Joint graph based embedding and feature weighting for image classification

Abstract Recently, several inductive and flexible nonlinear data projection methods for graph-based semi-supervised learning were proposed. These state-of-the art techniques have a good performance. However, they have not taken into account the relevance of the original features in their model estimation. In this paper, we propose a joint graph-based embedding and feature weighting for getting a flexible and inductive nonlinear data representation on manifolds. The proposed criterion explicitly estimates the feature weights together with the projected data and the linear transformation such that data smoothness and large margins are achieved in the projection space. Moreover, the paper introduces a kernel variant of the model in order to get an inductive nonlinear embedding that is close to a real nonlinear subspace for a good approximation of the embedded data. The proposed frameworks can be seamlessly used in semi-supervised and supervised settings. The resulting optimization problems can be solved efficiently. The proposed embedding methods are evaluated on six public scene and face datasets. Experiments on image classification, in a semi-supervised setting, show that our proposed methods can have a performance that is better than that of many state-of-the-art methods including linear and nonlinear methods.