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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.
We propose to jointly learn a Discriminative Bayesian dictionary along a linear classifier using coupled Beta-Bernoulli Processes. Our representation model uses separate base measures for the dictionary and the classifier, but associates them to the class-specific training data using the same Bernoulli distributions. The Bernoulli distributions control the frequency with which the factors (\eg dictionary atoms) are used in data representations, and they are inferred while accounting for the class labels in our approach. To further encourage discrimination in the dictionary, our model uses separate (sets of) Bernoulli distributions to represent data from different classes. Our approach adaptively learns the association between the dictionary atoms and the class labels while tailoring the classifier to this relation with a joint inference over the dictionary and the classifier. Once a test sample is represented over the dictionary, its representation is accurately labeled by the classifier due to the strong coupling between the dictionary and the classifier. We derive the Gibbs Sampling equations for our joint representation model and test our approach for face, object, scene and action recognition to establish its effectiveness.
We present a principled approach to learn a dis-criminative dictionary along a linear classifier for hyperspectral classification. Our approach places Gaussian Process priors over the dictionary to account for the relative smoothness of the natural spectra, whereas the classifier parameters are sampled from multi-variate Gaussians. We employ two Beta-Bernoulli processes to jointly infer the dictionary and the classifier. These processes are coupled under the same sets of Bernoulli distributions. In our approach, these distributions signify the frequency of the dictionary atom usage in representing class-specific training spectra, which also makes the dictionary dis-criminative. Due to the coupling between the dictionary and the classifier, the popularity of the atoms for representing different classes gets encoded into the classifier. This helps in predicting the class labels of test spectra that are first represented over the dictionary by solving a simultaneous sparse optimization problem. The labels of the spectra are predicted by feeding the resulting representations to the classifier. Our approach exploits the non-parametric Bayesian framework to automatically infer the dictionary size-the key parameter in discriminative dictionary learning. Moreover, it also has the desirable property of adaptively learning the association between the dictionary atoms and the class labels by itself. We use Gibbs sampling to infer the posterior probability distributions over the dictionary and the classifier under the proposed model, for which, we derive analytical expressions. To establish the effectiveness of our approach, we test it on benchmark hyperspectral images. The classification performance is compared with the state-of-the-art dictionary learning based classification methods.
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