Sparse Discriminative Multimanifold Grassmannian Analysis for Face Recognition With Image Sets

We propose an efficient and robust solution, called sparse discriminative multimanifold Grassmannian analysis (SDMMGA), for face recognition based on image set (FRIS), where each set contains face images belonging to the same subject and typically covering large variations. In our work, linearity constrained hierarchical agglomerative clustering (LC-HAC) method is first employed to partition each image set into several local linear models (LLMs), each depicted as a point on the Grassmannian manifold using positive definite Gaussian kernel function. In contrast to the standard discriminative learning algorithms that assume that all data are sampled from one single manifold and only one projection is derived for feature extraction, we model all the LLMs of each person as a manifold and present SDMMGA model to seek multiple projection matrices, which can uncover the geometrical information of different manifolds. Aiming to better separate manifold margins in the low-dimensional feature space, we introduce the ℓ₁ and ℓ₂ norms penalty in the SDMMGA objective function. An efficient regression method is presented for finding the most discriminative features. Comprehensive experiments on three standard data sets show that our method consistently outperforms the state of the art.