# Enhancing Utility in Anonymized Data against the Adversary's Background Knowledge
## 2 Related Work
### Anonymization with Adversary's Background Knowledge  
On the other hand, the type of adversary knowledge is one of the open challenges. None of the above models can preserve privacy against an adversary with BK [6; 26; 27]. The correlation between attribute values is a significant BK that complicates privacy protection [6; 26; 28; 29]. This work mitigates the risk posed by data correlation between sensitive and quasi-identifier (QI) attributes. Methods for modeling the BK are divided into logic-based [27; 30] and probability-based tools [6; 18; 26; 31]. The first category proposes a language for describing a particular level of knowledge and a set of techniques for limiting disclosure attacks. The second category models background knowledge (BK) as a probability distribution that links sensitive attribute values to individual respondents in the dataset. Another type of privacy models are the differential privacy models. These models have also attracted attention because of some noise addition and are categorized as semantic privacy models [32; 33]. However, studies have shown that such models are ineffective while the adversary possesses some BK [34]. Therefore, the work focused in this research (syntactic approach such as \(k\)-anonymity and its refinements) has more utility and \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Name** & **Gender** & **Age** & **Zip-Code** & **Disease** \\ \hline Cayla & F & 65 & 12040 & Cancer-II \\ Ganya & F & 66 & 12041 & Flu \\ Elisa & F & 66 & 12041 & Depression \\ Dior & F & 66 & 12041 & GRED \\ Harriet & F & 67 & 12041 & Alzheimer-I \\ Fiona & F & 65 & 12041 & Diabetes-II \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Original microdata. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**QI Group No. ** & **Gender** & **Age** & **Zip-Code** & **Disease** \\ \hline
1 & F & [65; 66; 67; 68; 69; 70; 71; 72; 73; 74; 75; 76; 77; 78; 79; 80; 81; 82; 83; 84; 85; 86; 87; 88; 89; 90; 91; 92; 93; 94; 95; 96; 97; 98; 99; 100; 99; 111; 112; 113; 114; 115; 116; 117; 118; 119; 120; 121; 122; 130; 122; 131; 132; 133; 134; 135; 136; 137; 138; 139; 140; 141; 142; 143; 144; 145; 146; 147; 148; 149; 150; 151; 152; 153; 154; 155; 156; 157; 158; 159; 160; 161; 162; 163; 164; 165; 166; 167; 168; 169; 170; 171; 172; 173; 174; 175; 176; 177; 178; 179; 180; 181; 182; 183; 184; 185; 186; 187; 188; 189; 190; 191; 192; 193; 194; 195; 196; 197; 198; 199; 200; 201; 2021; 203; 2041; 205; 206; 207; 208; 209; 2109; 221; 223; 224; 225; 226; 227; 228; 290; 223; 231; 232; 233; 234; 235; 236; 237; 238; 239; 240; 241; 242; 243; 244; 245;  
```
Input:\(T=\{r_{1},r_{2},\ldots,r_{n}\}\): The original microdata; \(PD^{\text{SJ}}\): Background Knowledge distributions of table \(T\); \(I\), \(t\), and \(k\): the parameters in privacy model. Output: A set of QI groups \(\{q_{1},\ldots,q_{n}\}\)
```  
**Algorithm 1**UHRA Algorithm. In the first step, a cluster of records is created using hierarchical agglomerative clustering. Jensen Shannon Divergence (JSD) [35] is used to calculate the similarity between probability distributions. The cutoff point is defined as the threshold J, below which the distribution difference between a node and its descendants is considered small enough. This step utilizes the complete linkage method to guarantee that the distance between any two records in a cluster is no greater than J. This step outputs a set of clusters, \(\{N_{1}\),..., \(N_{|N|}\}\), and for each cluster \(N_{i}\) with at least \(k\) records, the \(t\)-\(k\)-Utility algorithm is executed. Clusters with less than \(k\) records are not disseminated. The \(t\)-\(k\)-Utility algorithm partitions the cluster \(N_{i}\) into groups where \(k\)-anonymity and \(t\)-closeness are fulfilled. To enhance utility, records are moved between groups without violating the privacy requirements. The following lemma describes a guarantee condition in which the \(t\)-\(k\)-Utility produces \(k\)-anonymous data satisfying \(t\)-closeness.