Effective Discriminative Feature Selection With Nontrivial Solution.
IEEE Trans. Neural Netw. Learning Syst.(2016)
摘要
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 method linear discriminant analysis (LDA) and sparsity regularization. We impose row sparsity on the transformation matrix of LDA through ℓ₂₁-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 ℓ₂,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 ℓ₂,p-norm-based optimization problem and it is proved that the algorithm converges when 0 < p ≤ 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.
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关键词
linear discriminant analysis (lda).,p-norm minimization,ℓ₂,feature redundancy,feature selection
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