Least-Squares Regulation Based Graph Embedding

A large family of algorithms named graph embedding is widely accepted as an effective technique designed to provide better solutions to the problem of dimensionality reduction. Existing graph embedding algorithms mainly consider obtaining projection directions through preserving local geometrical structure of data. In this paper, a regulation formulation known as Least-Squares Reconstruction Errors, to unify various graph embedding methods within a common regulation framework for preserving both local and global structures, is proposed. With its properties of Least-Squares regulation, orthogonality constraint to data distributions and tensor extensions of supervised or semi-supervised scenarios, this common regulation framework makes a tradeoff between intrinsic geometrical structure and the global structure. Our experiments demonstrated that, our proposed method have better performances in keeping lower dimensional subspaces and higher classification results.