Group recursive discriminant subspace learning with image set decomposition

Discriminant subspace learning is a widely used feature extraction technique for image recognition, since it can extract effective discriminant features by employing the class information and Fisher criterion. A crucial research topic on this technique is how to rapidly extract sufficient and effective features. Recently, recursive discriminant subspace learning technique has attracted lots of research interest because it can acquire sufficient discriminant features. Generally, it recursively decomposes image samples and extracts features from a number of decomposed sample sets. The major drawback of most recursive discriminant subspace learning methods is that they calculate the projective vectors one by one, such that they suffer from big computational costs. The recursive modified linear discriminant method and the incremental recursive Fisher linear discriminant method employ a simple solution for this problem, which calculates the class number minus one projective vectors in each recursion. However, this solution produces the unfavorable projective vectors with poor discriminant capabilities, and it cannot provide the terminating criterion for recursive computation and make the projective vectors orthogonal. In this paper, we propose a novel recursive learning approach that is group recursive discriminant subspace learning, which can rapidly learn multiple orthogonal subspaces with each spanned by a group of projective vectors. And we present a rule to select favorable projective vectors per recursion and provide a matrix-form-based terminating criterion to determine the number of recursions. Experiments on three widely used databases demonstrate the effectiveness and efficiency of the proposed approach.