Utility metrics

The details of the three utility metrics implemented are presented below:

• Average equivalence class size (\(C_{avg}\)): Two versions are implemented depending on whether or not complete rows have been deleted from the original dataset (in this case, sup=True in get_utility_report_values). Be DB the original database and DB’ the anonymized one. Be |EC| the number of equivalence classes in the anonymized dataset and k the verified value for k-anonymity:

\[\begin{split}C_{avg} = \left\{ \begin{array}{ll} \frac{|DB'|}{k \hspace{0.1cm} |EC|} & \hspace{0.3cm} \mbox{if } sup=True\\ \frac{|DB|}{k \hspace{0.1cm} |EC|} & \mbox{if } sup=False\\ \end{array} \right.\end{split}\]

• Classification metric (CM): This metric is calculted for only one sensitive attribute. Be N the number of rows of the raw datatset. Be \(penalty(r_{i})=1\) if the row \(r_{i}\) has been suppresed or if its associated sensitive attribute takes a value other than the majority in the equivalence class to which it belongs, and 0 otherwise. The classification metric is defined as folows:

\[CM = \frac{1}{N}\sum_{i=1}^{N}penalty(r_{i}),\]

• Discernability metric (\(DM^{*}\)): A version of the classical discernability metric has been considered in order to penalize the deletion of records. Thus, it has been implemented according to the following equation, with DB the raw database, DB’ the anonymized one, \(N_{ec}\) the number of equivalence classes and \(EC_{i}\) the i-th equivalence class:

\[DM^{*} = \sum_{i=0}^{N_{ec}}|EC_{i}|^{2} + |DB|^{2}-|DB||DB'|\]

Note: for the calculation of these three metrics, it is necessary to enter the original dataset prior to anonymization.