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We propose a desigining method of a flexible sampling operator for graph signals via a difference-of-convex (DC) optimization algorithm. A fundamental challenge in graph signal processing is sampling, especially for graph signals that are…
While Annealing Machines (AM) have shown increasing capabilities in solving complex combinatorial problems, positioning themselves as a more immediate alternative to the expected advances of future fully quantum solutions, there are still…
Categorical variables are a natural choice for representing discrete structure in the world. However, stochastic neural networks rarely use categorical latent variables due to the inability to backpropagate through samples. In this work, we…
The \emph{Dominating $H$-Pattern} problem generalizes the classical $k$-Dominating Set problem: for a fixed \emph{pattern} $H$ and a given graph $G$, the goal is to find an induced subgraph $S$ of $G$ such that (1) $S$ is isomorphic to $H$,…
We study distributed optimization to minimize a global objective that is a sum of smooth and strongly-convex local cost functions. Recently, several algorithms over undirected and directed graphs have been proposed that use a gradient…
This paper proposes a method for vertex-wise flexible sampling of a broad class of graph signals, designed to attain the best possible recovery based on the generalized sampling theory. This is achieved by designing a sampling operator by…
Graduated optimization is a global optimization technique that is used to minimize a multimodal nonconvex function by smoothing the objective function with noise and gradually refining the solution. This paper experimentally evaluates the…
We develop a generalized optimization framework for graph-based semi-supervised learning. The framework gives as particular cases the Standard Laplacian, Normalized Laplacian and PageRank based methods. We have also provided new…
This paper proposes a distributed algorithm for a network of agents to solve an optimization problem with separable objective function and locally coupled constraints. Our strategy is based on reformulating the original constrained problem…
Gradient-based methods are widely used to solve various optimization problems, however, they are either constrained by local optima dilemmas, simple convex constraints, and continuous differentiability requirements, or limited to…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function so that along the iterations the objective function decreases. Such a simple principle allows to solve a large…
We describe a general-purpose method for finding high-quality solutions to hard optimization problems, inspired by self-organized critical models of co-evolution such as the Bak-Sneppen model. The method, called Extremal Optimization,…
The multicut problem is an NP-hard combinatorial optimization problem with diverse applications in fields such as bioinformatics, data mining and computer vision. Graph neural networks have been defined for the multicut problem but can be…
We consider network topology identification subject to a signal smoothness prior on the nodal observations. A fast dual-based proximal gradient algorithm is developed to efficiently tackle a strongly convex, smoothness-regularized network…
The recent work ``Combinatorial Optimization with Physics-Inspired Graph Neural Networks'' [Nat Mach Intell 4 (2022) 367] introduces a physics-inspired unsupervised Graph Neural Network (GNN) to solve combinatorial optimization problems on…
The burdensome training costs on large-scale graphs have aroused significant interest in graph condensation, which involves tuning Graph Neural Networks (GNNs) on a small condensed graph for use on the large-scale original graph. Existing…
Nowadays, optimization problem have more application in all major but they have problem in computation. Computation global point in continuous functions have high calculation and this became clearer in large space .In this paper, we…
The success of machine learning solutions for reasoning about discrete structures has brought attention to its adoption within combinatorial optimization algorithms. Such approaches generally rely on supervised learning by leveraging…
Fast, gradient-based structural optimization has long been limited to a highly restricted subset of problems -- namely, density-based compliance minimization -- for which gradients can be analytically derived. For other objective functions,…
In this work, we study the classical distributed optimization problem over digraphs, where the objective function is a sum of smooth local functions. Inspired by the implicit tracking mechanism proposed in our earlier work, we develop a…