We propose a Bayesian approach to learn discriminative dictionaries for sparse representation of data. The proposed approach infers probability distributions over the atoms of a discriminative dictionary using a Beta Process. It also computes sets of Bernoulli distributions that associate class labels to the learned dictionary atoms. This association signifies the selection probabilities of the dictionary atoms in the expansion of class-specific data. Furthermore, the non-parametric character of the proposed approach allows it to infer the correct size of the dictionary. We exploit the aforementioned Bernoulli distributions in separately learning a linear classifier. The classifier uses the same hierarchical Bayesian model as the dictionary, which we present along the analytical inference solution for Gibbs sampling. For classification, a test instance is first sparsely encoded over the learned dictionary and the codes are fed to the classifier. We performed experiments for face and action recognition; and object and scene-category classification using five public datasets and compared the results with state-of-the-art discriminative sparse representation approaches. Experiments show that the proposed Bayesian approach consistently outperforms the existing approaches.
The third category takes a hybrid approach for learning the discriminative sparse representation. In these approaches, the dictionaries are designed to have a set of shared atoms in addition to class-specific atoms. @cite_39 extended the SRC algorithm by appending an intra-class face variation dictionary to the training data. This extension achieves promising results in face recognition with a single training sample per class. Zhou and Fan @cite_63 employ a Fisher-like regularizer on the representation coefficients while learning a hybrid dictionary. Wang and Kong @cite_41 learned a hybrid dictionary to separate the common and particular features of the data. Their approach additionally encouraged the class-specific dictionaries to be incoherent during the optimization process. @cite_6 proposed to learn a multi-level dictionary for hierarchical visual categorization. To some extent, it is possible to reduce the size of the dictionary using the hybrid approach, which also results in reducing the classification time in comparison to the approaches that fall under the first category. However, it is often non-trivial to decide on how to balance between the shared and the class-specific parts of the hybrid dictionary @cite_20 , @cite_25 .
@cite_41 @cite_6 @cite_39 @cite_63 @cite_25 @cite_20
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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. In a sparse-representation-based face recognition scheme, the desired dictionary should have good representational power (i.e., being able to span the subspace of all faces) while supporting optimal discrimination of the classes (i.e., different human subjects). We propose a method to learn an over-complete dictionary that attempts to simultaneously achieve the above two goals. The proposed method, discriminative K-SVD (D-KSVD), is based on extending the K-SVD algorithm by incorporating the classification error into the objective function, thus allowing the performance of a linear classifier and the representational power of the dictionary being considered at the same time by the same optimization procedure. The D-KSVD algorithm finds the dictionary and solves for the classifier using a procedure derived from the K-SVD algorithm, which has proven efficiency and performance. This is in contrast to most existing work that relies on iteratively solving sub-problems with the hope of achieving the global optimal through iterative approximation. We evaluate the proposed method using two commonly-used face databases, the Extended YaleB database and the AR database, with detailed comparison to 3 alternative approaches, including the leading state-of-the-art in the literature. The experiments show that the proposed method outperforms these competing methods in most of the cases. Further, using Fisher criterion and dictionary incoherence, we also show that the learned dictionary and the corresponding classifier are indeed better-posed to support sparse-representation-based recognition. Sparse representation based classification (SRC) has recently been proposed for robust face recognition. To deal with occlusion, SRC introduces an identity matrix as an occlusion dictionary on the assumption that the occlusion has sparse representation in this dictionary. However, the results show that SRC's use of this occlusion dictionary is not nearly as robust to large occlusion as it is to random pixel corruption. In addition, the identity matrix renders the expanded dictionary large, which results in expensive computation. In this paper, we present a novel method, namely structured sparse representation based classification (SSRC), for face recognition with occlusion. A novel structured dictionary learning method is proposed to learn an occlusion dictionary from the data instead of an identity matrix. Specifically, a mutual incoherence of dictionaries regularization term is incorporated into the dictionary learning objective function which encourages the occlusion dictionary to be as independent as possible of the training sample dictionary. So that the occlusion can then be sparsely represented by the linear combination of the atoms from the learned occlusion dictionary and effectively separated from the occluded face image. The classification can thus be efficiently carried out on the recovered non-occluded face images and the size of the expanded dictionary is also much smaller than that used in SRC. The extensive experiments demonstrate that the proposed method achieves better results than the existing sparse representation based face recognition methods, especially in dealing with large region contiguous occlusion and severe illumination variation, while the computational cost is much lower. It is now well established that sparse representation models are working effectively for many visual recognition tasks, and have pushed forward the success of dictionary learning therein. Recent studies over dictionary learning focus on learning discriminative atoms instead of purely reconstructive ones. However, the existence of intraclass diversities (i.e., data objects within the same category but exhibit large visual dissimilarities), and interclass similarities (i.e., data objects from distinct classes but share much visual similarities), makes it challenging to learn effective recognition models. To this end, a large number of labeled data objects are required to learn models which can effectively characterize these subtle differences. However, labeled data objects are always limited to access, committing it difficult to learn a monolithic dictionary that can be discriminative enough. To address the above limitations, in this paper, we propose a weakly-supervised dictionary learning method to automatically learn a discriminative dictionary by fully exploiting visual attribute correlations rather than label priors. In particular, the intrinsic attribute correlations are deployed as a critical cue to guide the process of object categorization, and then a set of subdictionaries are jointly learned with respect to each category. The resulting dictionary is highly discriminative and leads to intraclass diversity aware sparse representations. Extensive experiments on image classification and object recognition are conducted to show the effectiveness of our approach.