Related papers: Ground Metric Learning on Graphs

Geometric graphs appear in many real-world data sets, such as road networks, sensor networks, and molecules. We investigate the notion of distance between embedded graphs and present a metric to measure the distance between two geometric…

Quantifying differences between flow fields is a key challenge in fluid mechanics, particularly when evaluating the effectiveness of flow control. Traditional vector metrics, such as the Euclidean distance, provide straightforward pointwise…

Optimal transport (OT) has gained popularity due to its various applications in fields such as machine learning, statistics, and signal processing. However, the balanced mass requirement limits its performance in practical problems. To…

Density-based distances (DBDs) provide a principled approach to metric learning by defining distances in terms of the underlying data distribution. By employing a Riemannian metric that increases in regions of low probability density,…

In machine learning and computer graphics, a fundamental task is the approximation of a probability density function through a well-dispersed collection of samples. Providing a formal metric for measuring the distance between probability…

With the widespread application of optimal transport (OT), its calculation becomes essential, and various algorithms have emerged. However, the existing methods either have low efficiency or cannot represent discontinuous maps. A novel…

We address the problem of defining a network graph on a large collection of classes. Each class is comprised of a collection of data points, sampled in a non i.i.d. way, from some unknown underlying distribution. The application we consider…

Graph distance metric learning serves as the foundation for many graph learning problems, e.g., graph clustering, graph classification and graph matching. Existing research works on graph distance metric (or graph kernels) learning fail to…

The Earth Mover's Distance is a popular similarity measure in several branches of computer science. It measures the minimum total edge length of a perfect matching between two point sets. The Earth Mover's Distance under Translation…

This paper presents a new distance metric to compare two continuous probability density functions. The main advantage of this metric is that, unlike other statistical measurements, it can provide an analytic, closed-form expression for a…

We investigate finding a map $g$ within a function class $G$ that minimises an Optimal Transport (OT) cost between a target measure $\nu$ and the image by $g$ of a source measure $\mu$. This is relevant when an OT map from $\mu$ to $\nu$…

Given samples from two joint distributions, we consider the problem of Optimal Transportation (OT) between them when conditioned on a common variable. We focus on the general setting where the conditioned variable may be continuous, and the…

Estimating the parameters of a probabilistic directed graphical model from incomplete data is a long-standing challenge. This is because, in the presence of latent variables, both the likelihood function and posterior distribution are…

Regularized discrete optimal transport (OT) is a powerful tool to measure the distance between two discrete distributions that have been constructed from data samples on two different domains. While it has a wide range of applications in…

Predicting commuting flows based on infrastructure and land-use information is critical for urban planning and public policy development. However, it is a challenging task given the complex patterns of commuting flows. Conventional models,…

We present a graph-regularized learning of Gaussian Mixture Models (GMMs) in distributed settings with heterogeneous and limited local data. The method exploits a provided similarity graph to guide parameter sharing among nodes, avoiding…

With the discovery of Wasserstein GANs, Optimal Transport (OT) has become a powerful tool for large-scale generative modeling tasks. In these tasks, OT cost is typically used as the loss for training GANs. In contrast to this approach, we…

Many tasks that rely on representations of nodes in graphs would benefit if those representations were faithful to distances between nodes in the graph. Geometric techniques to extract such representations have poor scaling over large graph…

Deep Metric Learning (DML) aims to find representations suitable for zero-shot transfer to a priori unknown test distributions. However, common evaluation protocols only test a single, fixed data split in which train and test classes are…

Data association across frames is at the core of Multiple Object Tracking (MOT) task. This problem is usually solved by a traditional graph-based optimization or directly learned via deep learning. Despite their popularity, we find some…