A statistic manifold kernel with graph embedding discriminant analysis for action and expression recognition

Graph embedding discriminant analysis is effective but computationally expensive for video-based recognition tasks. This paper proposes a statistic manifold kernel for visual modeling. Discriminant analysis can achieve effective computation with the proposed kernel for action and expression recognition. Firstly, symmetric positive definite (SPD) manifold is proposed to incorporate Gaussian mixture distribution of the video clips. Secondly, a projection kernel is constructed on the SPD manifold. Then an inter-class graph and an intra-class graph are introduced to measure the inter-class separability and intra-class compactness. The geometrical structure of the input data is thus exploited. A Marginal discriminant analysis(MDA) is finally performed on the kernel Hilbert space of the SPD Riemannian manifold. Recognition is achieved by the Nearest Neighbor (NN) method. Promising performances demonstrate the effectiveness of the proposed method for action and facial expression recognition.