Research On Optimization Algorithms With Matrix Factorization Models

Matrix factorization is to decompose the original data matrix into many matrices such that their product approximates the original data matrix.Matrix factorization can be used in data dimensional reduction or learning overcomplete bases.However,tradi-tional matrix factorization algorithms have many deficiencies.Firstly,they can easily trap into the local solution,but can not search the global optimal solution.Secondly,most of them for optimizing each subproblem have slow convergence,high computation and low accuracy.Therefore,several algorithms with faster convergence,smaller com-putation and higher accuracy are proposed to optimize matrix factorization.Theory and experiments demonstrate the feasibility and effectiveness of our proposed algorithms.In addition to researching the optimization algorithms for matrix factorization,this paper discusses how to apply matrix factorization to practical problems.Based on the principle of matrix factorization,a supervised learning method is proposed for image recognition.Our achievements are as follows:·A class of algorithms based on inertial neural network are proposed to optimize non-negative matrix factorization.The inertial neural network is proved to be stable by Lyapunov knowledge and can converge to the global optimal solution.Compared with existing algorithms,our proposed algorithms can search the global solution by changing the inertial term of neural networks.·A class of algorithms based on estimation sequence theory are proposed to opti-mize nonnegative matrix factorization:alternatively optimizing two constrained convex quadratic programming problems.Compared with traditional algorithms, the advantages are that the convergence rate of each subproblem is O(1/k~2)and our proposed algorithm has a faster convergence,lower computational cost and higher accuracy.·A class of algorithms based on estimation sequence theory are proposed to opti-mize sparse coding:alternatively optimizing an L1 problem and a constrained con-vex quadratic programming problem.Compared with traditional algorithms,our proposed algorithms learn overcomplete bases more quickly.·A supervised learning method based on matrix factorization is presented.Combin-ing Locality Preserving Projection and Linear Discriminant Analysis,our proposed method provides a compact representation which can respect the original data s-pace.In addition,the within-class distance of each class in the low-dimensional space is very close.Compared with traditional algorithms,our proposed method has a higher recognition rate in image recognition.