Manifold locality constrained low-rank representation and its applications

Low-rank representation (LRR) and its variations have recently attracted a great deal of attention because of its effectiveness in exploring low-dimensional subspace structures embedded in data. LRR-related algorithms have many applications in computer vision, signal processing, semi-supervised learning and pattern recognition. However, most of the existing LRR methods fail to take into account the non-linear geometric structures within data, thus the locality and the similarity information among data may be missing in the learning process, which have been shown to be beneficial for discriminative tasks. To improve LRR in this regard, we propose a manifold locality constrained low-rank representation framework (MLCLRR) for data representation. By taking the local manifold structure of the data into consideration, the proposed MLCLRR method not only can represent the global low-dimensional structures, but also capture the local intrinsic non-linear geometric information in the data. The experimental results on different types of vision problems demonstrate the effectiveness of the proposed method.