[Retracted] Differentially Private Singular Value Decomposition for Training Support Vector Machines

Algorithm 1

DPSVD.

 Input: Raw data matrix , instances n, features d, privacy parameters ε, δ and β, accumulative contribution rate of principal components γ;

 Output: Classification model , private singular vectors V_k;

 Begin

  Generate a noise matrix , every entry is i.i.d. and sampled from N(0, β²);

  Add the noise matrix to the raw data matrix D’ = D + E;

  Compute the singular values σ and singular matrices U, V of D′ by SVD, ;

  Select the target dimension k according to ;

  Select first k singular vectors V_k to project the original training instances to the low-dimensional singular subspace Y = DV_k;

  Compute the classification model f(x) in the singular subspace;

  Use f(x) and V_k to predict the new instances.

 End