Remote sensing data from hyperspectral cameras suffer limited spatial resolution, in which a single pixel of image may contain information several materials the field view. Blind unmixing is process identifying pure spectra individual (i.e., endmembers) and their proportions abundances) at each pixel. In this article, we propose novel blind model based on graph total variation (gTV) regularizat...

In many learning tasks with structural properties, structural sparsity methods help induce sparse models, usually leading to better interpretability and higher generalization performance. One popular approach is to use group sparsity regularization that enforces sparsity on the clustered groups of features, while another popular approach is to adopt graph sparsity regularization that considers ...

This article proposes a new framework to regularize imaging linear inverse problems using an adaptive non-local energy. A non-local graph is optimized to match the structures of the image to recover. This allows a better reconstruction of geometric edges and textures present in natural images. A fast algorithm computes iteratively both the solution of the regularization process and the non-loca...

A new method for diffusion tensor MRI (DT-MRI) regularization is presented that relies on graph diffusion. We represent a DT image using a weighted graph, where the weights of edges are functions of the geodesic distances between tensors. Diffusion across this graph with time is captured by the heat-equation, and the solution, i.e. the heat kernel, is found by exponentiating the Laplacian eigen...

Many real-world machine learning problems are situated on finite discrete sets, including dimensionality reduction, clustering, and transductive inference. A variety of approaches for learning from finite sets has been proposed from different motivations and for different problems. In most of those approaches, a finite set is modeled as a graph, in which the edges encode pairwise relationships ...

A regularized optimization problem over a large unstructured graph is studied, where the regularization term is tied to the graph geometry. Typical regularization examples include the total variation and the Laplacian regularizations over the graph. When applying the proximal gradient algorithm to solve this problem, there exist quite affordable methods to implement the proximity operator (back...

We propose a method called Topic Graph based NMF for Transfer Learning (TNT) based on Non-negative Matrix Factorization (NMF). Since NMF learns feature vectors to approximate the given data, the proposed approach tries to preserve the feature space which is spanned by the feature vectors to realize transfer learning. Based on the learned feature vectors in the source domain, a graph structure c...

Multi-label learning refers to the problems where an instance can be assigned to more than one category. In this paper, we present a novel Semi-supervised algorithm for Multi-label learning by solving a Sylvester Equation (SMSE). Two graphs are first constructed on instance level and category level respectively. For instance level, a graph is defined based on both labeled and unlabeled instance...