \left[ \frac {\displaystyle\sum\limits_{\scriptscriptstyle i,j\in \mathcal{N_{L}}}{\scriptscriptstyle A_{ij} {\delta\left( C_{\mathcal{L}}^{i}, C_{\mathcal{L}}^{h}\right)\delta\left( C_{\mathcal{L}}^{j}, C_{\mathcal{L}}^{h}\right)}} }{2m} - \gamma\frac{\displaystyle\sum\limits_{\scriptscriptstyle i,j\in \mathcal{N_{L}}}{\scriptscriptstyle deg^{in}(i)\delta\left( C_{\mathcal{L}}^{i}, C_{\mathcal{L}}^{h}\right) deg^{out}(j)\delta\left( C_{\mathcal{L}}^{j}, C_{\mathcal{L}}^{h}\right)}} {2m}\right]}\\ &=&\scriptscriptstyle \displaystyle \sum\limits_{\scriptscriptstyle C_{\mathcal{L}}^{h} \in \mathcal{C_{L}}}{\scriptscriptstyle \left[ \frac {\displaystyle\sum\limits_{\scriptscriptstyle i,j\in \mathcal{N_{L}}}{\scriptscriptstyle A_{ij} {\delta\left( C_{\mathcal{L}}^{i}, C_{\mathcal{L}}^{h}\right)\delta\left( C_{\mathcal{L}}^{j}, C_{\mathcal{L}}^{h}\right)}} }{2m} - \gamma\frac{\displaystyle\sum\limits_{\scriptscriptstyle i\in \mathcal{N_{L}}}{\scriptscriptstyle deg^{in}(i)\delta\left( C_{\mathcal{L}}^{i}, C_{\mathcal{L}}^{h}\right)}}{2m} \frac{\displaystyle\sum\limits_{\scriptscriptstyle j\in \mathcal{N_{L}}}{\scriptscriptstyle {deg^{out}(j)\delta\left( C_{\mathcal{L}}^{j}, C_{\mathcal{L}}^{h}\right)}}}{2m} \right]}. \end{array} $$

Introducing the following notation:

$$\begin{array}{@{}rcl@{}} e_{hh}&=&\frac{1}{2m}\sum\limits_{i,j\in\mathcal{N_{L}}}{A_{ij}\delta\left( C_{\mathcal{L}}^{i},C_{\mathcal{L}}^{h}\right)\delta\left( C_{\mathcal{L}}^{j},C_{\mathcal{L}}^{h}\right)},\\ a_{h}^{in}&=&\frac{1}{2m}\sum\limits_{i\in \mathcal{N_{L}}}{deg(i)^{in}\delta\left( C_{\mathcal{L}}^{i},C_{\mathcal{L}}^{h}\right)},\\ a_{h}^{out}&=&\frac{1}{2m}\sum\limits_{j\in \mathcal{N_{L}}}{deg(j)^{out}\delta\left( C_{\mathcal{L}}^{j},C_{\mathcal{L}}^{h}\right)}, \end{array} $$

the Reichardt-Bornholdt measure can be written as $\mathcal {RB}= \sum \limits _{C_{\mathcal {L}}^{h} \in \mathcal {C}_{L}}{\left (e_{hh}-\gamma a_{h}^{in}a_{h}^{out}\right )}$, as reported in Formula 6.