Algorithm Research And Related Applications Of Sparse Matrix Optimization

As the rapid development of computer information technology today,the data dimension disaster caused by its inflation is an important task of data processing.The method of sparse optimization is an effective means to achieve the goal of health reduction through feature selection.This paper considers a kind of lF-l2,p norm based matrix sparse optimization problem.Due to the negative impact of the ill-condition of iteration matrix,we present a lower bound to cut off the smallest rows iteratively.This truncation technique helps to not only avoid the bad breakdown of algorithm but also decrease the computational work.The convergence analysis guarantees the truncated algorithm to find an approximate sparse solution to the joint matrix optimization problem.Numerical experiments exhibit the improvement of the truncation technique over the previous algorithm.The sparse optimization problem based on l2,1 norm is widely used in the semi-supervised multitask feature selection.Plentv of study shows that the optimal solution of l2,p(0<p≤1)regularization sparse optimization problem is sparser than the l2,1 regularization spares optimization problem’s.Thus,in this paper,we consider a model of sparse optimization problem based on l2,p norm for the semi-supervised multitask feature selection.And we propose an algorithm to solve the model and analyze the algorithm convergence at the same time.Numerical experiments show that the solution of this feature selection problem is sparser.The accuracy of its classification of the disease prediction rate is higher,that is,the characteristics of the selected representative of the more representative.Combining the advantages of multitask learning and semi-supervised feature selection based on manifold regularization,we propose another semi-supervised multitask feature selection model based on l2,p norm.Since the l2,p norm is non-convex and non-lipschitz continuous,we propose a consistency algorithm to solve the model and also analyze the convergence of the algorithm.Numerical experiments are used to verify the validity of the model.The results of two semi-supervised multitask models show that the model is more representative.