tcloseness

T-closeness is a data anonymization privacy model designed to prevent attribute disclosure in published data. It builds on k-anonymity and l-diversity by requiring that the distribution of a sensitive attribute within every equivalence class of quasi-identifiers is "close" to the distribution of that attribute in the overall data. The closeness is measured with a distance function and bounded by a threshold t, which is chosen by the data publisher.

Formally, let S be a sensitive attribute with possible values and let P be the global distribution of S in the dataset. For each equivalence class G created by generalizing or suppressing quasi-identifiers, let P_G be the distribution of S within G. The dataset satisfies t-closeness if the distance between P_G and P does not exceed t for every class G. Common distance metrics include Earth Mover’s Distance (Wasserstein distance) or other distributional distances such as L1 or chi-squared measures.

Purpose and rationale: t-closeness aims to reduce the risk that an attacker, who knows an individual's quasi-identifiers, can infer sensitive information beyond what is implied by the overall data distribution. It addresses certain disclosure risks that k-anonymity and l-diversity do not fully mitigate, especially when the sensitive attribute has a skewed or narrow distribution.

Calculation and use: To achieve t-closeness, data custodians apply anonymization techniques that generalize or suppress quasi-identifiers until all equivalence classes meet the t-closeness criterion. If a class cannot be made to satisfy the threshold without excessive data distortion, the publisher may adjust t or the data release strategy.

Limitations: t-closeness does not provide formal guarantees like differential privacy and can still allow re-identification risks under adversaries with auxiliary information. It can also degrade data utility if the threshold is too strict or the data domain is highly imbalanced.