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Multidimensional data collection via interval-based perturbation under (ϵ,δ)-local differential privacy
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DOI：10.1016/j.cose.2026.105083.png)
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Abstract
En 中文
With the rapid development of the Internet of Things and mobile crowdsensing, collecting multidimensional numerical data while preserving users’ privacy has become a critical challenge. Existing (ϵ,δ)-local differential privacy (LDP) mechanisms typically adopt dimension sampling to alleviate privacy-budget splitting. However, these methods persistently rely on two-valued extreme perturbation structures, which increase estimation variance. To overcome this limitation, this paper proposes a multidimensional interval-based perturbation mechanism (MIPM). Rather than using two-valued extreme outputs, MIPM maps the original data to a three-interval distribution and assigns a higher probability to the input-dependent middle interval, thereby reducing single-dimensional perturbation variance. Furthermore, to balance dimension coverage against per-dimension noise, the selection of the sampling dimension k from d dimensions is formulated as a theoretical variance-minimization problem. The variance-minimizing sampling dimension is derived under each of the minimum worst-case variance (MWCV) and minimum average expected variance (MAEV) criteria to replace previous empirical approximation rules. We provide rigorous theoretical proofs of unbiasedness and multidimensional (ϵ,δ)-LDP guarantees, complemented by detailed security and complexity analyses. Extensive experiments on two synthetic and two real-world datasets demonstrate that the proposed MIPM consistently achieve lower estimation errors and tighter confidence intervals than Mechanism-2/MEMND, with MIPM-MAEV and MIPM-MWCV reducing the mean squared error (MSE) by an average of 53.7% and 46.2%, respectively.
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