An Improved Non-Negative Latent Factor Model for Missing Data Estimation via Extragradient-Based Alternating Direction Method

In this article, an improved double factorization-based symmetric and non-negative latent factor (Im-DF-SNLF) model is proposed to make the estimation for missing data in symmetric, high-dimensional, and sparse (SHiDS) matrices. The main idea of the Im-DF-SNLF model is fourfold: 1) considering the data variety in the practical engineering, non-negative latent factors (NLFs) in different cases are considered to better reflect the latent relationships between entries; 2) the
$l_{2}$
-norm regularization and the Lagrangian multiplier technique are simultaneously adopted to handle the overfitting and satisfy the non-negative constraint for latent factors (LFs); 3) the extragradient-based alternating direction (EGAD) method is utilized to accelerate the model training and rigidly guarantee the non-negativity of LFS; and 4) a rigorous proof is provided to show that, under the given assumption that the objective function is smooth and has a Lipschitz continuous gradient, the designed algorithm can find an
$\epsilon $
-optimal solution within
$O(1/\epsilon )$
, and the upper bound of the learning rate is given by 1/2. Finally, experimental results on public datasets are given to demonstrate the effectiveness of our proposed Im-DF-SNLF model with EGAD.