## 7 Conclusions  
Data quality assessment is a crucial part of data understanding and preparation in order to ensure valid data-driven results in data mining. Completeness of data is one of the most affecting quality dimensions, often discussed in the literature. However, the literature review reveals a gap for a task-dependent assessment of completeness at record level. The state-of-the-art considerations of completeness do not provide insights into the utilization of the feature space of a multi-dimensional data set. In order to evaluate if a multi-dimensional data set is suitable to describe the dependencies of the whole feature space, the availability and distribution of the different combinations of variable values in this data set should be observed. This paper introduces a metric and visualization for the so-called data set completeness assessing the utilization of the feature space in multi-dimensional data sets with independent input variables. The example of condition monitoring of control valves shows that the metric and visualization of data set completeness can identify the structure of the data set. Deficiencies in terms of missing variable combinations are detected. The state-of-the-art statistics and plots in data preparation are insufficient regarding the assessment of the utilization of the feature space. Besides, it is shown that the data set completeness significantly influences the accuracy of data-driven results. A complete data set achieves a coefficient of determination of 0.99 and a root mean squared error of 0.0026, while a data set with reduced data set completeness (reduction around 0.08 percentage points) achieves values of 0.97 and 0.045, respectively. In contrast to the state-of-the-art metrics for completeness, the introduced metric indicates the deficiencies in the completeness of the data set. Besides the application to the condition monitoring of control valves, the metric is applicable to further data sets with independent and numeric variables. The basic assumption is that a high utilization of the feature space is demanded, meaning the variables values appear in all possible combinations. The introduced metric is interval-scaled, providing values between 0 (perfectly bad data quality) and 1 (perfectly good data quality). This is in accordance with the requirement set for data quality metrics. The visualization facilitates the assessment of the data set completeness in highly dimensional data sets by displaying the values as a heat map. The introduced metric and visualization enable the expert to detect deficiencies and take appropriate countermeasures to increase data quality and model accuracy. In this way, valid data-driven results can be achieved. In future work, the parametrization should be automated. The proposed metric currently requires the input of the partitioning of the considered variables. In order to automate this task, a one-dimensional clustering should be implemented, partitioning the variables individually based on the characteristics of the distribution of the data. Furthermore, the visualization will be extended to identify the root of the deficiencies in data set completeness. On top of the heat map, a parallel plot should be inserted on request. In this way, the expert can identify which sections of the feature space cause the low data set completeness. To keep the visualization clear, the plot should be partially activated by selecting specific classes that should be examined in detail. Furthermore, the visualization, in particular the user experience with the visualization, has to be evaluated in usability studies. Otherwise, it is not ensured that the valuable information of the visualization is well perceived by the user. The system usability scale [61] could be a measure to assess the user experience. Conceptualization, I.W. and B.V.-H.; methodology, I.W. ; software, I.W. ; validation, I.W. ; formal analysis, I.W. ; investigation, I.W. ; resources, B.V.-H.; data curation, I.W. ; writing--original draft preparation, I.W.