相关论文: Averaging Atmospheric Gas Concentration Data using…
This paper presents a unified computational framework for the estimation of distances, geodesics and barycenters of merge trees. We extend recent work on the edit distance [106] and introduce a new metric, called the Wasserstein distance…
Wasserstein dictionary learning is an unsupervised approach to learning a collection of probability distributions that generate observed distributions as Wasserstein barycentric combinations. Existing methods for Wasserstein dictionary…
We propose an efficient federated dual decomposition algorithm for calculating the Wasserstein barycenter of several distributions, including choosing the support of the solution. The algorithm does not access local data and uses only…
Terse representation of high-dimensional weather scene data is explored, in support of strategic air traffic flow management objectives. Specifically, we consider whether aviation-relevant weather scenes are compressible, in the sense that…
We study the problem of estimating the barycenter of a distribution given i.i.d. data in a geodesic space. Assuming an upper curvature bound in Alexandrov's sense and a support condition ensuring the strong geodesic convexity of the…
Accurate determination of gravitational wave source parameters relies on transforming between the source and detector frames. All-sky searches for continuous wave sources are computationally expensive, in part, because of barycentering…
Wasserstein Barycenter is a principled approach to represent the weighted mean of a given set of probability distributions, utilizing the geometry induced by optimal transport. In this work, we present a novel scalable algorithm to…
Air pollution is a chronic problem in large cities worldwide and awareness is rising as the long-term health implications become clearer. Vehicular traffic has been identified as a major contributor to poor air quality. In a lot of cities…
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 in this paper a variant of Wasserstein barycenter problem, which we refer to as tree-Wasserstein barycenter, by leveraging a specific class of ground metrics, namely tree metrics, for Wasserstein distance. Drawing on the tree…
We present a simplified model of the atmosphere of a terrestrial planet as an open two-dimensional system described by an ideal gas with velocity $\vec{v}$, density $\rho$ and temperature $T$ fields. Starting with the Chern-Simons equations…
A key goal of exoplanet spectroscopy is to measure atmospheric properties, such as abundances of chemical species, in order to connect them to our understanding of atmospheric physics and planet formation. In this new era of high-quality…
There is a wealth of data on air pollution within several users' reach, including modelled concentrations and depositions as well as observations from air quality stations. However, data integration to perceive spatial and temporal trends…
This paper presents a Multi-Robot Multi-Source Term Estimation (MRMSTE) framework that enables teams of mobile robots to collaboratively sample gas concentrations and infer the parameters of an unknown number of airborne releases. The…
This paper presents a Wasserstein attraction approach for solving dynamic mass transport problems over networks. In the transport problem over networks, we start with a distribution over the set of nodes that needs to be "transported" to a…
The need of atmospheric information with a higher spatial and temporal resolution drives the development of small satellites and satellite constellations to complement satellite flagship missions. Since optical systems are a main…
Environmental sensors provide crucial data for understanding our surroundings. For example, air quality maps based on sensor readings help users make decisions to mitigate the effects of pollution on their health. Standard maps show…
Density estimation for geospatial data ideally relies on precise geocoordinates, typically defined by longitude and latitude. However, such detailed information is often unavailable due to confidentiality constraints. As a result, analysts…
In this work we introduce the concept of Bures-Wasserstein barycenter $Q_*$, that is essentially a Fr\'echet mean of some distribution $\mathbb{P}$ supported on a subspace of positive semi-definite Hermitian operators $\mathbb{H}_{+}(d)$.…
Data fusion models are widely used in air quality monitoring to integrate in situ and large-scale gridded products, offering spatially complete and temporally detailed estimates. However, traditional Gaussian-based models often…