## 5 Application and Discussion of the Proposed Metric and Visualization
### Comparison of the Different Data Sets  
The original data set and the manipulated data sets A and B are compared to demonstrate the weakness of common metrics and visualizations of data in detecting the utilization of the feature space. The descriptive statistics and the histograms and boxplots of the different data sets are shown in Figure 13 The major difference between the original data set and the manipulated data sets is the absolute number of observations (cf. Figure 13 histograms). The original data set contains frequencies of the stroke up to 1000, while the frequencies of the manipulated data sets are reduced to around 800. However, the structure is unchanged. The histograms of pressure and pressure difference of data set A and B display the four different operating points unaffected. The descriptive statistics show a maximum pressure and pressure difference of 0.92 and 0.95 for data set B (cf. Figure 13 marked cells). This shows that some values in the upper range of the variables are no longer included in the data set. Furthermore, the interquartile range of the pressure difference in data set B is reduced significantly. The missing observations for higher values cause this. For pressure, a reduced interquartile range is not detected due to the still right-skewed distribution. Despite a reduced number of observations and the absence of a small value range in pressure and pressure difference, the common visualizations do not indicate major changes in the data sets structure. The state-of-the-art metrics (cf. Table 1 on page 8) cannot reveal the differences in data set A and B either. An excerpt of the data set B is given in Figure 14, illustrating the numbers. Since 25% of the observations are deleted in both data sets, the Record Completeness [37] and the Weak Tuple Completeness [34] is 75% for both data sets and the Empty Records in a Data File [37] are 25%, respectively (record level task-independent). In total, 6750 records out of 27,000 are missing. The Strong Tuple Completeness [34] equals 0 for both data sets since one missing record already reduces this metric to 0. Other task-independent metrics concerning the item and variable level are also similar in data set A and B. The completeness on item level is also 75%. In total, 20,250 items out of 81,000 are NULL values. The completeness on variable level is 75% for each variable and the Strong Attribute Completeness [34] is 0 for each variable since each variable includes at least one NULL value. For the task-dependent metrics, only the Data Value Completeness [37] is different in data set A and B. Since data set B is missing values for pressure higher than 0.92 and pressure difference higher than 0.95, the Data Value Completeness is reduced slightly. This was already detected by the descriptive statistics (cf. Figure 13). The completeness regarding the schema is unchanged compared to the original data set. All relevant variables are available. In conclusion, the state-of-the-art statistics and metrics cannot detect structural differences in data set A and B, which could influence model training and model accuracy. Figure 14: State-of-the-art metrics for completeness for data set B.  
Figure 13: Descriptive statistics of the original data set and the manipulated data sets A and B (**left**) and histograms and boxplots of the respective data sets (**right**). Application and Comparison of the Data Set Completeness Metric and Visualization of the Different Data Sets  
In contrast to the metrics and visualizations in Section 4.1, the proposed data set completeness reveals the changes in the data set's structure in data set B (cf. Figure 15). While the random deletion of observations in data set A does not change the utilization of the features space, the manipulation in data set B causes significant changes. Most classes show a reduced data set completeness (cf. Figure 15c). For stroke, the data set completeness decreases further with higher values.