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.
In SRC @cite_30 , @math in Eq. ), which encourages the computed representation @math to be sparse. In Superposed-SRC (SSRC), @cite_16 modified the residual computation step of SRC. For SSRC, @math consists of class centroids and sample-to-centroid differences. While computing the residuals, SSRC keeps the coefficients of @math corresponding to the sample-to-centroid differences fixed in each @math . The CR-based classifier proposed by @cite_5 uses @math and solves Eq. ) using the Regularized Least Squares (RLS) method, hence denoted as CRC-RLS. @cite_1 used @math in Eq. ) and solved it as the standard least squares problem for face recognition. Chi and Porikli @cite_31 used a linear combination of a CR-based classifier and a nearest subspace classifier @cite_7 for improved classification performance.
@cite_30 @cite_7 @cite_1 @cite_5 @cite_31 @cite_16
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Sparse representation based classification (SRC) has received much attention in computer vision and pattern recognition. SRC codes a testing sample by sparse linear combination of all the training samples and classifies the testing sample into the class with the minimum representation error. Recently, Zhang analyzes the working mechanism of SRC and points out that it is the collaborative representation but not the L1-norm sparsity that makes SRC powerful. Based on the analysis, they propose a very simple and much more efficient classification scheme, called collaborative representation based classification with regularized least square (CRC_RLS). CRC_RLS is a linear method in nature. Here we propose a kernel collaborative representation based classification with regularized least square (Kernel CRC_RLS, KCRC_RLS) by implicitly mapping the sample into high-dimensional space via kernel tricks. Our approach is highly motivated by the kernel methods which can capture the nonlinear similarity among samples and have been successfully applied in pattern recognition and machine learning. The experimental results on the CENPAMI handwritten digital database, ETH80 database, FERET face database, ORL database, AR face database, demonstrate that Kernel CRC_RLS is effective in classification, leading to promising performance. 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. Recently, sparse representation based classification (SRC) and collaborative representation based classification (CRC) have been successfully used for visual recognition and have demonstrated impressive performance. Given a test sample, SRC or CRC formulates its linear representation with respect to the training samples and then computes the residual error for each class. SRC or CRC assumes that the training samples from each class contribute equally to the dictionary in the corresponding class, i.e., the dictionary consists of the training samples in that class. This, however, leads to high residual error and instability. To overcome this limitation, we propose a class specific dictionary learning algorithm. To be specific, by introducing the dual form of dictionary learning, an explicit relationship between the basis vectors and the original image features is represented, which also enhances the interpretability. SRC or CRC can be thus considered as a special case of the proposed algorithm. Blockwise coordinate descent algorithm and Lagrange multipliers are then adopted to optimize the corresponding objective function. Extensive experimental results on five benchmark face recognition datasets show that the proposed algorithm achieves superior performance compared with conventional classification algorithms. HighlightsA novel class specific dictionary learning (CSDL) approach is proposed, where the standard collaborative representation based classification (CRC) or sparse representation based classification (SRC) can be considered as its special cases.The dual form of dictionary learning is proposed to enhance the interpretability.Our proposed CSDL achieves superior face recognition performance on several benchmark datasets. Applications of sparse signal representation in image processing and pattern recognition have attracted a great deal of attention. Sparse representation based classification (SRC) methods emphasizes on sparse representation computed by l"1-minimization to exploit the underlying sparsity in the problem domain, and argued the importance of sparse representation that improved the discrimination to achieve robust and accurate classification results. Recently, many studies have shown the role of collaborative representation (CR) in SRC, which actually improved the classification accuracy. In this paper, we proposed a novel collaborative neighbor representation method for multi-class classification based on l"2-minimization approach with the assumption of locally linear embedding (LLE). The proposed method represents a test sample over the dictionary by automatically choosing optimal nearest basis spanned in the same linear subspace as of test sample. The proposed representation method achieves competitive classification accuracy via optimal neighbor representation having discriminative learning power. Extensive experiments on real-world face and digit databases are performed to analyze the performance of the proposed method against SRC methods. Result clearly shows that the proposed method achieves competitive results for face recognition and pattern classification, and is significantly much faster and comparably accurate than SRC based classification methods.