Advances in data collection and storage technologies have given way to the establishment of transactional databases among companies and organizations, as they allow enormous amounts of data to be stored efficiently. Useful knowledge can be mined from these data, which can be used in several ways depending on the nature of the data. Quite often companies and organizations are willing to share data for the sake of mutual benefit. However, the sharing of such data comes with risks, as problems with privacy may arise. Sensitive data, along with sensitive knowledge inferred from this data, must be protected from unintentional exposure to unauthorized parties. One form of the inferred knowledge is frequent patterns mined in the form of frequent itemsets from transactional databases. The problem of protecting such patterns from being discovered, is known as the frequent itemset hiding problem. In this paper we present a toolbox, which provides several implementations of frequent itemset hiding algorithms. Firstly, we summarize the most important aspects of each algorithm. We then introduce the architecture of the toolbox and its novel features. Finally, we provide experimental results on real world datasets, demonstrating the capabilities of the toolbox and the convenience it offers in comparing different algorithms.
@cite_17 were the first to introduce an integer linear programming formulation of the frequent itemset hiding problem. The solution of the integer linear program points out which transactions need to be sanitized in order to conceal the sensitive patterns. The sanitization process is addressed as a separate phase, independently of the linear programming solution, in a heuristic yet suboptimal way. Sun and Yu @cite_16 introduce a greedy border-based approach for hiding sensitive frequent itemsets. They propose a heuristic algorithm that takes advantage of the interplay between preserving maximally non-sensitive and downsizing minimally sensitive frequent itemsets, and gives, as a result, an accurate and efficient hiding solution.
@cite_16 @cite_17
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In this paper, we propose a novel approach to address the frequent item set hiding problem, by formulating it as an integer linear program (ILP). The solution of the ILP points out the transactions that need to be sanitized in order to achieve the hiding of the sensitive frequent item sets, while the impact on other non-sensitive item sets is minimized. We present a novel heuristic approach to calculate the coefficients of the objective function of the ILP, while at the same time we minimize the side effects introduced by the hiding process. We also propose a sanitization algorithm that performs the hiding on the selected transactions. Finally, we evaluate the proposed method on real datasets and we compare the results of the newly proposed method with those of other state of the art approaches. We propose a methodology for hiding all sensitive frequent itemsets in a transaction database. Our methodology relies on a novel technique that enumerates the minimal transversals of a hypergraph in order to induce the ideal border between frequent and sensitive itemsets. The ideal border is then utilized to formulate an integer linear program (ILP) that answers whether a feasible sanitized database that attains the ideal border, exists. The solution of the program identifies the set of transactions that need to be modified (sanitized) so that the hiding can be achieved with the maximum accuracy. If no solution exists, we modify the ILP by relaxing the constraints needed to be satisfied so that the sanitized database preserves the privacy with guarantee but with minimum effect in data quality. Experimental evaluation of the proposed approach on a number of real datasets has shown that the produced sanitized databases exhibit higher accuracy when compared with the solutions of other well-known approaches. Inverse frequent set mining (IFM) is the problem of computing a transaction database D satisfying given support constraints for some itemsets, which are typically the frequent ones. This article proposes a new formulation of IFM, called IFMI (IFM with infrequency constraints), where the itemsets that are not listed as frequent are constrained to be infrequent; that is, they must have a support less than or equal to a specified unique threshold. An instance of IFMI can be seen as an instance of the original IFM by making explicit the infrequency constraints for the minimal infrequent itemsets, corresponding to the so-called negative generator border defined in the literature. The complexity increase from PSPACE (complexity of IFM) to NEXP (complexity of IFMI) is caused by the cardinality of the negative generator border, which can be exponential in the original input size. Therefore, the article introduces a specific problem parameter κ that computes an upper bound to this cardinality using a hypergraph interpretation for which minimal infrequent itemsets correspond to minimal transversals. By fixing a constant k, the article formulates a k-bounded definition of the problem, called k-IFMI, that collects all instances for which the value of the parameter κ is less than or equal to k—its complexity is in PSPACE as for IFM. The bounded problem is encoded as an integer linear program with a large number of variables (actually exponential w.r.t. the number of constraints), which is thereafter approximated by relaxing integer constraints—the decision problem of solving the linear program is proven to be in NP. In order to solve the linear program, a column generation technique is used that is a variation of the simplex method designed to solve large-scale linear programs, in particular with a huge number of variables. The method at each step requires the solution of an auxiliary integer linear program, which is proven to be NP hard in this case and for which a greedy heuristic is presented. The resulting overall column generation solution algorithm enjoys very good scaling as evidenced by the intensive experimentation, thereby paving the way for its application in real-life scenarios. Reducing hidden bias in the data and ensuring fairness in algorithmic data analysis has recently received significant attention. We complement several recent papers in this line of research by introducing a general method to reduce bias in the data through random projections in a fair'' subspace. We apply this method to densest subgraph and @math -means. For densest subgraph, our approach based on fair projections allows to recover both theoretically and empirically an almost optimal, fair, dense subgraph hidden in the input data. We also show that, under the small set expansion hypothesis, approximating this problem beyond a factor of @math is NP-hard and we show a polynomial time algorithm with a matching approximation bound. We further apply our method to @math -means. In a previous paper, [NIPS 2017] showed that problems such as @math -means can be approximated up to a constant factor while ensuring that none of two protected class (e.g., gender, ethnicity) is disparately impacted. We show that fair projections generalize the concept of fairlet introduced by to any number of protected attributes and improve empirically the quality of the resulting clustering. We also present the first constant-factor approximation for an arbitrary number of protected attributes thus settling an open problem recently addressed in several works.