Explicit discriminative representation for improved classification of manifold features

• We study the problem of extracting Euclidean features for Riemannian manifolds.
• We propose two max-margin learning approaches to extract the features representation.
• The proposed methods outperform recent state-of-the-arts in various tasks.

We tackle the problemof extracting explicit discriminative feature representation for manifold features. Manifold features have already been shown to have excellent performance in a number of image/video classification tasks. Nevertheless, as most manifold features lie in a non-Euclidean space, the existing machineries operating in Euclidean space are not applicable. The proposed explicit feature representation enables us to use the existing Euclidean machineries, significantly reducing the challenges of processing manifold features. To that end, we first embed the manifold features into a Reproducing Kernel Hilbert Space that can encode the manifold geometry. Then, we extract the explicit representation by using the empirical kernel feature space, an explicit lower dimensional space wherein the inner product is equivalent to the corresponding kernel similarity. The final feature representation is then derived from a linear combination of multiple explicit representations from various manifold kernels. We propose a max-margin approach to learn an effective linear combination that will improve the feature discriminative power. Evaluations in various image classification tasks show that the proposed approach consistently and significantly outperforms recent state-of-the-art methods.