Abstract

In a sparse-representation-based face recognition scheme, the desired dictionary should have good repre-sentational power (i.e., being able to span the subspace of all faces) while supporting optimal discrimination of the classes (i.e., different human subjects). We propose a method to learn an over-complete dictionary that attempts to simultaneously achieve the above two goals. The pro-posed method, discriminative K-SVD (D-KSVD), is based on extending the K-SVD algorithm by incorporating the classification error into the objective function, thus allow-ing the performance of a linear classifier and the represen-tational power of the dictionary being considered at the same time by the same optimization procedure. The D-KSVD algorithm finds the dictionary and solves for the clas-sifier using a procedure derived from the K-SVD algorithm, which has proven efficiency and performance. This is in contrast to most existing work that relies on iteratively solv-ing sub-problems with the hope of achieving the global op-timal through iterative approximation. We evaluate the pro-posed method using two commonly-used face databases, the Extended YaleB database and the AR database, with de-tailed comparison to 3 alternative approaches, including the leading state-of-the-art in the literature. The experi-ments show that the proposed method outperforms these competing methods in most of the cases. Further, using Fisher criterion and dictionary incoherence, we also show that the learned dictionary and the corresponding classifier are indeed better-posed to support sparse-representation-based recognition. 1.