An Improvement of Privacy-Preserving Scheme Based on Random Substitutions

Data perturbation techniques are one of the most popular models for privacy-preserving data mining due to their practical utility [1]. In a typical data perturbation, before the data owner publishes the data, they randomly change the data in certain way to disguise the private information while preserving some statistical properties for obtaining meaningful data mining models. Agrawal and Haritsa [2] have proposed a generalized matrix-theoretic framework of random perturbation that facilitates a systematic approach to the design of random substitutions. They used a privacy measure called ρ1-to-ρ2 privacy breach [5], and chose a special type of optimal perturbation matrix called the γ-diagonal matrix. Agrawal and Haritsa [2] explored their framework in the context of privacy-preserving association rule mining, and Dowd et al. [4] extended the results to privacy-preserving decision tree mining. Also the authors of [4] explained that random substitution with γ-diagonal matrix is fundamentally different from adding noise and it is secure against data-recovery attacks of [7] and [6]. In this research we discuss a theoretical upper bound of the estimation error for the matrix-based random perturbation method, and concretely examine the relationship among the parameters used in the random substitutions by γ-diagonal matrices. Moreover we propose a method of improving the accuracy of random substitutions and theoretically analyze its effect of improvement on the view point of the estimation error.