## 4 The Concept for the Assessment of Data Set Completeness
### Visualization of the Data Set Completeness  
The proposed metric for the data set completeness \(DSC_{j}\) provides values for each class \(j\) of the variable \(i\). In a big data set with several variables and classes, an evaluation based on the numeric values for \(DSC_{j}\) is not easily accessible for an expert. Therefore, a visualization is required to represent the results clearly and intuitively. A heat map is proposed, coding the data set completeness of each class in a color bar. In this way, the expert can easily access and identify classes with insufficient data set completeness. An abstracted example showing the structure of the visualization is given in Figure 7. Each variable is represented by one bar. The bottom and the top of the bar mark the minimum and the maximum value of this variable, respectively. The border of the variable classes segments the bar. Each segment is colorized based on the value for data set completeness of the respective class. The color bar on the right edge of the visualization informs about the interpretation of the colors. The color bar is fixed with a minimum of 0 and a maximum of 1, representing perfectly poor and perfectly good data quality in terms of data set completeness. In order to enable the iterative assessment of the data set completeness, the visualization is implemented as a graphical user interface in Python 3.7 prototypically. Based on the package 'dash' (version 1.18.1), a web-based interface is created given the expert the possibility to select and deselect variables of a drop-down menu. The recalculation based on the variable choice is triggered automatically, updating the heat map of the data set completeness. The data set completeness is highly dependent on the composition of the data set. Adding or excluding variables changes the dimensionality of the feature space and the data set completeness for every single class. Therefore, assessing data set completeness and identifying the appropriate composition of variables is an iterative task. Since each variable requires an own bar, the use of the metric and visualization for data set completeness is limited by the width of the plot. Furthermore, the dependency of the metric's value on the dimensionality of the feature space raises issues regarding the curse of dimensionality [47], particularly the trend of the metric values to equalize each other. In order to preserve clarity and prevent the curse of dimensionality, the number of variables restricts the applicability. However, in model-based data-driven condition monitoring, expert knowledge and data are combined to solve the task. This is not reasonable in systems with several hundred variables or more. In those cases, massive amounts of data are required to extract information with artificial intelligence methods rather than model the dependencies based on the experts' input. Use cases of smaller systems with the problem of limited amounts of data are the focus of this work. In this case, model-based data-driven condition monitoring is reasonable and a multi-dimensional but not high dimensional feature is expected. The workflow in Figure 8 shows the assessment of the data set completeness in the context of a data mining process. In the data cleaning process, the prerequisites (cf. Section 4.1) are created. The relevant, independent variables for the task at hand need to be identified and variables with zero variance should be excluded. Subsequent to the data cleaning, the partitioning of the variables is performed. The expert needs to identify the operating points to partition the variables appropriately. Based on this,  
Figure 7: Schematic concept of the heat map for visualizing data set completeness in multi-dimensional data sets. the data set completeness of each class of the variables is calculated and visualized. The expert iteratively prepares a data set with high data quality by gathering more data or by excluding variables with low data set completeness.