## 6 Evaluation of the Metric
\begin{table}
\begin{tabular}{p{142.3 pt} p{142.3 pt}} \hline \hline
**Existence of Minimum and Maximum Metric Values (R1)** & **Fulfilled** \\ \hline The proposed indicator for data set completeness \(DSC_{j}\) consists of two factors: section balance \(SB_{j}\) CV/ \(SB_{j}\) quantifies the unbalance of the observation in one class compared to the worst possible distribution of this class for the given data set. In this way, the factor ranges from 0 to 1, representing the worst possible distribution and the best possible distribution, respectively. The class volume \(CV_{j}\) quantifies the balance of the observations in one variable. This factor also ranges from 0 to 1, representing a maximal unbalanced distribution and an equal distribution of the observations in one variable. Consequently, the data set completeness \(DSC_{j}\) has a minimum value of 0, indicating perfectly poor data quality in terms of the utilization of the future space. The maximum value of 1, indicating perfectly good data quality, is reached by equally distributed data in the whole feature space. The existence of a minimum and a maximum metric value is given and the requirement is rated as fulfilled. \\ \hline
**Interval-scaled metric values (R2)** & **fulfilled** \\ \hline The metric for data set completeness \(DSC_{j}\) express the quality of the data relative to the best – case scenario and worst – case scenario, respectively. A data set completeness \(DSC_{j}\) of 0.4 is half as good as a data set completeness \(DSC_{j}\) of 0.8. Therefore, the requirement for an interval-scaled metric value is rated as fulfilled. \\ \hline
**Quality of the configuration parameters (R3)** & **not yet fulfilled** \\ \hline The calculation of the data set completeness only requires the experts’ input regarding the partitioning of the variables. The experts need to identify the operating points of the considered machine to define the classes that the proposed metric should evaluate. No further input or parameter tuning is required. \\ However, the partitioning highly influences the data set completeness metric results due to changes in the allocation of observations. Therefore, two different experts might receive different results in terms of data quality due to a different opinion on the partitioning of the variables. Automatic partitioning of every sin gle variable based on one – dimensional clustering can solve this. \\ Implementing and evaluating such an approach is intended for future work. Nevertheless, the requirement concerning the quality of the configuration parameters has to be rated as not yet fulfilled at the current stage. Another aspect concerns the parameter \(\alpha\) which determine the balance between \(SB_{j}\) and \(CV_{j}\). The default of 0.5 weights both factors equally. However, the user of the metric can adjust \(\alpha\) if required. In order to evaluate the impact and the result further research on the sensitivity of \(\alpha\) is required. \\ \hline
**Sound aggregation of the metric values (R4)** & **fulfilled** \\ \hline The proposed metric for data set completeness is calculated for each class individually, representing the utilization of the feature space in multi-dimensional data sets. To further aggregate the data set completeness, the mean value for each variable is proposed. Furthermore, the standard deviation should be considered providing information about the homogeneity of the classes of one specific variable. A further aggregation is possible by taking the mean value for the whole data set. \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Discussion of the requirements for efficient data quality metrics. sections of the feature space, increasing data quality. In this way, efficient and accurate models can be trained. The metric and visualization of the data set completeness provide a meaningful advance in data quality assessment of multi-dimensional data sets.