Learning a discriminant graph-based embedding with feature selection for image categorization.

Graph-based embedding methods are very useful for reducing the dimension of high-dimensional data and for extracting their relevant features. In this paper, we introduce a novel nonlinear method called Flexible Discriminant graph-based Embedding with feature selection (FDEFS). The proposed algorithm aims to classify image sample data in supervised learning and semi-supervised learning settings. Specifically, our method incorporates the Manifold Smoothness, Margin Discriminant Embedding and the Sparse Regression for feature selection. The weights add ℓ-norm regularization for local linear approximation. The sparse regression implicitly performs feature selection on the original features of data matrix and of the linear transform. We also provide an effective solution method to optimize the objective function. We apply the algorithm on six public image datasets including scene, face and object datasets. These experiments demonstrate the effectiveness of the proposed embedding method. They also show that proposed the method compares favorably with many competing embedding methods.