A novel initialization method of fixed point continuation for recommendation systems

Abstract

In recent years, the problem of matrix completion based on rank minimization has received widespread attention in machine learning. The tightest convex relaxation of this problem is the linearly constrained nuclear norm minimization. Fixed point continuation (FPC), as a representative nuclear norm relaxation matrix completion algorithm, has been proven to perform well in theories and experiments. However, the traditional FPC algorithm initializes the matrix to be completed by zero, which does not make full use of the shrinkage characteristics of the singular value shrinkage operator on the matrix elements and the known field data information, then will lead to slow convergence and poor accuracy. Aiming at this problem, this paper analyzes the shrinkage properties of matrix elements in the iterative process of the FPC algorithm. Combined with the known rating information in the recommendation systems, a new initialization method of overestimation based on FPC is proposed, and it is applied to the rating prediction in the recommendation systems. The experimental results show that the initialization method proposed in this paper greatly improves the algorithm efficiency and prediction accuracy.