## 3 Related Work in the Area of the Data Quality Dimension Completeness  
Completeness is one data quality dimension. It is mentioned as one of the most affecting quality dimensions besides accuracy, timeliness and consistency [27]. Completeness is defined as 'the extent to which data are sufficient in breadth, depth, and scope for the task at hand' [15]. This definition reveals already three different aspects of the dimension, namely the breadth, depth and scope. These aspects are data quality attributes representing different viewpoints of the dimension [11]. In order to structure the related work on completeness and to identify the research gap, the attributes introduced in the literature are classified into two categories and four levels. The category divides the attributes into task-independent and task-dependent. Task-independent attributes are assessed without knowledge about the context of the data mining task. In contrast, task-dependent attributes consider the constraints and requirements of the use case [16]. Consequently, the former can be applied regardless of their usage. In contrast, the latter demands experts' input in the form of their expectations to assess whether the data is useful for the task at hand or not. Thereby, the user's constraints and requirements can address expectations on the amount of data as well as the content itself. Other literature refers to these categories as context-independent/context-dependent [28], intrinsic/contextual [15] or internal/external [11]. The four different levels of the classification refer to the data hierarchy (cf. Figure 4). On the lowest level, data quality is evaluated on field/item level [29,30]. One data item refers to a single value of the data set. Furthermore, data is evaluated on variable and record level [29,30], considering one column or one row of the data set, respectively. On the highest level, the schema is the subject of the analysis [13]. The schema specifies the data set structure, given the number of variables and defining the variables' names and data types. Based on these categories and levels, research on completeness is classified in Table 1. Besides the level and category, the proposed name of the attribute is given, and it is indicated whether the considerations are based on sensor and actuator data or other data. Latter is an interesting aspect reflecting the trend of addressing data quality in distinct sectors or application areas [31]. Furthermore, the column F.5 of Table 1 link the attributes to the respective example in Figure 5, which is a fictitious data set of stroke and pressure. This should support the theoretical description of the task-independent attributes by applying the respective metrics to a simple example. Figure 4: Data hierarchy is used to classify different attributes of completeness. It is revealed that the state-of-the-art literature introduces many attributes of completeness considering the different levels and categories. The initial research in data quality focuses on describing data quality dimensions qualitatively without proposing metrics. [PERSON] 1996 identified two different attributes for completeness [29]. The so-called Attribute Completeness is task-independent and evaluates the completeness of the single items regardless of the use case. Data sets with single missing values are not complete. In contrast, the Entity Completeness considers whether all possible values of a variable are included in the data or not. This requires prior knowledge of the expected values (task-dependent). The variable stroke from the example in Figure 1 is not complete, since the values 'fully closed' (stroke = 0%) and 'fully opened' (stroke = 100%) are missing in the data. For [PERSON] and [PERSON], a variable is complete, if all items are available [32]. \begin{table}
\begin{tabular}{l l c c c c c c c} \hline \multicolumn{1}{c}{**Literature, Which Introduces Completeness Qualitatively**} & \multicolumn{5}{c}{**Level**} & \multirow{2}{*}{**Cat.