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.
Collaborative representation is also commonly used by discriminative dictionary learning techniques, e.g. @cite_21 , @cite_8 . Although such approaches a dictionary instead of directly using the training data as @math , explicit correspondence between the learned dictionary atoms and the class labels allows them to exploit the CR-based classification scheme. For instance, the Global Classifier (GC) used by Kong and Wang @cite_21 is the same variant of Algorithm that is used by SSRC @cite_16 . The dictionary learned by the DL-COPAR algorithm @cite_21 consists of COmmon atoms for all classes and PARticular atoms specific to each class. The particular atoms behave like class centroids whereas the common atoms act as centroid-to-sample differences in SSRC. Similarly, the GC used in the Fisher Discriminant Dictionary Learning (FDDL) @cite_8 is a direct variant of CRC-RLS @cite_5 .
@cite_5 @cite_21 @cite_16 @cite_8
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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. Empirically, we find that, despite the class-specific features owned by the objects appearing in the images, the objects from different categories usually share some common patterns, which do not contribute to the discrimination of them. Concentrating on this observation and under the general dictionary learning (DL) framework, we propose a novel method to explicitly learn a common pattern pool (the commonality) and class-specific dictionaries (the particularity) for classification. We call our method DL-COPAR, which can learn the most compact and most discriminative class-specific dictionaries used for classification. The proposed DL-COPAR is extensively evaluated both on synthetic data and on benchmark image databases in comparison with existing DL-based classification methods. The experimental results demonstrate that DL-COPAR achieves very promising performances in various applications, such as face recognition, handwritten digit recognition, scene classification and object recognition. The success of sparse representation based classification (SRC) has largely boosted the research of sparsity based face recognition in recent years. A prevailing view is that the sparsity based face recognition performs well only when the training images have been carefully controlled and the number of samples per class is sufficiently large. This paper challenges the prevailing view by proposing a prototype plus variation'' representation model for sparsity based face recognition. Based on the new model, a Superposed SRC (SSRC), in which the dictionary is assembled by the class centroids and the sample-to-centroid differences, leads to a substantial improvement on SRC. The experiments results on AR, FERET and FRGC databases validate that, if the proposed prototype plus variation representation model is applied, sparse coding plays a crucial role in face recognition, and performs well even when the dictionary bases are collected under uncontrolled conditions and only a single sample per classes is available.