You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
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.

Cited Abstract(s):
[1]: The traditional SPM approach based on bag-of-features (BoF) requires nonlinear classifiers to achieve good image classification performance. This paper presents a simple but effective coding scheme called Locality-constrained Linear Coding (LLC) in place of the VQ coding in traditional SPM. LLC utilizes the locality constraints to project each descriptor into its local-coordinate system, and the projected coordinates are integrated by max pooling to generate the final representation. With linear classifier, the proposed approach performs remarkably better than the traditional nonlinear SPM, achieving state-of-the-art performance on several benchmarks. Compared with the sparse coding strategy [22], the objective function used by LLC has an analytical solution. In addition, the paper proposes a fast approximated LLC method by first performing a K-nearest-neighbor search and then solving a constrained least square fitting problem, bearing computational complexity of O(M + K2). Hence even with very large codebooks, our system can still process multiple frames per second. This efficiency significantly adds to the practical values of LLC for real applications.

[2]: The variations of pose lead to significant performance decline in face recognition systems, which is a bottleneck in face recognition. A key problem is how to measure the similarity between two image vectors of unequal length that viewed from different pose. In this paper, we propose a novel approach for pose robust face recognition, in which the similarity is measured by correlations in a media subspace between different poses on patch level. The media subspace is constructed by canonical correlation analysis, such that the intra-individual correlations are maximized. Based on the media subspace two recognition approaches are developed. In the first, we transform non-frontal face into frontal for recognition. And in the second, we perform recognition in the media subspace with probabilistic modeling. The experimental results on FERET database demonstrate the efficiency of our approach.

[3]: As a recently proposed technique, sparse representation based classification (SRC) has been widely used for face recognition (FR). SRC first codes a testing sample as a sparse linear combination of all the training samples, and then classifies the testing sample by evaluating which class leads to the minimum representation error. While the importance of sparsity is much emphasized in SRC and many related works, the use of collaborative representation (CR) in SRC is ignored by most literature. However, is it really the l 1 -norm sparsity that improves the FR accuracy? This paper devotes to analyze the working mechanism of SRC, and indicates that it is the CR but not the l1-norm sparsity that makes SRC powerful for face classification. Consequently, we propose a very simple yet much more efficient face classification scheme, namely CR based classification with regularized least square (CRC_RLS). The extensive experiments clearly show that CRC_RLS has very competitive classification results, while it has significantly less complexity than SRC.

[4]:
Some works have focused on the above problem and provided several solutions. [1] proposed locality constraints in spatial sparse representation. [2] maximized the intra-individual correlations to address the pose difference for face recognition. imposed the @math -norm constraint on the coefficients and proposed CRC (Collaborative Representation based Classification with regularized least square). In [3] , Zhang pointed out that the success of SRC comes from the collaborative representation of @math over all training samples. The @math -norm is supposed to take advantage of data correlation [4] . Thus, the query image @math is represented by the over-complete dictionary with @math -norm rather than @math -norm to constrain the coding vector in CRC. The objective function is defined as: The @math -minimization guarantees that CRC gets a stable result with a much denser representation vector. However, CRC does not perform sample selection for representation. It may not perform well when the training data are not highly correlated.