Linear Subspace Learning based on a Learned Discriminative Dictionary for Sparse Coding

Learning linear subspaces for high-dimensional data is an important task in pattern recognition. A modern approach for linear subspace learning decomposes every training image into a more discriminative part (MDP) and a less discriminative part (LDP) via sparse coding before learning the projection matrix. In this paper, we present a new linear subspace learning algorithm through discriminative dictionary learning. Our main contribution is a new objective function and its associated algorithm for learning an overcomplete discriminative dictionary from a set of labeled training examples. We use a Fisher ratio defined over sparse coding coefficients as the objective function. Atoms from the optimized dictionary are used for subsequent image decomposition. We obtain local MDPs and LDPs by dividing images into rectangular blocks, followed by blockwise feature grouping and image decomposition. We learn a global linear projection with higher classification accuracy through the local MDPs and LDPs. Experimental results on benchmark face image databases demonstrate the effectiveness of our method.