Sparse Matrix-based Optimization Methods Study And Application

In today,s information age, the data dimension disaster caused by the inflation is a important task of data processing. In recent years, sparse optimization method for feature selection that is achieved by the purpose of reducing dimension is an important means of data processing. Sparse optimization method is that is constructed by sparse optimization model based on the characteristics of the structure of the data, and is designed by algorithm to obtain the sparse solution. Sparse optimization model is divided into sparse vector model and sparse matrix model.Joint sparse matrix optimization has the function of joint sparse optimization information and allows multiple information enjoy the same sparse optimization model, so this paper designs lF-l2,p sparse optimization model of matrices, and we establish lower bound for l2-norm of nonzero row in local optimal solution of lF-l2,p model, which can be used to identify nonzero rows l2 norm in any numerical solution. Therefore, we use the lower bound test the iterative algorithm approximate numerical solution of the nonzero row l2 norm to improve the efficiency of algorithm and obtain more sparse solution. Then, we use this model for feature selection on the gene expression data sets, and choose the stronger expressing ability of the gene for classification.Numerical experiments show the effectiveness of using lower bound algorithm.l2,1 -norm based sparse optimization is widely used in the semi-supervision feature selection. A large number of calculation shows that the solution of l2,p(0<p?1) regularization sparse optimization is sparser than the solution of l2,1regularization spares optimization. Therefore, in this paper, we consider l2,p-norm based sparse optimization model for semi-supervision feature selection. We propose consistency algorithm to solve the problem for this sparse optimization model,and analyze the algorithm convergence. Numerical experiments show that the solution of this sparse optimization problem is sparser. It can choose the more representative features, and used for face recognition accuracy is higher.