Adaptive Manifold Graph representation for Two-Dimensional Discriminant Projection

Two-dimensional (2D) local discriminant analysis is one of the popular techniques for image representation and recognition. Conventional 2D methods extract features of images relying on the affinity relationships among samples. However, affinity graph learning and dimensionality reduction are two separate processes, and the predefined affinity graph is sensitive to noisy and irrelevant features. To this end, we propose a graph embedding model, named as Two-Dimensional Discriminant Projection with Adaptive Manifold Graph (2DDP-AMG). In our model, the local manifold structure of data is characterized by the k-nearest-neighbor (kNN) graph within each class. More importantly, the above graph is updated adaptively in the process of dimensionality reduction to eliminate the interference of irrelevant features and noise. Furthermore, F-norm is introduced to measure the distance between homogeneous samples and improve the robustness of the model to outliers. To solve this model, an efficient algorithm is developed to update each variable iteratively. Extensive experiments conducted on benchmark face image data sets show the superiority and robustness of our model compared to state-of-the-art alternatives.