Microaggregation is a technique for disclosure limitation aimed at protecting the privacy of data subjects in microdata releases. It has been used as an alternative to generalization and suppression to generate @math -anonymous data sets, where the identity of each subject is hidden within a group of @math subjects. Unlike generalization, microaggregation perturbs the data and this additional masking freedom allows improving data utility in several ways, such as increasing data granularity, reducing the impact of outliers, and avoiding discretization of numerical data. @math -Anonymity, on the other side, does not protect against attribute disclosure, which occurs if the variability of the confidential values in a group of @math subjects is too small. To address this issue, several refinements of @math -anonymity have been proposed, among which @math -closeness stands out as providing one of the strictest privacy guarantees. Existing algorithms to generate @math -close data sets are based on generalization and suppression (they are extensions of @math -anonymization algorithms based on the same principles). This paper proposes and shows how to use microaggregation to generate @math -anonymous @math -close data sets. The advantages of microaggregation are analyzed, and then several microaggregation algorithms for @math -anonymous @math -closeness are presented and empirically evaluated.
While microaggregation has been proposed to satisfy another refinement of @math -anonymity ( @math -sensitive @math -anonymity, @cite_8 ), no attempt has been made to use it for @math -closeness.
@cite_8
1992286709 2164649498 2033472483 2136114025
It is not uncommon in the data anonymization literature to oppose the "old" @math k -anonymity model to the "new" differential privacy model, which offers more robust privacy guarantees. Yet, it is often disregarded that the utility of the anonymized results provided by differential privacy is quite limited, due to the amount of noise that needs to be added to the output, or because utility can only be guaranteed for a restricted type of queries. This is in contrast with @math k -anonymity mechanisms, which make no assumptions on the uses of anonymized data while focusing on preserving data utility from a general perspective. In this paper, we show that a synergy between differential privacy and @math k -anonymity can be found: @math k -anonymity can help improving the utility of differentially private responses to arbitrary queries. We devote special attention to the utility improvement of differentially private published data sets. Specifically, we show that the amount of noise required to fulfill @math ? -differential privacy can be reduced if noise is added to a @math k -anonymous version of the data set, where @math k -anonymity is reached through a specially designed microaggregation of all attributes. As a result of noise reduction, the general analytical utility of the anonymized output is increased. The theoretical benefits of our proposal are illustrated in a practical setting with an empirical evaluation on three data sets. The k-anonymity privacy requirement for publishing microdata requires that each equivalence class (i.e., a set of records that are indistinguishable from each other with respect to certain “identifying” attributes) contains at least k records. Recently, several authors have recognized that k-anonymity cannot prevent attribute disclosure. The notion of l-diversity has been proposed to address this; l-diversity requires that each equivalence class has at least l well-represented (in Section 2) values for each sensitive attribute. In this paper, we show that l-diversity has a number of limitations. In particular, it is neither necessary nor sufficient to prevent attribute disclosure. Motivated by these limitations, we propose a new notion of privacy called “closeness.” We first present the base model t-closeness, which requires that the distribution of a sensitive attribute in any equivalence class is close to the distribution of the attribute in the overall table (i.e., the distance between the two distributions should be no more than a threshold t). We then propose a more flexible privacy model called (n,t)-closeness that offers higher utility. We describe our desiderata for designing a distance measure between two probability distributions and present two distance measures. We discuss the rationale for using closeness as a privacy measure and illustrate its advantages through examples and experiments. k-Anonymity is a useful concept to solve the tension between data utility and respondent privacy in individual data (microdata) protection. However, the generalization and suppression approach proposed in the literature to achieve k-anonymity is not equally suited for all types of attributes: (i) generalization suppression is one of the few possibilities for nominal categorical attributes; (ii) it is just one possibility for ordinal categorical attributes which does not always preserve ordinality; (iii) and it is completely unsuitable for continuous attributes, as it causes them to lose their numerical meaning. Since attributes leading to disclosure (and thus needing k-anonymization) may be nominal, ordinal and also continuous, it is important to devise k-anonymization procedures which preserve the semantics of each attribute type as much as possible. We propose in this paper to use categorical microaggregation as an alternative to generalization suppression for nominal and ordinal k-anonymization; we also propose continuous microaggregation as the method for continuous k-anonymization. The k-anonymity privacy requirement for publishing microdata requires that each equivalence class (i.e., a set of records that are indistinguishable from each other with respect to certain "identifying" attributes) contains at least k records. Recently, several authors have recognized that k-anonymity cannot prevent attribute disclosure. The notion of l-diversity has been proposed to address this; l-diversity requires that each equivalence class has at least l well-represented values for each sensitive attribute. In this paper we show that l-diversity has a number of limitations. In particular, it is neither necessary nor sufficient to prevent attribute disclosure. We propose a novel privacy notion called t-closeness, which requires that the distribution of a sensitive attribute in any equivalence class is close to the distribution of the attribute in the overall table (i.e., the distance between the two distributions should be no more than a threshold t). We choose to use the earth mover distance measure for our t-closeness requirement. We discuss the rationale for t-closeness and illustrate its advantages through examples and experiments.