Piece-wise max-margin-based discriminative feature learning

Abstract

Max-margin-based discriminative feature learning method (MMLDF) learns a low-dimensional feature representation such that the global margin of the data is maximised and samples of the same class become as close as possible. Non-linear version of MMLDF uses kernel method. In this paper, we first prove that the kernel MMLDF cannot be used for discriminative feature learning. Strictly speaking, the kernel MMLDF maps input vectors into zero vectors which cannot then be classified. Therefore, to overcome this problem, we propose a novel non-linear MMLDF which uses piece-wise learning technique. Then, by using alternating optimisation, an algorithm is proposed to solve our proposed model. Experimental results on real datasets confirm that our proposed piece-wise MMLDF outperforms linear MMLDF and piece-wise SVM.