Structure Maintaining Discriminant Maps (SMDM) for Grassmann Manifold Dimensionality Reduction with Applications to the Image Set Classification

For the image-set based classification, a considerable advance has been made by representing original image sets on Grassmann manifold. In order to extend the advantages of the Euclidean based dimensionality reduction methods to the Grassmann Manifold, several methods have been suggested recently to jointly perform dimensionality reduction and metric learning on Grassmann manifold and they have achieved good results in some computer vision tasks. Nevertheless, when handling the classification tasks on the complicated datasets, the learned features do not exhibit enough discriminatory ability and the data distribution of the resulted Grassmann manifold also be ignored which may lead to overfitting. To overcome the two problems, we propose a new method named Structure Maintaining Discriminant Maps (SMDM) for manifold dimensionality reduction problems. As to SMDM, we mainly design a new discriminant function for metric learning. We make experiments on two tasks: face recognition and object categorization to evaluate the proposed method, the achieved better results compared with the state-of-the-art methods, showing the feasibility and effectiveness of the proposed algorithm.