相关论文: Wasserstein-based Graph Alignment

This paper provides a simple procedure to fit generative networks to target distributions, with the goal of a small Wasserstein distance (or other optimal transport costs). The approach is based on two principles: (a) if the source…

The mathematical forces at work behind Generative Adversarial Networks raise challenging theoretical issues. Motivated by the important question of characterizing the geometrical properties of the generated distributions, we provide a…

In graph signal processing, data samples are associated to vertices on a graph, while edge weights represent similarities between those samples. We propose a convex optimization problem to learn sparse well connected graphs from data. We…

In recent work arXiv:2109.07820 we have shown the equivalence of the widely used nonconvex (generalized) branched transport problem with a shape optimization problem of a street or railroad network, known as (generalized) urban planning…

We provide an implementation to compute the flat metric in any dimension. The flat metric, also called dual bounded Lipschitz distance, generalizes the well-known Wasserstein distance $W_1$ to the case that the distributions are of unequal…

We study transport distances on metric graphs representing gas networks. Starting from the dynamic formulation of the Wasserstein distance, we review extensions to networks, with and without the possibility of storing mass on the vertices.…

The graph matching problem seeks to find an alignment between the nodes of two graphs that minimizes the number of adjacency disagreements. Solving the graph matching is increasingly important due to it's applications in operations…

We develop a fast and scalable numerical approach to solve Wasserstein gradient flows (WGFs), particularly suitable for high-dimensional cases. Our approach is to use general reduced-order models, like deep neural networks, to parameterize…

Multiple marginal matching problem aims at learning mappings to match a source domain to multiple target domains and it has attracted great attention in many applications, such as multi-domain image translation. However, addressing this…

Computing high-quality graph partitions is a challenging problem with numerous applications. In this paper, we present a novel meta-heuristic for the balanced graph partitioning problem. Our approach is based on integer linear programs that…

Topological Data Analysis methods can be useful for classification and clustering tasks in many different fields as they can provide two dimensional persistence diagrams that summarize important information about the shape of potentially…

We consider the optimization problem of minimizing a functional defined over a family of probability distributions, where the objective functional is assumed to possess a variational form. Such a distributional optimization problem arises…

Wasserstein distances provide a powerful framework for comparing data distributions. They can be used to analyze processes over time or to detect inhomogeneities within data. However, simply calculating the Wasserstein distance or analyzing…

We study the reverse shortest path problem on disk graphs in the plane. In this problem we consider the proximity graph of a set of $n$ disks in the plane of arbitrary radii: In this graph two disks are connected if the distance between…

We develop in this paper a new regularized flow dynamic approach to construct efficient numerical schemes for Wasserstein gradient flows in Lagrangian coordinates. Instead of approximating the Wasserstein distance which needs to solve…

This paper addresses the Graph Matching problem, which consists of finding the best possible alignment between two input graphs, and has many applications in computer vision, network deanonymization and protein alignment. A common approach…

We propose a novel benchmarking methodology for graph neural networks (GNNs) based on the graph alignment problem, a combinatorial optimization task that generalizes graph isomorphism by aligning two unlabeled graphs to maximize overlapping…

In the decremental $(1+\epsilon)$-approximate Single-Source Shortest Path (SSSP) problem, we are given a graph $G=(V,E)$ with $n = |V|, m = |E|$, undergoing edge deletions, and a distinguished source $s \in V$, and we are asked to process…

We propose to align distributional data from the perspective of Wasserstein means. We raise the problem of regularizing Wasserstein means and propose several terms tailored to tackle different problems. Our formulation is based on the…

We consider the problem of estimating the topology of multiple networks from nodal observations, where these networks are assumed to be drawn from the same (unknown) random graph model. We adopt a graphon as our random graph model, which is…