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

Algorithm 3

ALS with output perturbation of SVD++ (DPSASOut++).

Input: – “user-item” rating matrix

    – number of factors

    – regularization parameter of SVD++ objective function

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

    – number of gradient descent iterations

    – differential privacy parameter

Output: Latent factor matrices  

(1) Initialize random latent factor matrices :

(2) for   do

(3)  for    do

(4)  

(5)  

(6)  for  ,  do

(7)   Generate random noise vector with pdf

(8)     

(9)     

(10)  end for

(11)  for    do

(12)  Generate random noise vector with pdf

(13)    

(14)    

(15)  end for

(16)  end for

(17) end for

(18)  return