  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.
