# A Grid-Based Swarm Intelligence Algorithm for Privacy-Preserving Data Mining
## 1 Introduction  
Data mining, also called knowledge discovery in databases [1; 2; 3; 4; 5; 6], is used to find the useful and meaningful information for further decision-making, and can be utilized in many domains and applications, including basket analytics, DNA sequence analysis, or recommendations. During the mining process, although useful information is discovered, confidential/sensitive information is also revealed at the same time, which causes security and privacy threats. Privacy-preserving data mining (PPDM) [7; 8; 9; 10] has thus become an important topic in recent decades because it cannot only hide private information but also discover the required information through varied data mining techniques. Data sanitization is a way to hide sensitive information by perturbing the database, although this process can also bring about side effects such as a _hiding failure_, _missing cost_, or _artificial cost_. A _hiding failure_ indicates confidential information that has been thought to be hidden but still remains after a sanitization process and can be discovered during the mining process. A _missing cost_ indicates already discovered information that may be missed after the sanitization process, whereas an _artificial cost_ indicates meaningless or unnecessary information that has not been discovered but is mined after the sanitization process. Such side effects can also be regarded as an Non-deterministic Polynomial-time (NP)-hard problem [7; 10] because more confidential information is hidden, and greater loss or an increased amount of information can appear. Many algorithms have been developed to minimize these three side effects during the sanitization process, including straightforward (conventional) or optimization processes. [PERSON] and [PERSON] presented an ID3 algorithm [11] to solve the problem of PPDM based on a decision-tree. [PERSON] et al. then presented a toolkit to solve the problem of a PPDM [12]. [PERSON] et al. [13] designed several algorithms for handling published noisy statistics to vertically partitioned databases. [PERSON] et al. [14] then designed several algorithms to reduce the support/confidence for hiding sensitive information. [PERSON] et al. [15] utilized the Term Frequency-Inverse Document Frequency (TF-IDF) method and presented the Sensitive Itemset Frequency-Inverse Document Frequency (SIF-IDF) algorithm to evaluate the score of each transaction for data sanitization. Several studies related to PPDM have been conducted, most of which are based on a deletion procedure to hide sensitive information [15; 16; 17; 18]. Because the PPDM is a non-trivial and NP-hard problem, it is thus difficult to find optimized solutions between the side effects. Several algorithms based on the evolutionary computation have been designed to obtain the optimal solutions. For instance, [PERSON] et al. utilized genetic algorithms (GAs) to sanitize a database and presented the cpGA2 DT and pGA2 DT algorithms [19; 20]. A good performance has been shown in terms of side effects as compared to a greedy-based algorithm. Although the above algorithms can achieve a good performance in terms of side effects, they rely on the pre-defined weights of three side effects in their pre-defined fitness function. This problem causes the results of the side effects to be seriously influenced by the weighted values; the results are occasionally not optimized, which requires a priori knowledge or an expert to set up these weighted values. To handle this problem, [PERSON] et al. [21] developed the Evolutionary Multiobjective Optimization (EMO)-based algorithm to consider \"data distortion\" and \"knowledge distortion\" in the sanitization process through item deletion. Although this approach concerns multi-objective functions, it may lead to finding incomplete knowledge for decision-making because it directly deletes the attributes from the database, which is not applicable to a sequential dataset.