Efficient Regression with Feature Selection Based on L12-Norm

This is the authors' abstract. We don't add key points for this paper.

Feature selection is one of the most important components of many machine learning applications. Most of the existing sparse coding-based methods only concerned with the regularization of the transformation matrix, but ignoring the sparsity of projected features in the intrinsic feature space. In this paper, we introduce a novel regularization with ℓ<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</inf>-norm, called class specificity distribution term. It aims to ensure that samples with the same label could obey a specific distribution, while data from the different categories should have different distributions in the intrinsic feature space. Then we propose a novel embedded feature selection framework based on regression and class specificity distribution term measured by ℓ<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</inf>-norm, termed RL12. An efficient augmented Lagrange multipliers based optimization algorithm is proposed to solve the ℓ<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</inf>-norm regularization iteratively. Experimental results demonstrate the effectiveness of our method.