相关论文: Wasserstein-based Graph Alignment

We propose a new functional analytic approach to Stein's method of exchangeable pairs that does not require the pair at hand to satisfy any approximate linear regression property. We make use of this theory in order to derive abstract…

Graphs are ubiquitous in various fields, and deep learning methods have been successful applied in graph classification tasks. However, building large and diverse graph datasets for training can be expensive. While augmentation techniques…

The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain…

Missing node attributes is a common problem in real-world graphs. Graph neural networks have been demonstrated power in graph representation learning while their performance is affected by the completeness of graph information. Most of them…

Many tasks in machine learning and signal processing can be solved by minimizing a convex function of a measure. This includes sparse spikes deconvolution or training a neural network with a single hidden layer. For these problems, we study…

This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…

We propose a new algorithm that uses an auxiliary neural network to express the potential of the optimal transport map between two data distributions. In the sequel, we use the aforementioned map to train generative networks. Unlike WGANs,…

This paper studies the problem of recovering a hidden vertex correspondence between two correlated graphs when both edge weights and node features are observed. While most existing work on graph alignment relies primarily on edge…

Graphs are ubiquitous in modelling relational structures. Recent endeavours in machine learning for graph-structured data have led to many architectures and learning algorithms. However, the graph used by these algorithms is often…

We propose a new algorithm for finding the center of a graph, as well as the rank of each node in the hierarchy of distances to the center. In other words, our algorithm allows to partition the graph according to nodes distance to the…

This paper presents a spectral framework for quantifying the differentiation between graph data samples by introducing a novel metric named Graph Geodesic Distance (GGD). For two different graphs with the same number of nodes, our framework…

In this paper, we address the numerical solution of the Optimal Transport Problem on undirected weighted graphs, taking the shortest path distance as transport cost. The optimal solution is obtained from the long-time limit of the gradient…

Efficient layout of large-scale graphs remains a challenging problem: the force-directed and dimensionality reduction-based methods suffer from high overhead for graph distance and gradient computation. In this paper, we present a new graph…

This article details a novel numerical scheme to approximate gradient flows for optimal transport (i.e. Wasserstein) metrics. These flows have proved useful to tackle theoretically and numerically non-linear diffusion equations that model…

This paper proposes a family of graph metrics for measuring distances between graphs of different sizes. The proposed metric family defines a general form of the graph generalised optimal sub-pattern assignment (GOSPA) metric and is also…

This paper proposes a metric to measure the dissimilarity between graphs that may have a different number of nodes. The proposed metric extends the generalised optimal subpattern assignment (GOSPA) metric, which is a metric for sets, to…

The adapted Wasserstein distance is a metric for quantifying distributional uncertainty and assessing the sensitivity of stochastic optimization problems on time series data. A computationally efficient alternative to it, is provided by the…

This paper studies iterative schemes for measure transfer and approximation problems, which are defined through a slicing-and-matching procedure. Similar to the sliced Wasserstein distance, these schemes benefit from the availability of…

This paper tackles the challenging problem of jointly inferring time-varying network topologies and imputing missing data from partially observed graph signals. We propose a unified non-convex optimization framework to simultaneously…

This paper presents a novel distribution-agnostic Wasserstein distance-based estimation framework. The goal is to determine an optimal map combining prior estimate with measurement likelihood such that posterior estimation error optimally…