Compound Rank-k Projections for Bilinear Analysis
  In many real-world applications, data are represented by matrices or high-order tensors. Despite the promising performance, the existing two-dimensional discriminant analysis algorithms employ a single projection model to exploit the discriminant information for projection, making the model less flexible. In this paper, we propose a novel Compound Rank-k Projection (CRP) algorithm for bilinear analysis. CRP deals with matrices directly without transforming them into vectors, and it therefore preserves the correlations within the matrix and decreases the computation complexity. Different from the existing two dimensional discriminant analysis algorithms, objective function values of CRP increase monotonically.In addition, CRP utilizes multiple rank-k projection models to enable a larger search space in which the optimal solution can be found. In this way, the discriminant ability is enhanced. 
Xiaojun Chang, Feiping Nie, Sen Wang, Yi Yang, Xiaofang Zhou and   Chengqi Zhang
cs.LG