Related papers: Graph Matching via convex relaxation to the simple…
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…
Convex clustering is a recent stable alternative to hierarchical clustering. It formulates the recovery of progressively coalescing clusters as a regularized convex problem. While convex clustering was originally designed for handling…
Given an affine space of matrices $\mathcal{L}$ and a matrix $\Theta\in \mathcal{L}$, consider the problem of computing the closest rank deficient matrix to $\Theta$ on $\mathcal{L}$ with respect to the Frobenius norm. This is a nonconvex…
A fruitful approach for solving signal deconvolution problems consists of resorting to a frame-based convex variational formulation. In this context, parallel proximal algorithms and related alternating direction methods of multipliers have…
This paper deals with problem of blind identification of a graph filter and its sparse input signal, thus broadening the scope of classical blind deconvolution of temporal and spatial signals to irregular graph domains. While the…
We consider the problem of minimizing a convex objective which is the sum of a smooth part, with Lipschitz continuous gradient, and a nonsmooth part. Inspired by various applications, we focus on the case when the nonsmooth part is a…
In recent years, there has been a growing interest in mathematical models leading to the minimization, in a symmetric matrix space, of a Bregman divergence coupled with a regularization term. We address problems of this type within a…
Vertex similarity is a major problem in network science with a wide range of applications. In this work we provide novel perspectives on finding (dis)similar vertices within a network and across two networks with the same number of vertices…
The graph isomorphism (GI) problem, which asks whether two graphs are structurally identical, occupies a unique position in computational complexity -- it is neither known to be solvable in polynomial time, nor proven to be NP-complete. We…
We study the problem of prediction for evolving graph data. We formulate the problem as the minimization of a convex objective encouraging sparsity and low-rank of the solution, that reflect natural graph properties. The convex formulation…
Finding the exact integrality gap $\alpha$ for the LP relaxation of the 2-edge-connected spanning multigraph problem (2EC) is closely related to the same problem for the Held-Karp relaxation of the metric traveling salesman problem (TSP).…
Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with…
We study sample complexity of optimizing "hill-climbing friendly" functions defined on a graph under noisy observations. We define a notion of convexity, and we show that a variant of best-arm identification can find a near-optimal solution…
Correspondence is a ubiquitous problem in computer vision and graph matching has been a natural way to formalize correspondence as an optimization problem. Recently, graph matching solvers have included higher-order terms representing…
The graph partitioning problem is a well-known NP-hard problem. In this paper, we formulate a 0-1 quadratic integer programming model for the graph partitioning problem with vertex weight constraints and fixed vertex constraints, and…
A popular class of algorithms to optimize the dual LP relaxation of the discrete energy minimization problem (a.k.a.\ MAP inference in graphical models or valued constraint satisfaction) are convergent message-passing algorithms, such as…
In recent years, graph signal processing (GSP) technology has become popular in various fields, and graph Laplacian regularizers have also been introduced into convolutional sparse representation. This paper proposes a convolutional sparse…
Exact solution of hard combinatorial optimization problems often relies on strong convex relaxations, but solving these relaxations repeatedly inside a branch-and-bound algorithm can be prohibitively expensive. Hence, we consider this…
In this paper, we consider convex quadratic optimization problems with indicator variables when the matrix $Q$ defining the quadratic term in the objective is sparse. We use a graphical representation of the support of $Q$, and show that if…
A Graph of Convex Sets (GCS) is a graph in which vertices are associated with convex programs and edges couple pairs of programs through additional convex costs and constraints. Any optimization problem over an ordinary weighted graph…