New Collaborative Filtering Algorithms Based on SVD++ and Differential Privacy

Algorithm 1

SGD with gradient perturbation for SVD++ (DPSS++).

Input:   – “user-item” rating matrix

    – number of factors

    – learning rate

    – regularization parameter of SVD++ objective function

    – regularization parameters for computing the item bias, user bias, and implicit feedback factor

    – number of gradient descent iterations

    – upper and lower bounds on the per-rating error

    – differential privacy parameter

Output: Latent factor matrices

(1) Initialize the random latent factor matrices

(2) for     iterations  do

(3)  for each    do

(4)  

(5)  

(6)   

(7)   

(8)   Clamp   to  

(9)    update  

(10)  update  

(11)   end for

(12) end for

(13) return