Some Applications Of Homotopy Method

Homotopy method is an algorithm based on Lasso. It is known to induce sparsity in the sense that, a number of coefficients of solution, depending on the strength of the regularization, will be exactly equal to zero. Therefore it has widely application in data mining. Based on this, we apply Homotopy method to following models with algorithms. The main work is:In Chapter3, we apply Homotopy to SVM. SVM is a non-probabilistic binary linear classifier used for classification and regression analysis. It is based on SRM and performs well on small samples with high dimension. We introduce Homotopy method to primal SVM model. We argue that the new model may perform better than classic SVM when dealing with classification. We also propose an efficient algorithm that computes the whole solution path of the new model, hence facilitates adaptive selection of the tuning parameter.In Chapter4, we introduce Ll-norm to variable separable quadratic problem. With L1-norm subdifferential, we construct a new homotopy mapping with algorithm.