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.
@cite_41: 
@cite_6: For the task of visual categorization, the learning model is expected to be endowed with discriminative visual feature representation and flexibilities in processing many categories. Many existing approaches are designed based on a flat category structure, or rely on a set of pre-computed visual features, hence may not be appreciated for dealing with large numbers of categories. In this paper, we propose a novel dictionary learning method by taking advantage of hierarchical category correlation. For each internode of the hierarchical category structure, a discriminative dictionary and a set of classification models are learnt for visual categorization, and the dictionaries in different layers are learnt to exploit the discriminative visual properties of different granularity. Moreover, the dictionaries in lower levels also inherit the dictionary of ancestor nodes, so that categories in lower levels are described with multi-scale visual information using our dictionary learning approach. Experiments on Image Net object data subset and SUN397 scene dataset demonstrate that our approach achieves promising performance on data with large numbers of classes compared with some state-of-the-art methods, and is more efficient in processing large numbers of categories.
@cite_39: Sparse Representation-Based Classification (SRC) is a face recognition breakthrough in recent years which has successfully addressed the recognition problem with sufficient training images of each gallery subject. In this paper, we extend SRC to applications where there are very few, or even a single, training images per subject. Assuming that the intraclass variations of one subject can be approximated by a sparse linear combination of those of other subjects, Extended Sparse Representation-Based Classifier (ESRC) applies an auxiliary intraclass variant dictionary to represent the possible variation between the training and testing images. The dictionary atoms typically represent intraclass sample differences computed from either the gallery faces themselves or the generic faces that are outside the gallery. Experimental results on the AR and FERET databases show that ESRC has better generalization ability than SRC for undersampled face recognition under variable expressions, illuminations, disguises, and ages. The superior results of ESRC suggest that if the dictionary is properly constructed, SRC algorithms can generalize well to the large-scale face recognition problem, even with a single training image per class.
@cite_63: Object recognition is challenging especially when the objects from different categories are visually similar to each other. In this paper, we present a novel joint dictionary learning (JDL) algorithm to exploit the visual correlation within a group of visually similar object categories for dictionary learning where a commonly shared dictionary and multiple category-specific dictionaries are accordingly modeled. To enhance the discrimination of the dictionaries, the dictionary learning problem is formulated as a joint optimization by adding a discriminative term on the principle of the Fisher discrimination criterion. As well as presenting the JDL model, a classification scheme is developed to better take advantage of the multiple dictionaries that have been trained. The effectiveness of the proposed algorithm has been evaluated on popular visual benchmarks.
@cite_25: Dictionary learning (DL) for sparse coding has shown promising results in classification tasks, while how to adaptively build the relationship between dictionary atoms and class labels is still an important open question. The existing dictionary learning approaches simply fix a dictionary atom to be either class-specific or shared by all classes beforehand, ignoring that the relationship needs to be updated during DL. To address this issue, in this paper we propose a novel latent dictionary learning (LDL) method to learn a discriminative dictionary and build its relationship to class labels adaptively. Each dictionary atom is jointly learned with a latent vector, which associates this atom to the representation of different classes. More specifically, we introduce a latent representation model, in which discrimination of the learned dictionary is exploited via minimizing the within-class scatter of coding coefficients and the latent-value weighted dictionary coherence. The optimal solution is efficiently obtained by the proposed solving algorithm. Correspondingly, a latent sparse representation based classifier is also presented. Experimental results demonstrate that our algorithm outperforms many recently proposed sparse representation and dictionary learning approaches for action, gender and face recognition.
@cite_20: The employed dictionary plays an important role in sparse representation or sparse coding based image reconstruction and classification, while learning dictionaries from the training data has led to state-of-the-art results in image classification tasks. However, many dictionary learning models exploit only the discriminative information in either the representation coefficients or the representation residual, which limits their performance. In this paper we present a novel dictionary learning method based on the Fisher discrimination criterion. A structured dictionary, whose atoms have correspondences to the subject class labels, is learned, with which not only the representation residual can be used to distinguish different classes, but also the representation coefficients have small within-class scatter and big between-class scatter. The classification scheme associated with the proposed Fisher discrimination dictionary learning (FDDL) model is consequently presented by exploiting the discriminative information in both the representation residual and the representation coefficients. The proposed FDDL model is extensively evaluated on various image datasets, and it shows superior performance to many state-of-the-art dictionary learning methods in a variety of classification tasks.
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 .