Local and global regressive mapping for manifold learning with out-of-sample extrapolation

Over the past few years, a large family of manifold learning algorithms have been proposed, and applied to various applications. While designing new manifold learning algorithms has attracted much research atten-tion, fewer research efforts have been focused on out-of-sample extrapolation of learned manifold. In this paper, we propose a novel algorithm of manifold learning. The proposed algorithm, namely Local and Global Regres-sive Mapping (LGRM), employs local regression mod-els to grasp the manifold structure. We additionally im-pose a global regression term as regularization to learn a model for out-of-sample data extrapolation. Based on the algorithm, we propose a new manifold learn-ing framework. Our framework can be applied to an