Additive Randomization has been a primary tool to hide sensitive private information during privacy preserving data mining. The previous work based on Spectral Filtering empirically showed that individual data can be separated from the perturbed one and as a result privacy can be seriously compromised. Our previous work initiated the theoretical study on how the estimation error varies with the noise and gave an upper bound for the Frobenius norm of reconstruction error using matrix perturbation theory. In this paper, we propose one Singular Value Decomposition (SVD) based reconstruction method and derive a lower bound for the reconstruction error. We then prove the equivalence between the Spectral Filtering based approach and the proposed SVD approach and as a result the achieved lower bound can also be considered as the lower bound of the Spectral Filtering based approach.
[1]
V. N. Bogaevski,et al.
Matrix Perturbation Theory
,
1991
.
[2]
Charu C. Aggarwal,et al.
On the design and quantification of privacy preserving data mining algorithms
,
2001,
PODS.
[3]
Wenliang Du,et al.
Deriving private information from randomized data
,
2005,
SIGMOD '05.
[4]
Yehuda Lindell,et al.
Privacy Preserving Data Mining
,
2002,
Journal of Cryptology.
[5]
Qi Wang,et al.
On the privacy preserving properties of random data perturbation techniques
,
2003,
Third IEEE International Conference on Data Mining.
[6]
Xintao Wu,et al.
On the use of spectral filtering for privacy preserving data mining
,
2006,
SAC '06.