# Fibers of Failure: Classifying Errors in Predictive Processes
## 3 Results and Discussion
### EE Consumption Model
#### 3.2.2 Qualitative  
The Mapper graph is shown in Figure 9. It is possible to observe an ability for Mapper to separate subgroups with high positive error from subgroups with high negative error.  
Near zero p-values are present for all top-five KS-value variables in all four groups highlighted in Figure 10. However, the differences in KS-values, which take values from 0 to 1, vary between 0.331 to 0.792. A higher KS-value indicates that the two samples are not from the same distribution compared to a KS-value that is lower, as discussed in Section 2.4.2.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Type** & \(R^{2}\) & \(Avg.\Delta E_{EI}\) & \(Std.\Delta E_{EI}\) & \(Min.\Delta E_{EI}\) & \(Max.\Delta E_{EI}\) \\
**Unit** & **-** & **kWh** & **kWh** & **kWh** & **kWh** \\ \hline Original & 0.50 & \(-\)70 & 1988 & \(-\)13,954 & 6520 \\ Adjusted & 0.56 & \(-\)81 & 1867 & \(-\)12,284 & 7123 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Results before and after the adjustments on the test data using logistic regression with \(C=1\). The chosen logistic regression classifier ensemble was the one that, to the highest extent, reduced the standard deviation of error and increased \(R^{2}\). (See Appendix A) C for the results from the logistic regression classifier ensembles with the other \(C\)-values.  
Figure 9: The Mapper graph. The groups 1247, 1248, 1250, and 1252 have highlighted nodes and are marked in the figure. The color-bar represents values, with respective coloring in the graph, for \(\Delta E_{El}\). The values are in kWh/heat. The line between the adjacent groups 1248 and 1252 is present for interpretability purposes. Number of data points and \(\Delta E_{El}\) for each group; **group 1247:** 165, 2160 kWh/heat. **Group 1248:** 202, \(-\)2740 kWh/heat. **Group 1250:** 213, 2350 kWh/heat. **Group 1252:** 355, \(-\)2970 kWh/heat.  
The use of FifA made it possible to pinpoint raw material types C and D as two of the most predominant variables in separating each of the four groups from the rest of the data. From process experience it is known that raw material types have a large effect on the energy dynamics within the furnace and thus also on the EE consumption. Since raw material types are variable in the  
Figure 10: Distribution plots for the 5 variables with the highest **(left)** and lowest **(right)** KS-values, respectively. Truncated distributions (values within the 1000-quantiles) for the group (black) and the rest (gray) are shown. The dashed lines indicate the means of respective distribution. The values in parenthesis show the KS-values. Number of data points and \(\Delta E_{El}\) for each group; **group 1247:** 165, 2160 kWh/heat. **Group 1248:** 202, \(-\)2740 kWh/heat. **Group 1250:** 213, 2350 kWh/heat. **Group 1252:** 355, \(-\)2970 kWh/heat.  
prediction model, it is clear that the model misjudges the impact of these raw material types on the true EE consumption.  
The effective energy is a proprietary variable estimating the amount of energy that is effectively utilized during the EAF process. It is closely related to the energy dynamics of the process, but was not used as a input variable for the prediction model. However, it is possible to observe that group 1247 and group 1250 have lower effective energy than the rest of the data, while group 1252 has a higher effective energy than the rest of the data. The prediction model overestimates the EE for the heats in group 1247 and group 1250, while it underestimates the EE for the heats in group 1252.