A generalized least-squares approach regularized with graph embedding for dimensionality reduction

Abstract In current graph embedding methods, low dimensional projections are obtained by preserving either global geometrical structure of data or local geometrical structure of data. In this paper, the PCA (Principal Component Analysis) idea of minimizing least-squares reconstruction errors is regularized with graph embedding, to unify various local manifold embedding methods within a generalized framework to keep global and local low dimensional subspace. Different from the well-known PCA method, our proposed generalized least-squares approach considers data distributions together with an instance penalty in each data point. In this way, PCA is viewed as a special instance of our proposed generalized least squares framework for preserving global projections. Applying a regulation of graph embedding, we can obtain projection that preserves both intrinsic geometrical structure and global structure of data. From the experimental results on a variety of face and handwritten digit recognition, our proposed method has advantage of superior performances in keeping lower dimensional subspaces and higher classification results than state-of-the-art graph embedding methods.