Deep Dictionary Learning: A PARametric NETwork Approach

Deep dictionary learning seeks multiple dictionaries at different image scales to capture complementary coherent characteristics. We propose a method for learning a hierarchy of synthesis dictionaries with an image classification goal. The dictionaries and classification parameters are trained by a classification objective, and the sparse features are extracted by reducing a reconstruction loss in each layer. The reconstruction objectives in some sense regularize the classification problem and inject source signal information in the extracted features. The performance of the proposed hierarchical method increases by adding more layers, which consequently makes this model easier to tune and adapt. The proposed algorithm furthermore, shows remarkably lower fooling rate in presence of adversarial perturbation. The validation of the proposed approach is based on its classification performance using four benchmark datasets and is compared to a CNN of similar size

Image registration with sparse approximations in parametric dictionaries

We examine in this paper the problem of image registration from the new perspective where images are given by sparse approximations in parametric dictionaries of geometric functions. We propose a registration algorithm that looks for an estimate of the global transformation between sparse images by examining the set of relative geometrical transformations between the respective features. We propose a theoretical analysis of our registration algorithm and we derive performance guarantees based on two novel important properties of redundant dictionaries, namely the robust linear independence and the transformation inconsistency. We propose several illustrations and insights about the importance of these dictionary properties and show that common properties such as coherence or restricted isometry property fail to provide sufficient information in registration problems. We finally show with illustrative experiments on simple visual objects and handwritten digits images that our algorithm outperforms baseline competitor methods in terms of transformation-invariant distance computation and classification

Classification via Incoherent Subspaces

This article presents a new classification framework that can extract individual features per class. The scheme is based on a model of incoherent subspaces, each one associated to one class, and a model on how the elements in a class are represented in this subspace. After the theoretical analysis an alternate projection algorithm to find such a collection is developed. The classification performance and speed of the proposed method is tested on the AR and YaleB databases and compared to that of Fisher's LDA and a recent approach based on on $\ell_1$ minimisation. Finally connections of the presented scheme to already existing work are discussed and possible ways of extensions are pointed out.Comment: 22 pages, 2 figures, 4 table

Middle-Level Features for the Explanation of Classification Systems by Sparse Dictionary Methods.

Machine learning (ML) systems are affected by a pervasive lack of transparency. The eXplainable Artificial Intelligence (XAI) research area addresses this problem and the related issue of explaining the behavior of ML systems in terms that are understandable to human beings. In many explanation of XAI approaches, the output of ML systems are explained in terms of low-level features of their inputs. However, these approaches leave a substantive explanatory burden with human users, insofar as the latter are required to map low-level properties into more salient and readily understandable parts of the input. To alleviate this cognitive burden, an alternative model-agnostic framework is proposed here. This framework is instantiated to address explanation problems in the context of ML image classification systems, without relying on pixel relevance maps and other low-level features of the input. More specifically, one obtains sets of middle-level properties of classification inputs that are perceptually salient by applying sparse dictionary learning techniques. These middle-level properties are used as building blocks for explanations of image classifications. The achieved explanations are parsimonious, for their reliance on a limited set of middle-level image properties. And they can be contrastive, because the set of middle-level image properties can be used to explain why the system advanced the proposed classification over other antagonist classifications. In view of its model-agnostic character, the proposed framework is adaptable to a variety of other ML systems and explanation problems