Study On Group Lasso Modeland Coordinate Descent Algorithm

With the further exploration of data mining, the feature dimension of the objectsincreases dramatically and emerges a large amount of high-dimension data. Most of themare redundant, which affect the classification accuracy and reduce the computing speed. Inorder to find out the useful information from large number of high-dimension datas,feature selection has become the first choice of many experts and scholars. This paperintroduces a feature selection method, named Lasso, for achieving sparsity of model andhas carried on the simple elaboration. In view of its limitation, we introduce the groupLasso and sparse group Lasso method emphatically, and the following work has been doneon the basis of research on existing.First, we show the principle of group Lasso under the linear model and the blockcoordinate descent algorithm for it which is based on the coordinate descent algorithm;with the analysis of the geometric properties of penalty function of ridge regression, Lassoand group Lasso and the simulation experiment, it proves that the group Lasso method canguarantee the sparsity between groups.And then, the group Lasso method is extended to logistic model for recognition andclassification, and applied in the diagnosis of erythemato squamous diseases. Because ofthe nominal data, we give the definition of virtual code and then do experiment ondifferent groups of encoded variables. The result of the experiment shows that it can solvethe promble of diagnosis for erythemato squamous diseases effectively.Finally, with the combination of single variable sparsity of Lasso and the groupsparsity of group Lasso, we introduce a method named sparse group Lasso and thesimulation experiment verify the superiority of it. We experiment on EEG datasets of BCIcompetition IV, the result shows that this method can achieve the channel selection andfeature selection simultaneously with the lower error.