Low-rank Matrix Completion Methods Based On Particle Swarm Optimization

Low-rank matrix completion is an emerging technique that can accurately recover a great number of missing entries by using a small number of observed elements in a matrix.Due to the high accuracy and speed of the recovery methods,it has been now widely used in image processing,signal processing,and artificial intelligence.The low-rank matrix completion methods based on weighted nuclear norm minimization are one of the most popular improvements with high convergence accuracy,mainly including weighted singular value thresholding,truncated kernel norm minimization,schatten＿p norm minimization and iterative reweighted nuclear norm minimization.However,all these methods have certain problems: 1)convergence accuracy still has some room for improvement.Existing studies suggest that the values of the singular value weights should be inversely proportional to the singular value.However,in what way should the weight function of singular values be incremented: linearly,by a convex function or by a concave function?(2)Weights are simple to set and parameters are tedious to adjust: Traditional weighted kernel parametric minimization methods usually set a fixed threshold adjustment function to generate the weights of singular values,and the relevant parameters are fixed during program operation.Since a set of parameters may only fit a certain test matrix,the parameters need to be readjusted after data changes.To address the above problems,this paper adopts a particle swarm optimization algorithm with strong global search performance to dynamically and adaptively match suitable thresholds for the singular values of the matrices and proposes an improvement method.The main work of this paper includes.1)Proposing an improved particle swarm optimization algorithm based on aggregation detection,abbreviated as ADPSO.the ADPSO algorithm has a strong ability to jump out of the local optimal region,so the global search capability is stronger,and its convergence accuracy is higher than that of the traditional particle swarm methods.2)A weighted kernel norm minimization method based on particle swarm optimization,abbreviated as PWNNM,is proposed.The PWNNM method makes full use of the global search capability of the ADPSO algorithm to search for optimal parameter combinations for three different types of thresholds generating functions,and then generates thresholds for singular values.Due to the good parameter robustness,strong global search capability and high convergence accuracy of ADPSO algorithm,the improved PWNNM algorithm also has the advantages of high convergence accuracy and simple parameter setting,easy adjustment and low data dependency.The experimental results fully demonstrate that the improved ADPSO algorithm has better convergence accuracy than the traditional particle swarm optimization algorithm;the improved PWNNM has higher convergence accuracy and lower data dependence than the traditional low-rank matrix complementation method.