Manifold-Regularized Adaptive Lasso

摘要

Adaptive Lasso preserves oracle properties comparing to classical Lasso. It performs as well as if the true underlying model is provided in advance. In order to let feature subset selected by Adaptive Lasso preserve more local information, which is discriminative and benefit for classification, Manifold-regularized Adaptive Lasso (MrALasso) is proposed for feature selection. Reconstructing response by linear sum of features is considered in manifold embedded in high-dimensional space. A similarity graph of data points is built. Connected points are restricted to stay together as close as possible so that the intrinsic geometry of the data and the local structure are preserved. An effective iterative algorithm, with detailed proof of convergence, is proposed to solve the optimization problem. Experimental results of feature selection on several classical gene datasets show the effectiveness and superiority of the proposed method.