Research On Non-convex Regularization Method

With the development of the digital age,a large number of high-dimensional data has been collected in various disciplines and fields.Faced with the large amount of collected data,it is a great challenge for us to transform it into a material that can not only be stored and analyzed,but also can provide a reference for solving practical problems.In view of the current state of data storage,the distributed storage has emerged properly,in which data sets are stored in different machines in a certain way without any repetition,so as to solve the problem of data storage.This storage method has been widely used in information science and medicine.After solving the storage problem,how to design and find out a machine learning algorithm which is suitable for dis-tributed data storage becomes another problem to be solved.As the theory of information technology has developed rapidly,the formulation and development of regularization methods provide us with an effective tool for processing and analyzing massive high-dimensional data,but they are all fit for single-machine data processing,in which data is stored in the same machine.Concerning the superiority of non-convex regularization for variable selection and feature extrac-tion,combining distributed storage with non-convex regularization methods,we focus more attention on non-convex regularization methods based on distributed computing to solve the storage and analysis of massive high-dimensional data.The content structure of each chapter of this paper is organized as follows:In chapter 1,we briefly introduce the significance,background and current circumstances of distributed storage and various machine learning algorithms in the research.In chapter 2,we mainly study the distributed MCP regularization method,which is proposed based on ADMM algorithm and its whose convergence is proved.Finally,through simulation experiments and real data experiments,the effectiveness of the proposed method in processing massively distributed data is demonstrated.In chapter 3,we mainly study the reciprocal L1 regularization method.Based on the re-weighted iterative algorithm,the reciprocal L1 regularization is solved,and then the effectiveness and efficiency of the reciprocal L1 regularization are verified by sparse signal reconstruction experiments.