# Publishing Anonymized Set-Valued Data via Disassociation towards Analysis
## 2 Disassociation and Utility Awareness for Associations
### Ant-Based Clustering Effect on Associations  
In [1], the efficiency of the UGAC technique in terms of preservation of the associations represented in the utility rule is evaluated alongside other experiments analyzing the privacy-utility trade-off. Results are very promising for the preservation of the utility rules. In this section, we investigate the effect of ant-based clustering for the predefined utility rules \(UR\) on the associations beyond \(UR\).  
We chose for the experiment the BMS1 dataset, which contains click-stream E-commerce data, and a set of 70 distinct utility rules \(UR\), extracted from the dataset with different characteristics: highest frequency= 1204 representing frequent association and Lowest frequency = 2 representing a very rare association. Only records that are supersets of the utility rules (36,141 records from the original set of 149,639 records) are clustered and evaluated.  
We compare UGAC (with \(\alpha=0.6\)) to normal horizontal partitioning for disassociation and investigate the overall preservation of associations for the 2 clustering techniques using the Relative Association Error (RAE) defined as:  
\[RAE=\sum_{\forall A\in\mathcal{T}_{|UR}}\frac{(s(A,\mathcal{T}_{|UR})-s(A, \mathcal{T}_{|UR}{}^{*}))}{AVG(s(A,\mathcal{T}_{|UR}),s(A,\mathcal{T}_{|UR}{}^{ *}))} \tag{9}\]  
where \(A\) is any type of associations present in \(\mathcal{T}_{|UR}\) and \(s(A,\mathcal{T}_{|UR})\), \(s(A,\mathcal{T}_{|UR}{}^{*})\) represent respectively the support of the association \(A\) in \(\mathcal{T}_{|UR}\) and its disassociated result \(\mathcal{T}_{|UR}{}^{*}\). In this experiment, two types of associations are evaluated: first, the set of all the couples present in the records related to the utility rules, \(\forall(x,y)\in T_{|UR}\), denoted by \(GA\) and second the set of utility rules \(UR\).  
Table 3 shows that the results of UGAC for \(GA\) and \(UR\) are much better than normal horizontal partitioning. This indicates that for the records that are treated through UGAC, the associations are not deteriorated on the expense of preserving the \(UR\). Finally, we can say that UGAC is reliable for analysis for the utility rules in question and beyond them.  
The above work, as presented, offers an optimization for disassociating interesting rules in the datasets for analysis. However, a disassociated dataset is not the most appropriate data format for knowledge extraction because it breaks down a set of items into disconnected subsets of items. For this reason,  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Technique** & \(RAE\) **for \(GA\)** & \(RAE\) **for \(UR\)** \\ \hline Horizontal Partitioning & 90,171 & 66 \\ \(UGAC\) & 26,636 & 34 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Relative association error (RAE) for \(GA\) and \(UR\).  
we present in the next section, an algorithm that generates a re-associated dataset from the disassociated one, that we intend to call it a neighbor dataset, by re-associating statistically partitioned subsets to restore the original format of set-valued dataset.