Related papers: Discretization and Optimization using Graphs: One-…

A novel approach is put forth that utilizes data similarity, quantified on a graph, to improve upon the reconstruction performance of principal component analysis. The tasks of data dimensionality reduction and reconstruction are formulated…

Optimization, a key tool in machine learning and statistics, relies on regularization to reduce overfitting. Traditional regularization methods control a norm of the solution to ensure its smoothness. Recently, topological methods have…

Combinatorial optimization is a fundamental problem found in many fields. In many real life situations, the constraints and the objective function forming the optimization problem are naturally distributed amongst different sites in some…

Spectral discretizations of fractional derivative operators are examined, where the approximation basis is related to the set of Jacobi polynomials. The pseudo-spectral method is implemented by assuming that the grid, used to represent the…

Summarizing large-scaled directed graphs into small-scale representations is a useful but less studied problem setting. Conventional clustering approaches, which based on "Min-Cut"-style criteria, compress both the vertices and edges of the…

We are interested in multilayer graph clustering, which aims at dividing the graph nodes into categories or communities. To do so, we propose to learn a clustering-friendly embedding of the graph nodes by solving an optimization problem…

Matching and partitioning problems are fundamentals of computer vision applications with examples in multilabel segmentation, stereo estimation and optical-flow computation. These tasks can be posed as non-convex energy minimization…

Certifying feasibility in decision-making, critical in many industries, can be framed as a constraint satisfaction problem. This paper focuses on characterising a subset of parameter values from an a priori set that satisfy constraints on a…

Computing the rate-distortion function for continuous sources is commonly regarded as a standard continuous optimization problem. When numerically addressing this problem, a typical approach involves discretizing the source space and…

We present a general graph-based modeling abstraction for optimization that we call an OptiGraph. Under this abstraction, any optimization problem is treated as a hierarchical hypergraph in which nodes represent optimization subproblems and…

We describe a strategy for solving nonlinear eigenproblems numerically. Our approach is based on the approximation of a vector-valued function, defined as solution of a non-homogeneous version of the eigenproblem. This approximation step is…

In this paper, we hope to bring closer graph theory and consensus algorithms. Firstly, we give a brief introduction to graph theory by listing a concise definition. Then we analyze and visualize some commonly used graphs. Secondly, we…

The metric dimension of a graph is the smallest number of nodes required to identify all other nodes based on shortest path distances uniquely. Applications of metric dimension include discovering the source of a spread in a network,…

We consider a group of computation units trying to cooperatively solve a distributed optimization problem with shared linear equality and inequality constraints. Assuming that the computation units are communicating over a network whose…

Many problems can be presented in an abstract form through a wide range of binary objects and relations which are defined over problem domain. In these problems, graphical demonstration of defined binary objects and solutions is the most…

Data collected nowadays by social-networking applications create fascinating opportunities for building novel services, as well as expanding our understanding about social structures and their dynamics. Unfortunately, publishing…

We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…

In this paper, we propose an interpretable denoising method for graph signals using regularization by denoising (RED). RED is a technique developed for image restoration that uses an efficient (and sometimes black-box) denoiser in the…

Graph-based methods have been proposed as a unified framework for discrete calculus of local and nonlocal image processing methods in the recent years. In order to translate variational models and partial differential equations to a graph,…

Shape-based regularization has proven to be a useful method for delineating objects within noisy images where one has prior knowledge of the shape of the targeted object. When a collection of possible shapes is available, the specification…