Hessian Semi-Supervised Sparse Feature Selection Based on <formula formulatype="inline"><tex Notation="TeX">${L_{2,1/2}}$</tex> </formula>-Matrix Norm

Abstract

Semi-supervised sparse feature selection, which can exploit the small number labeled data and large number unlabeled data simultaneously, has become an important technique in many applications on large-scale web image owing to its high efficiency and effectiveness. Recently, graph Laplacian-based semi-supervised sparse feature selection has obtained considerable attention, but it suffers with only few labeled data because Laplacian regularization is short of extrapolating power. In this paper we propose a novel semi-supervised sparse feature selection framework based on Hessian regularization and l2,1/2- matrix norm, namely Hessian sparse feature selection based on L2,1/2- matrix norm (HFSL). Hessian regularization favors functions whose values vary linearly with respect to geodesic distance and preserves the local manifold structure well, leading to good extrapolating power to boost semi-supervised learning, and then to enhance HFSL performance. The l2,1/2-matrix norm model makes HFSL select the most discriminative sparse features with good robustness. An efficient iterative algorithm is designed to optimize the objective function. We apply our algorithm into the image annotation task and conduct extensive experiments on two web image datasets. The results demonstrate that our algorithm outperforms state-of-the-art sparse feature selection methods and is promising for large-scale web image applications.