Robust Multiple Rank- $k$ Bilinear Projections for Unsupervised Learning

In this paper, we propose a novel bilinear projections model for unsupervised learning, which can be directly applied to dimension reduction and feature extraction for image analysis. Compared to previous 2-dimensional (2D) methods, our method seeks multiple rank-k bilinear projections (MRBP), which makes a balance between two opposite problems of enhancing the degree of freedom and avoiding the problem of over-fitting by adjusting k . Besides, each renewed feature in our method is extracted independently, rather than dimensions reduced by row or column like before, and thus our reduced dimension is not restricted by the size of a sample. In addition, we demonstrate that our model could be optimized via two equivalent optimization problems based on the criteria of maximum separability and nearest reconstruction respectively. Motivated by this, the corresponding robust version (RMRBP) achieving a better performance to occluded data is introduced as well. Extensive experiments on several datasets have been done to verify the effectiveness and superiority of our methods.