Feature selection and feature transformation, the two main ways to reduce dimensionality, are often presented separately. In this paper, a feature selection method is proposed by combining the popular transformation based dimensionality reduction met
hod Linear Discriminant Analysis (LDA) and sparsity regularization. We impose row sparsity on the transformation matrix of LDA through ${ell}_{2,1}$-norm regularization to achieve feature selection, and the resultant formulation optimizes for selecting the most discriminative features and removing the redundant ones simultaneously. The formulation is extended to the ${ell}_{2,p}$-norm regularized case: which is more likely to offer better sparsity when $0<p<1$. Thus the formulation is a better approximation to the feature selection problem. An efficient algorithm is developed to solve the ${ell}_{2,p}$-norm based optimization problem and it is proved that the algorithm converges when $0<ple 2$. Systematical experiments are conducted to understand the work of the proposed method. Promising experimental results on various types of real-world data sets demonstrate the effectiveness of our algorithm.
Recently, a logarithmic decrease of conductivity has been observed in topological insulators at low temperatures, implying a tendency of localization of surface electrons. Here, we report quantum transport experiments on the topological insulator Bi2
Te3 thin films with arrayed antidot nanostructures. With increasing density of the antidots, a systematic decrease is observed in the slope of the logarithmic temperature-dependent conductivity curves, indicating the electron-electron interaction can be tuned by the antidots. Meanwhile, the weak anti-localization effect revealed in magnetoconductivity exhibits an enhanced dominance of electron-electron interaction among decoherence mechanisms. The observation can be understood from an antidot-induced reduction of the effective dielectric constant, which controls the interactions between the surface electrons. Our results clarify the indispensable role of the electron-electron interaction in the localization of surface electrons and indicate the localization of surface electrons in an interacting topological insulator.
