Compound Rank-k Projections for Bilinear Analysis
This is an incremental improvement for applications involving matrix or tensor data analysis, such as image processing or pattern recognition.
The paper tackles the inflexibility of existing two-dimensional discriminant analysis algorithms by proposing the Compound Rank-k Projection (CRP) algorithm, which uses multiple rank-k projection models to enhance discriminant ability and ensures monotonic increase in objective function values.
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.