# Quality-Aware Resource Model Discovery
## 4 Implementation
### Visualization  
As discussed earlier, it is essential the derived model is effectively visualized for the model-based analysis. This section introduces three elements exploited for enhanced visualization in the implemented tool: the model layout, color-coding, and thickness of arcs. Figure 7 provides the visualization details of the derived model.  
Figure 6: The interactive viewer in the implemented tool.  
In the implemented tool, it is required that color-coding is applied to highlight three elements in the model: arcs, border of nodes, and inside of nodes. The color of arcs illustrates how many superior or inferior cases have passed through the corresponding arcs. As far as the color of arcs is concerned, we utilize \(BWS^{e}\) and \(BWD^{e}\) defined in Section 3.4. First, it is determined that a specific arc is significant compared to the other arcs with \(BWS^{e}\). Here, the arcs that have lower \(BWS^{e}\) than the user-defined threshold are coded to _gray_. Note that \(BWS^{e}\) has a range from 0 to 1. The rest of the arcs, i.e., the arcs with higher \(BWS^{e}\), are evaluated whether they have a positive or a negative effect on the quality with \(BWS^{e}\). In more detail, the arcs that have higher or lower \(BWD^{e}\) than the two different thresholds are painted in _blue_ and _red_, respectively. Note that \(BWD^{e}\) has a range from \(-1\) to 1. Figure 8 provides an example of the model that applied the color-coding. In this example, the user-defined criteria for \(BWS^{e}\) are 0.5, while those for \(BWD^{e}\) are 0.75 (for _blue_) and \(-0.75\) (for _red_), respectively. In Figure 8, the \(BWS^{e}\) values of arcs (1), (3), and (7) are less than 0.5; thus, they are painted to _gray_, as shown in the model on the right. Then, the \(BWD^{e}\) values are calculated for the remaining arcs, and they are evaluated with the predefined thresholds. In Figure 8, we can identify that the arcs (2) and (5) are presented as _blue_ in color, i.e., their values are higher than 0.75. Contrariwise, the arcs (7) and (8) have lower \(BWD^{e}\) values than \(-0.75\), and they are coded into _red_. The resulting model is depicted on the right of Figure 8.  
Figure 8: An example of the model that applied the arc color-coding.  
Figure 7: Visualization details of the model.  
Similar to the arc, the color in the border of nodes indicates how many of the superior or inferior cases go through the states that the corresponding nodes represent. The procedure to determine the color is analogous to the one described in the arc highlighting, whereas we now employ \(BWS^{s}\) and \(BWD^{s}\). The inside color of nodes is established with the statistical results on machines proposed in Section 3.5.  
Lastly, the thickness of the arc denotes how many transitions occur through particular states; thus, the broader the arcs are, the higher the frequency of arcs. We employed the Equation (1) [27] to determine the thickness of arcs.  
\[y_{ij}=y_{min}+(y_{max}-y_{min})\times\frac{x_{ij}-x_{min}}{x_{max}-x_{min}} \tag{1}\]  
Given an ATS = \((S,E,T,A^{s},A^{e})\), assume that \(x_{ij}\) denotes the frequency of the transition \(t=(s_{i},e,\ s_{j})\in T\) and \(y_{ij}\) denotes the degree of thickness of the arc that connects \(s_{i}\) and \(s_{j}\). Then, the thickness of the arc \(y_{ij}\) is determined with the following values: the minimum and maximum frequency of transitions, i.e., \(x_{min}\) and \(x_{max}\), and the user-defined minimum and maximum of the arc thickness, i.e., \(y_{min}\) and \(y_{max}\). Note that \(y_{ij}\) becomes \(y_{min}\) or \(y_{max}\) as \(x_{ij}\) gets closer to \(x_{min}\) or \(x_{max}\).