## 2 Materials and Methods
### Anonymization and Information Loss Estimation
#### 2.2.4 Information Loss  
Anonymization provides the benefit of data privacy, but at the same time negatively affects data utility by causing information loss. Three metrics that can be used for the estimation of information loss due to anonymization are generalized information loss, discernibility and average equivalence class size [35]. Generalized information loss represents the penalty induced from the generalization of a specific attribute by taking into account the fraction of the domain values that have been generalized. The generalized information loss for an anonymized table \(T^{*}\) was calculated according to Equation (1), where \(T\) is the original table, \(i\) = 1,..., \(n\) corresponds to an attribute, \(j\) = 1,..., \(\mid T\mid\) corresponds to a table record, \(U_{i}\), \(L_{i}\) are the upper and lower values of each arithmetic attribute \(i\), \(U_{ij}\), \(L_{ij}\) are the upper and lower values of arithmetic attribute \(i\) for the equivalence class the record \(j\) belongs in, \(N_{i}\) is the number of different values for each categorical attribute \(i\), and \(N_{ij}\) is the number of different values for categorical attribute \(i\) in the equivalence class the record \(j\) belongs in [35; 36; 37]. The discernibility metric captures the indistinguishability of a table record compared to the rest by assigning a penalty to each record, equal to the size of the equivalence class it belongs in. The discernibility metric for an anonymized table \(T^{*}\) was calculated according to Equation (2), where \(\mid EQ\mid\) is the number of records in the equivalence class \(EQ\)[23; 35; 38]. The average equivalence class size estimates how well the equivalence class formulation approaches the optimal case, in which every equivalence class contains \(k\) records. It is calculated according to Equation (3), where \(\mid T\mid\) is the number of table records, \(\mid EQs\mid\) is the total number of equivalence classes created in the anonymized table \(T^{*}\), and \(k\) is the minimum equivalence class size allowed [23; 35]. \[GIL(T*)=\frac{1}{|T|n}\times\sum_{i=1}^{n}\sum_{j=1}^{|T|} \begin{cases}\frac{U_{ ij}-U_{ij}}{U_{i}-U_{i}},&\text{if $i$ is arithmetic}\\ \frac{U_{ij}-1}{N_{i}-1},&\text{if $i$ is categorical}\end{cases}  \tag{1}\]  
\[DM(T*)=\sum_{\forall\text{Eqs.},|EQ|\geq k}|EQ|^{2} \tag{2}\]  
\[C_{AVG}(T*)=\frac{|T|}{|EQ\text{s}|k} \tag{3}\]  
After one-hot decoding, the original dataset was subjected to anonymization by applying the Mondrian algorithm for various \(k\) values and quasi identifier (\(QI\)) set attributes. The algorithm choice is justified due to its performance as well as the fact that the dataset does not contain sensitive attributes (Table 1). The information loss that occurred due to the anonymization process was measured with generalized information loss (\(GIL\)), discriminbility metric (\(DM\)) and average class size (\(C_{AVG}\)) metrics for each parameter combination. The different dataset versions that were generated from the anonymization process, the corresponding anonymization parameter values and the obtained values of the information loss metrics can be seen in Table 2.