# A Grid-Based Swarm Intelligence Algorithm for Privacy-Preserving Data Mining
## 6 Experimental Results
### Side Effects  
In this section, the state-of-the-art single-objective cpGA2 DT [19] and multi-objective NSGA-II-based model [23] are then compared to the designed GMPSO in terms of the _hiding failure (\(\alpha\))_, _missing cost (\(\beta\))_, _artificial cost (\(\gamma\))_ and database dissimilarity (_Dis_). The number of populations for all evolutionary algorithms is set to 50. Because a multi-objective algorithm will produce a set of Pareto-front solutions, we evaluated the side effects based on the average of the produced solutions. The results of _hiding failure_ for the four datasets are shown in Figure 4.  
Figure 4: Hiding failure under varied percentages of sensitivity. Figure 3: Runtime under varied percentages of sensitivity. From Figure 4, we can clearly see that the designed GMPSO reaches a lower side effect in terms of _hiding failure_, which indicates that most confidential information is hidden after the sanitization process. For example, when the percentage of sensitivity is set as 4% for the chess dataset, the hiding failures of cpGA2 DT, the NSGA-II-based model, and the designed GMPSO are 50, 52.5, and 25, respectively, which indicates that the GMPSO achieves the lowest _hiding failure_ compared with the other approaches. When the percentage of sensitivity is set as 6% for the foodmart dataset, the designed GMPSO has no side effects in terms of a _hiding failure_, nor does the NSGA-II-based model. The results of GMPSO under the chess and mushroom datasets outperform the results under the foodmart and T10I4D100K datasets. This is reasonable because the chess and foodmart datasets belong to a dense dataset, and most itemsets have a high relevance to each other, and thus the contents of the transactions even have a high overlap. Therefore, the deleted transactions may have high overlap of confidential information; more confidential information can be deleted together and a lower hiding failure can be achieved. We then applied the results of _missing cost_, as shown in Figure 5.  
From Figure 5, it can be seen that the GMPSO occasionally achieves a higher _missing cost_ under the chess and mushroom datasets, the reason for which is that these two datasets belong to a dense dataset; in addition, the contents of most transactions have a high overlap. Thus, when more confidential information is deleted from the dataset, more discovered information may be deleted together. Based on the results shown in Figure 4a,b, we can see that the GMPSO achieves the lowest _hiding failure_ than the other algorithms. Thus, the GMPSO occasionally produces a higher _missing cost_ in very dense datasets. However, for spare datasets such as foodmart and T10I4D100K shown in Figure 5c,d, respectively, the designed GMPSO produced no _missing cost_ under varied percentages of sensitivity of frequent itemsets compared to the cpGA2 DT and NSGA-II-based model. From Figure 4c,d, we can see that the GMPSO occasionally has no _hiding failure_ and achieves almost optimized solutions as compared to the cpGA2 DT and NSGA-II-based model; we then concluded that the GMPSO achieves a good performance in terms of the _missing cost_. The results of the _artificial cost_ are shown in Figure 6.  
Figure 5: Missing cost under varied percentages of sensitivity. From Figure 6, we can see that GMPSO generates a higher _artificial cost_ than cpGA2 DT and the NSGA-II-based model for very dense datasets such as chess and mushroom, as shown in Figure 6a,b. The reason for this is that, when more of the _hiding failure_ is prohibited, as the results in Figure 4a,b show, for example, the size of the database is reduced; more unexpected rules then arise as new information after the sanitization process owing to the change in threshold. This is reasonable because there is a trade-off relationship between the _hiding failure_ and _artificial cost_.