Study On The Theory And Application Of The Fused Lasso Penalty Model

In the era of big data, in order to find out the useful information from large number of high-dimension datas, variable selection has become the first choice of many experts and scholars. The result of variable selection model should be sparsity, the traditional model selection methods can not meet the requirements. Lasso and a series of penalty regularization methods provide a feasible way dealing with high dimensional data. The paper introduces the Lasso penalty model in brief, and Lasso penalty model is used to select variable which is based on a single variable, but it does not have the advantage of processing continuous variable data model. In view of its limitation, we introduce the Fused Lasso penalty model emphatically, and make further study on the related theory and application.Firstly, the principle of fused Lasso penalty model is introduced and the fused Lasso penalty model is solved through Linear ADMM(LADMM) algorithm. The colon tumor dataset and the leukemia cancer dataset verify that linear ADMM algorithm can use less run time to obtain a lower error than existing algorithm.And then, using fused lasso definition formula approximating one- and higher –dimensional signals, which we call one dimensional and generalized fused lasso signal approximator and we derived its algorithm. Applying one dimensional fused lasso signal approximator to comparative genomic hybridization data, we found it detecting DNA copy number gains and losses more rapidly than traditional method. However, The generalized fusion Lasso signal approximation is more suitable for processing the case of two-dimensional data, Applying generalized fused lasso signal approximator to the gray image denoising, we found it achieved good denoising effect.Finally, this paper will generalize the Fused Lasso penalty model to a group framework, leading to the Group Fused Lasso penalty model, generalize fusion Lasso penalty(TV penalty) to the group total variation(GTV) model.we will show their basic principles, and derived their solving methods. Applying Group Fused Lasso penalty model to regression data simulation model, we find Group Fused Lasso model can detect the data of potential model and establish model capture it more easily than the lasso, the group lasso, the fused lasso.Applying the group total variation model to color image denoising, we find that both in the visual effect and in peak signal noise ratio(PSNR) result, the denoising effect of the group total variation model is optimal in comparative methods.