On the Lower Bound of Reconstruction Error for Spectral Filtering Based Privacy Preserving Data Mining

  • Songtao Guo
  • Xintao Wu
  • Yingjiu Li
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4213)


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.


Singular Value Decomposition Reconstruction Error Frobenius Norm Data Owner Spectral Filter 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Songtao Guo
    • 1
  • Xintao Wu
    • 1
  • Yingjiu Li
    • 2
  1. 1.UNC Charlotte 
  2. 2.Singapore Management Univ. 

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