Sparse representation (or coding)-based classification (SRC) has gained great success in face recognition in recent years. However, SRC emphasizes the sparsity too much and overlooks the correlation information which has been demonstrated to be critical in real-world face recognition problems. Besides, some paper considers the correlation but overlooks the discriminative ability of sparsity. Different from these existing techniques, in this paper, we propose a framework called adaptive sparse representation-based classification (ASRC) in which sparsity and correlation are jointly considered. Specifically, when the samples are of low correlation, ASRC selects the most discriminative samples for representation, like SRC; when the training samples are highly correlated, ASRC selects most of the correlated and discriminative samples for representation, rather than choosing some related samples randomly. In general, the representation model is adaptive to the correlation structure that benefits from both l 1 -norm and l 2 -norm. Extensive experiments conducted on publicly available data sets verify the effectiveness and robustness of the proposed algorithm by comparing it with the state-of-the-art methods.
@cite_29: We consider linear equations y = Φx where y is a given vector in ℝn and Φ is a given n × m matrix with n 0 so that for large n and for all Φ's except a negligible fraction, the following property holds: For every y having a representation y = Φx0by a coefficient vector x0 ∈ ℝmwith fewer than ρ · n nonzeros, the solution x1of the 1-minimization problem is unique and equal to x0. In contrast, heuristic attempts to sparsely solve such systems—greedy algorithms and thresholding—perform poorly in this challenging setting. The techniques include the use of random proportional embeddings and almost-spherical sections in Banach space theory, and deviation bounds for the eigenvalues of random Wishart matrices. © 2006 Wiley Periodicals, Inc.
@cite_26: Suppose we wish to recover a vector x0 ∈ R m (e.g., a digital signal or image) from incomplete and contaminated observations y = Ax0 + e; A is an n × m
To overcome these limitations, introduced the Sparse Representation based Classification (SRC) method to represent the query image @math based on the over-complete dictionary @math with sparse coefficients, The above @math -norm minimization problem is non-convex and actually NP-hard. It has been proved in @cite_29 @cite_26 that problem ) is equal to @math -minimization problem under certain conditions: To deal with the noises, the @math -minimization problem is extended to the following formulation: where @math is a given tolerance. It is generally regarded that SRC is an extension of NN and NFS. The difference is that the coding of @math is performed over the over-complete dictionary @math instead of its subset. With a sufficient number of training samples, SRC with random projection-based features can outperform NFCs on conventional features. The sparse model is also more robust and effective for object recognition in the case that objects are corrupted by outliers.