Design of Non-Linear Discriminative Dictionaries for Image Classification

Abstract

Abstract. In recent years there has been growing interest in designing dictionaries for image classification. These methods, however, neglect the fact that data of interest often has non-linear structure. Motivated by the fact that this non-linearity can be handled by the kernel trick, we propose learning of dictionaries in the high-dimensional feature space which are simultaneously reconstructive and discriminative. The proposed optimization approach consists of two main stages-coefficient update and dictionary update. We propose a kernel driven simultaneous orthogonal matching pursuit algorithm for the task of sparse coding in the feature space. The dictionary update step is performed using an efficient approximate KSVD algorithm in feature space. Extensive experiments on image classification demonstrate that the proposed non-linear dictionary learning method is robust and can perform significantly better than many competitive discriminative dictionary learning algorithms.

Unsupervised domain adaptation using parallel transport on Grassmann manifold

“…We believe that the main reason for the improved performance of our method is due to the multiple intermediate union of subspaces and sparse representation of the data. Constructing separate subspace for each class followed by sparse approximation of a test sample on the concatenation of all the subspaces is a popular idea in dictionary learning literature and has demonstrated a significant performance improvement in many computer vision tasks [31,28,20,29].…”

Max residual classifier

“…Shortly after, various discriminative dictionary learning methods have been proposed in the literature [24,29,47,31,45,35]. In [24], a multiclass version of the logistic function on the residual errors is used to control the trade-off between reconstruction and discrimination.…”

“…In particular, a novel signal is assigned to the class with the smallest residual error resulting from a sparse approximation. The residual classifier works surprisingly well and, in many cases [35,41], outperforms sophisticated classifiers like support vector machine (SVM) [38]. One of the main reasons behind the successes is the highly compact and robust data representation.…”

Dictionaries for image-based recognition

“…Hence, generative dictionaries may lead to poor performance in classification even when data is non-linearly mapped to a feature space. To overcome this, a method for designing non-linear dictionaries that are simultaneously generative and discriminative was proposed in [35]. Figure 5 presents an important comparison in terms of the discriminative power of learning a discriminative dictionary in the feature space where kernel LDA type of discriminative term has been included in the objective function.…”

“…A scatter plot of the sparse coefficients obtained using different approaches show that such a discriminative dictionary is able to learn the underlying non-linear sparsity of data as well as it provides more discriminative representation. See [35], [34] for more details on the design of non-linear kernel dictionaries.…”