Recently, label consistent k-svd (LC-KSVD) algorithm has been successfully applied in image classification. The objective function of LC-KSVD is consisted of reconstruction error, classification error and discriminative sparse codes error with L0-norm sparse regularization term. The L0-norm, however, leads to NP-hard problem. Despite some methods such as orthogonal matching pursuit can help solve this problem to some extent, it is quite difficult to find the optimum sparse solution. To overcome this limitation, we propose a label embedded dictionary learning (LEDL) method to utilise the L1-norm as the sparse regularization term so that we can avoid the hard-to-optimize problem by solving the convex optimization problem. Alternating direction method of multipliers and blockwise coordinate descent algorithm are then exploited to optimize the corresponding objective function. Extensive experimental results on six benchmark datasets illustrate that the proposed algorithm has achieved superior performance compared to some conventional classification algorithms.
SRC was proposed by @cite_24 . Assume that we have @math classes of training samples, denoted by @math , where @math is the training sample matrix of class @math . Each column of the matrix @math is a training sample feature from the @math class. The whole training sample matrix can be denoted as @math , where @math represents the dimensions of the sample features and @math is the number of training samples. Supposing that @math is a testing sample vector, the sparse representation algorithm aims to solve the following objective function: where, @math is the regularization parameter to control the tradeoff between fitting goodness and sparseness. The sparse representation based classification is to find the minimum value of the residual error for each class. where @math represents the predictive label of @math , @math is the sparse code of @math class. The procedure of SRC is shown in Algorithm . Obviously, the residual @math is associated with only a few images in class @math .
@cite_24
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We consider the problem of automatically recognizing human faces from frontal views with varying expression and illumination, as well as occlusion and disguise. We cast the recognition problem as one of classifying among multiple linear regression models and argue that new theory from sparse signal representation offers the key to addressing this problem. Based on a sparse representation computed by C1-minimization, we propose a general classification algorithm for (image-based) object recognition. This new framework provides new insights into two crucial issues in face recognition: feature extraction and robustness to occlusion. For feature extraction, we show that if sparsity in the recognition problem is properly harnessed, the choice of features is no longer critical. What is critical, however, is whether the number of features is sufficiently large and whether the sparse representation is correctly computed. Unconventional features such as downsampled images and random projections perform just as well as conventional features such as eigenfaces and Laplacianfaces, as long as the dimension of the feature space surpasses certain threshold, predicted by the theory of sparse representation. This framework can handle errors due to occlusion and corruption uniformly by exploiting the fact that these errors are often sparse with respect to the standard (pixel) basis. The theory of sparse representation helps predict how much occlusion the recognition algorithm can handle and how to choose the training images to maximize robustness to occlusion. We conduct extensive experiments on publicly available databases to verify the efficacy of the proposed algorithm and corroborate the above claims.