Sparse Feature Grouping based on $\ell_{1/2}$ Norm Regularization
Wentao Mao, Wentao Xu, Yuan Li · 2018
In recent years, feature grouping technique has shown its promising performance in many practical engineering applications. However, it's still challenging to determine the inner group structure of highly related features automatically while keeping the model sparser on the high-dimensional data. In this paper, a new sparse feature grouping algorithm is proposed based on$\ell_{1/2}$norm regularization. Different from the existing Lasso-like methods which generally use$\ell_{1}$norm, the proposed algorithm introduces a$\ell_{1/2}$norm regularizer for the feature coefficients to make the learning model sparser. Moreover, the proposed algorithm adopts a grouping regularizer to encourage the feature coefficients in one group to be similar. To solve this problem, a new alternating direction optimization algorithm is proposed. Experiments are conducted on synthetic and real-life datasets, and the results show the comparative performance of the proposed method compared with several state-of-the-art methods.