Many classification approaches first represent a test sample using the training samples of all the classes. This collaborative representation is then used to label the test sample. It was a common belief that sparseness of the representation is the key to success for this classification scheme. However, more recently, it has been claimed that it is the collaboration and not the sparseness that makes the scheme effective. This claim is attractive as it allows to relinquish the computationally expensive sparsity constraint over the representation. In this paper, we first extend the analysis supporting this claim and then show that sparseness explicitly contributes to improved classification, hence it should not be completely ignored for computational gains. Inspired by this result, we augment a dense collaborative representation with a sparse representation and propose an efficient classification method that capitalizes on the resulting representation. The augmented representation and the classification method work together meticulously to achieve higher accuracy and lower computational time compared to state-of-the-art collaborative representation based classification approaches. Experiments on benchmark face, object and action databases show the efficacy of our approach.
A label consistent K-SVD (LC-KSVD) algorithm to learn a discriminative dictionary for sparse coding is presented. In addition to using class labels of training data, we also associate label information with each dictionary item (columns of the dictionary matrix) to enforce discriminability in sparse codes during the dictionary learning process. More specifically, we introduce a new label consistency constraint called "discriminative sparse-code error" and combine it with the reconstruction error and the classification error to form a unified objective function. The optimal solution is efficiently obtained using the K-SVD algorithm. Our algorithm learns a single overcomplete dictionary and an optimal linear classifier jointly. The incremental dictionary learning algorithm is presented for the situation of limited memory resources. It yields dictionaries so that feature points with the same class labels have similar sparse codes. Experimental results demonstrate that our algorithm outperforms many recently proposed sparse-coding techniques for face, action, scene, and object category recognition under the same learning conditions. In a sparse-representation-based face recognition scheme, the desired dictionary should have good representational 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 proposed method, discriminative K-SVD (D-KSVD), is based on extending the K-SVD algorithm by incorporating the classification error into the objective function, thus allowing the performance of a linear classifier and the representational 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 classifier 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 solving sub-problems with the hope of achieving the global optimal through iterative approximation. We evaluate the proposed method using two commonly-used face databases, the Extended YaleB database and the AR database, with detailed comparison to 3 alternative approaches, including the leading state-of-the-art in the literature. The experiments 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.