A Curvature-based Manifold Learning Algorithm

Manifold learning aims to find a low dimensional parameterization for data sets which lie on nonlinear manifolds in a high-dimensional space. Applications of manifold learning include face recognition, image retrieval, machine learning, classification, visualization, and so on. By studying the existing manifold learning algorithms and geometric properties of local tangent space of a manifold, we propose an adaptive curvature-based manifold learning algorithm (CBML). With the algorithm, noises and the samples that do not belong to the neighborhood can be detected by computing the deflection between centralized samples and its local tangent space. It can not only be used to select adaptive neighborhood, but also take full advantage of information of neighbors. The algorithm can also be applied to manifold learning with local high curvature. Experiments show that the proposed algorithm in this paper is effective.