# Data Protection and Multi-Database Data-Driven Models
## 4 Experiment and Analysis  
The experiments show that when we integrate two masked protected files, the number of correct reidentifications degrades very quickly for most masking methods. That is, the number of records that are correctly linked (i.e., one record in one file is associated with the right record in the other file) is very small, even for parameters providing very low protection. This holds for most masking methods except for the ones based on SVD and NMF, which have, in general, quite large reconstruction rates when the number of singular values is high and when the number of components is high. Figure 1 illustrates the case of microaggregation (MDAV, Mondrian), and noise addition (Gaussian and Laplacian noise). When their parameters are equal to zero, there is no protection. Here, we see that even with six common attributes, the number of reidentifications decreases very rapidly. Figure 2 represents the number of correct reidentifications for SVD and NMF-based protection. We can see that there is a drop in the number of reidentifications in this case as well. This drop is not so fast as it is for microaggregation. The figures also show that using more attributes for integration does not mean that the database integration is better. In the case of the Concrete data set, observe that for SVD, one and two attributes lead to better reidentification levels than more attributes (for a number of singular values between three and six). The same pattern appears in the Tarragona data set, and, to some extent, also for NMF-based protection. In contrast, the experiments show that even when we have a low number of correct reidentifications, the machine learning model produced from the  
Figure 1: Number of correct links for the Concrete data set (**top**) and the Tarragona data set (**bottom**) when data are protected using MDAV (**top left**), Mondrian (**top right**), noise addition using Gaussian distribution (**bottom left**), and noise addition using Laplacian distribution (**bottom right**). Each figure includes curves for different numbers of common attributes (from 1 to 6). integrated database can have similar performance to the one obtained with the original database. We have these results for a significant number of protection levels. Figure 3 top displays the error obtained for machine learning models extracted from the Concrete data set when these data are protected using Mondrian. In the figures, we have a value of \(k\) up to 20, which accounts for significant protection. Note that in the experiments, we use a training set of 824 records, which means that for \(k=20\), the \(k\)-anonymous file has only \(824/20=41\) different records. Figure 3 bottom shows the difference between the error when we apply the masking method and the error when we do not apply the masking method (i.e., the mean error of the model trained with the original data set). Naturally, larger values of \(k\) will result in more distortion of the protected file (fewer different records) and produce a protected database that has low accuracy. In particular, for \(k\) equal to or larger than 50 the error becomes extremely large. To illustrate this latter case, we provide in Figure 4 the error for larger values of \(k\). Results are also given for the Concrete database protected using both MDAV (left) and Mondrian (right). In this case, the results correspond to those obtained using a linear regression model. The figures provide the results of different numbers of common attributes. Figure 2: Number of correct links for the Concrete data set (**top**) and the Tarragona data set (**bottom**). Data are protected using SVD and NMF-based protection. The number of correct links decreases when protection is increased (i.e., singular values in SVD and components in NMF). Different curves correspond to different numbers of attributes in the reidentification. Figure 3 shows that the error is about 1.1 with significant protection (\(k=20\) for microaggregation using MDAV).