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

Algorithm 2

ALS with objective perturbation for SVD++ (DPSAObj++).

Input: – “user-item” rating matrix

    – number of factors

    – total number of ratings

    – 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

    – the parameter for computing the slack term

Output: Latent factor matrices

(1) Initialize random latent factor matrices  :

(2) for   do

(3)   for    do

(4)   

(5)   

(6)     for  , do

(7)    let  

(8)    if   then

(9)    else  

(10)    Generate random noise vector    with pdf

(11)    Compute  

(12)   end for

(13)    for    do

(14)     Omit (the same as (7)~(10))

(15)  Compute  

(16)    end for

(17)   end for

(18) end for

(19)   return