# Publishing Anonymized Set-Valued Data via Disassociation towards Analysis
## 6 Conclusion  
Anonymization is challenging when data must be analyzed, studied and explored afterwards. Unstructured data complicate the anonymization process, since in a very general way data items may vary tremendously in structure and value without following a pattern. Set-valued data is a type of unstructured data representing multi-sets of sets. In this work, we are interested in publishing an anonymized set-valued dataset, ready for future accurate analysis. In this context, set-valued data is considered for isolated data, without temporality, and without semantics. This scenario is a generalization of specific data values, which can be considered for a broader investigation of set-value data. Disassociation is an anonymization technique for set-valued datasets, presented by [2]. It guarantees \(k^{m}\)-anonymity for associations without altering the value of the data items. It proceeds by grouping the data records in different clusters and then \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Frequent 3-Itemset Acronyms** & **Count in \(\mathcal{T}\)** & **Count in \(\mathcal{T}^{\prime}\)** & **Rank in \(\mathcal{T}\)** & **Rank in \(\mathcal{T}^{\prime}\)** \\ \hline Itemset1 & 417 & 338 & 1 & 1 \\ Itemset2 & 351 & 281 & 2 & 2 \\ Itemset3 & 335 & 274 & 3 & 3 \\ Itemset4 & 322 & 238 & 4 & 5 \\ Itemset5 & 315 & 223 & 5 & 8 \\ Itemset6 & 310 & 231 & 6 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Frequent three-itemsets (minimum support = 0.005). Figure 6: Frequent association rules mining (support \(\geq\) 0.001). vertically separate items of the records when \(k^{m}\)-anonymity is not verified, thus creating ambiguity on the level of associations for the items that are vertically separated in a cluster. This paper is an extension of the work done in [1], where the utility-privacy trade-off in a disassociated dataset is studied deeply. The loss of associations for aggregate analysis is considered for the theoretical study. We came to the conclusion that the loss of the utility is directly linked to the clustering process of disassociation. Driven by this problem we propose in [1], UGAC, to drive the process of clustering for a set of records representing predefined utility rules. As a continuity of the previous work, we tackle the problem of knowledge extraction in a disassociated dataset. We know from the aggregate analysis that it is hard to evaluate itemsets that are split on multiple record chunks. The problematic becomes: how can we re-associate the itemsets from the disassociated result while staying faithful to anonymization and knowledge extraction at the same time, in set-valued datasets? To solve this problem, we define a general notion of similarity between datasets: neighbor datasets. Neighbor datasets are datasets that are not copies but synthetic representation, that leads to trustworthy data analysis. To standardize our notion of a neighborhood, we need a distance to assess it. Up to our knowledge, there exists no specific metric for set-valued data which is mathematically defined as a multiset of sets. Our first contribution in this work is the formalization of the datasets into trees and the use of tree edit distance that calculates the number of transformations needed to move from one tree to another. This way we are able to calculate a distance between two multisets of sets, also known as datasets. Our second contribution is an algorithm that intuitively generates neighbor datasets. We propose a probabilistic wheel re-association algorithm to generate a re-associated dataset from the result of disassociation of the original dataset. Finally, we test our utility guided ant-based clustering and probabilistic wheel re-association algorithms to evaluate their efficiency especially for knowledge extraction and data analysis in the context of general set-valued data. From the experiments, we can see that re-associated datasets create a neighborhood to the original dataset that depends on the privacy level imposed by disassociation.