# Protecting Sensitive Data in the Information Age: State of the Art and Future Prospects
## 3 State-of-the-Art Privacy Measures
### Differential Privacy  
The previously discussed privacy techniques focused on data from individual users, which are distorted before processing. When transforming the data to knowledge, the base data of multiple users are often merged. This can be seen, e.g., in the recommender systems presented in Section 2.6. Here, the models that constitute the basis for the recommendations are trained on the preferences of all users. To this end, [PERSON] [158] introduces _differential privacy_ as a measure for assessing the privacy threat to an individual when he or she shares his or her data. The goal is to maximize the accuracy of statistical information about a data collection (e.g., the models of the recommender systems) while minimizing the potential privacy risks for individuals. This can be illustrated by a simple example: In collaborative filtering, let there be a cluster consisting of two persons. Even if the interests of the individual users cannot be derived directly from the trained models, person \(A\) can be sure that if a new item is recommended to him or her, person \(B\) is interested in this very item. Thus, the privacy of person \(B\) has still been violated.  
The basic idea of differential privacy is straightforward, as shown in Figure 14. Database 1 contains data about the four users. If the red user wants to know whether her privacy is disclosed when a statistic is computed on these bases data using the function \(f\) (respectively, a model is trained on these data), a _neighboring database_ Database 2 can be created, which contains all datasets of Database 1 except the data about the user in question. If the function \(f\) is applied to Database 2 and the results are similar, the privacy of the red user has not been exposed. So, formally speaking, the following must apply:  
\[\mathbb{P}[f(\mathcal{D}_{1})\in\mathcal{R}]\leq exp(\epsilon)\mathbb{P}[f( \mathcal{D}_{2})\in\mathcal{R}] \tag{4}\]  
A function \(f\) is \(\epsilon\)_-differentially private_ if its results \(\mathcal{R}\) for all of database \(\mathcal{D}_{1}\)'s neighboring databases \(\mathcal{D}_{2}\) only differ by an insignificant \(\epsilon\). Since there are different privacy requirements depending on the data and processing context, there are approaches that adjust the degree of applied obfuscation according to the level of exposure. That is, there is not a single \(\epsilon\) that describes the privacy requirements but rather many such measures that are applied depending on the current situation [159].  
While this sounds promising in theory, it turns out that differential privacy is rarely applied in practice. One reason for this is that there is a lack of awareness of differential privacy principles in the development of algorithms, and in particular, the handling of complex types of data proves to be difficult [160]. In research, however, there is a variety of noise algorithms that establish the \(\epsilon\)-differentially private properties without impairing the quality of the outcomes excessively [161]. Especially for application scenarios such as recommender systems, differential privacy is therefore suitable [162].  
The key strengths and weaknesses of differential privacy approaches are the following:  
Strengths:  
* Differential privacy approaches allow statistical analysis while preserving the privacy of each individual involved.
* In order to guarantee the differential privacy property, the method is not restricted to any particular technique, which means that an appropriate obfuscation technique can be chosen depending on the base data.  
Weaknesses:  
* Differential privacy approaches can only be applied when large amounts of data from many different individuals are analyzed.
* Ensuring the differential privacy property is difficult depending on the base data requires the use of destructive noise algorithms. As a result, potentially relevant aspects in the data are lost.