Bi-Orthogonal Projection Learning for Dimensionality Reduction

This paper proposes a novel bi-orthogonal projection learning (BOPL) for dimensionality reduction (DR) methods, which further extends the existing DR to a more flexible, robust, and sparse embedding framework. Unlike conventional methods that use only one kind of projection for learning in DR, the proposed BOPL introduces two kinds of projection, which are orthogonal and provides the true projection the freedom for more accurate data transformation in subspace learning. Inspired by the observation that the two projections share many similar data structures, the projections are expected to preserve the similarity structure of data by using two different reconstruction ways. The proposed method can also handle data corrupted by noises since a sparse item is employed to compensate for the noises during DR. Several novel unsupervised DR methods (i.e., BOPL_PCA, BOPL_NPE, and BOPL_LPP) are derived from the proposed framework. The results of experiments on the natural and synthetic data sets demonstrate that the proposed methods outperform the existing well-established DR methods.