A Improve Direct Path Seeking Algorithm for L1/2 Regularization, with Application to Biological Feature Selection

The special importance of L_1/2 regularization has been recognized in recent studies on sparsity problems, particularly, on feature selection. The L_1/2 regularization is nonconvex optimization problem, it is difficult in general to has a efficient algorithm to solutions. The direct path seeking method can produce solutions that closely approximate those for any convex loss function and nonconvex constraints. The improve path seeking methods provide us an effect way to solve the problem of L_1/2 regularization with nonconvex penalty. In this paper, we investigate a improve direct path seeking algorithm to solve the L_1/2 regularization. This method adopts initial ordinary regression coefficients as warm start for first step increment, it is significantly faster than ordinary path seeking algorithm. We demonstrate its performance of feature selection on several simulated and real data sets.