Privacy Preserving RBF Kernel Support Vector Machine

Algorithm 1

Hybrid SVM algorithm.

Input: Public data 𝐷_public, private data 𝐷_private, the dimensionality 𝐷 of 𝝆, a regularization parameter 𝐶,

and privacy budget 𝜖;

Output: Differentially private SVM;

(1) Use the public data to compute 𝝆=(𝝆₁,…,𝝆_𝐷)^𝑇 via (5), (6);

(2) Transform each record of the private data to new 2D-dimensional data via the mapping function 𝑧(𝑥)

defined by (7);

(3) Compute the parameter 𝜶 in the dual space with the transformed private data, and 𝐰 in the primal space

via 𝐰=∑^𝑛_𝑖=1𝑦_𝑖𝛼_𝑖𝑧(𝐱_𝑖);

(4) Draw 𝝁 from Lap(𝜆)^2𝐷, 𝜆=2^2.5𝐶√𝐷/𝑛𝜖, then return 𝐰=𝐰+𝝁 and 𝝆.