Low-Rank Discriminant Embedding for Multiview Learning

This paper focuses on the specific problem of multiview learning where samples have the same feature set but different probability distributions, e.g., different viewpoints or different modalities. Since samples lying in different distributions cannot be compared directly, this paper aims to learn a latent subspace shared by multiple views assuming that the input views are generated from this latent subspace. Previous approaches usually learn the common subspace by either maximizing the empirical likelihood, or preserving the geometric structure. However, considering the complementarity between the two objectives, this paper proposes a novel approach, named low-rank discriminant embedding (LRDE), for multiview learning by taking full advantage of both sides. By further considering the duality between data points and features of multiview scene, i.e., data points can be grouped based on their distribution on features, while features can be grouped based on their distribution on the data points, LRDE not only deploys low-rank constraints on both sample level and feature level to dig out the shared factors across different views, but also preserves geometric information in both the ambient sample space and the embedding feature space by designing a novel graph structure under the framework of graph embedding. Finally, LRDE jointly optimizes low-rank representation and graph embedding in a unified framework. Comprehensive experiments in both multiview manner and pairwise manner demonstrate that LRDE performs much better than previous approaches proposed in recent literatures.