Adaptive and efficient high-order rating distance optimization model with slack variable

Abstract The classical high-order rating distance model which aims to minimize not only (i) the difference between the estimated and real ratings of the same user–item pair (i.e., the first-order rating distance), but also (ii) the difference between the estimated and real rating difference of the same user across different items (i.e., the second-order rating distance), and use stochastic gradient descent to solve this convex optimization problem in recommender systems, has good performance in prediction accuracy. However, when the manually set parameter for the second-order rating difference is fixed, this model will not converge as the size of dataset increasing, and its performance on efficiency is slow compared with the matrix factorization method. Aiming at improving such model’s adaptability and efficiency, we propose an improved high-order rating distance model with omitting rules based on slack variable, in which the static parameter used to balance the first-order rating distance and the second-order rating distance is replaced by a data-scale sensitive function. We choose Newton method to solve the convex recommendation optimization problem defined in this paper instead of stochastic gradient descent. Our model not only achieves the adaptability by eliminating several static parameters for module balancing, reduces the computation complexity, but also accelerates the optimization function convergence speed. We provide solid theoretical support and conduct comprehensive experiments on four real-world datasets. Experimental results show the proposed model has good performance in terms of prediction accuracy and efficiency.