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Graph signals offer a very generic and natural representation for data that lives on networks or irregular structures. The actual data structure is however often unknown a priori but can sometimes be estimated from the knowledge of the application domain. If this is not possible, the data structure has to be inferred from the mere signal observations. This is exactly the problem that we address in this paper, under the assumption that the graph signals can be represented as a sparse linear combination of a few atoms of a structured graph dictionary. The dictionary is constructed on polynomials of the graph Laplacian, which can sparsely represent a general class of graph signals composed of localized patterns on the graph. We formulate a graph learning problem, whose solution provides an ideal fit between the signal observations and the sparse graph signal model. As the problem is non-convex, we propose to solve it by alternating between a signal sparse coding and a graph update step. We provide experimental results that outline the good graph recovery performance of our method, which generally compares favourably to other recent network inference algorithms.

Graph learning methods have recently been receiving increasing interest as means to infer structure in datasets. Most of the recent approaches focus on different relationships between a graph and data sample distributions, mostly in settings where all available relate to the same graph. This is, however, not always the case, as data is often available in mixed form, yielding the need for methods that are able to cope with mixture data and learn multiple graphs. We propose a novel generative model that explains a collection of distinct data naturally living on different graphs. We assume the mapping of data to graphs is not known and investigate the problem of jointly clustering a set of data and learning a graph for each of the clusters. Experiments in both synthetic and real-world datasets demonstrate promising performance both in terms of data clustering, as well as multiple graph inference from mixture data.

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In recent years, light field imaging has attracted the attention of the academic and industrial communities thanks to its enhanced rendering capabilities that allow to visualise contents in a more immersive and interactive way. However, those enhanced capabilities come at the cost of a considerable increase in content size when compared to traditional image and video applications. Thus, advanced compression schemes are needed to efficiently reduce the volume of data for storage and delivery of light field content. In this paper, we introduce a novel method for compression of light field images. The proposed solution is based on a graph learning approach to estimate the disparity among the views composing the light field. The graph is then used to reconstruct the entire light field from an arbitrary subset of encoded views. Experimental results show that our method is a promising alternative to current compression algorithms for light field images, with notable gains across all bitrates with respect to the state of the art.

Optimal transport aims to estimate a transportation plan that minimizes a displacement cost. This is realized by optimizing the scalar product between the sought plan and the given cost, over the space of doubly stochastic matrices. When the entropy regularization is added to the problem, the transportation plan can be efficiently computed with the Sinkhorn algorithm. Thanks to this breakthrough, optimal transport has been progressively extended to machine learning and statistical inference by introducing additional application-specific terms in the problem formulation. It is however challenging to design efficient optimization algorithms for optimal transport based extensions. To overcome this limitation, we devise a general forward-backward splitting algorithm based on Bregman distances for solving a wide range of optimization problems involving a differentiable function with Lipschitz-continuous gradient and a doubly stochastic constraint. We illustrate the efficiency of our approach in the context of continuous domain adaptation. Experiments show that the proposed method leads to a significant improvement in terms of speed and performance with respect to the state of the art for domain adaptation on a continually rotating distribution coming from the standard two moon dataset.

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