Related papers: An Explicit Formulation of the Earth Movers Distan…
Earth System Models (ESMs) are the primary tools for investigating future Earth system states at time scales from decades to centuries, especially in response to anthropogenic greenhouse gas release. State-of-the-art ESMs can reproduce the…
We derive distributional limits for empirical transport distances between probability measures supported on countable sets. Our approach is based on sensitivity analysis of optimal values of infinite dimensional mathematical programs and a…
Persistence diagrams (PDs) are the most common descriptors used to encode the topology of structured data appearing in challenging learning tasks; think e.g. of graphs, time series or point clouds sampled close to a manifold. Given random…
The earth mover's distance is a measure of the distance between two probabilistic measures. It plays a fundamental role in mathematics and computer science. The Kantorovich-Rubinstein theorem provides a formula for the earth mover's…
Optimal transport induces the Earth Mover's (Wasserstein) distance between probability distributions, a geometric divergence that is relevant to a wide range of problems. Over the last decade, two relaxations of optimal transport have been…
This paper describes continuous-space methodologies to estimate the collision probability, Euclidean distance and gradient between an ellipsoidal robot model and an environment surface modeled as a set of Gaussian distributions.…
The multivariate normal density is a monotonic function of the distance to the mean, and its ellipsoidal shape is due to the underlying Euclidean metric. We suggest to replace this metric with a locally adaptive, smoothly changing…
Path planning for walking characters in complicated virtual environments is a fundamental task in simulations and games. A navigation mesh is a data structure that allows efficient path planning. The Explicit Corridor Map (ECM) is a…
Accurate source localization in Multi-Platform Radar Networks (MPRNs) benefits from exploiting both range and angle measurements under robust estimation. In this paper, we propose a robust Euclidean distance matrix (EDM) optimization model…
Although many well-known algorithms can solve each bipartite matching problem instance efficiently, it remains an open question how one could estimate the expected optimal matching distance for arbitrary numbers of randomly distributed…
In autonomous driving, deep learning enabled motion prediction is a popular topic. A critical gap in traditional motion prediction methodologies lies in ensuring equivariance under Euclidean geometric transformations and maintaining…
This paper presents a fundamental algorithm, called VDB-EDT, for Euclidean distance transform (EDT) based on the VDB data structure. The algorithm executes on grid maps and generates the corresponding distance field for recording distance…
We establish the validity of asymptotic limits for the general transportation problem between random i.i.d. points and their common distribution, with respect to the squared Euclidean distance cost, in any dimension larger than three.…
This paper introduces a mobility equity metric (MEM) for evaluating fairness and accessibility in multi-modal intelligent transportation systems. The MEM simultaneously accounts for service accessibility and transportation costs across…
How to dynamically measure the local-to-global spatio-temporal coherence between demand and supply networks is a fundamental task for ride-sourcing platforms, such as DiDi. Such coherence measurement is critically important for the…
Distributed distribution comparison aims to measure the distance between the distributions whose data are scattered across different agents in a distributed system and cannot even be shared directly among the agents. In this study, we…
Geometric data sets arising in modern applications are often very large and change dynamically over time. A popular framework for dealing with such data sets is the evolving data framework, where a discrete structure continuously varies…
We investigate the estimation of an optimal transport map between probability measures on an infinite-dimensional space and reveal its minimax optimal rate. Optimal transport theory defines distances within a space of probability measures,…
The metric dimension of a graph is the smallest number of nodes required to identify all other nodes based on shortest path distances uniquely. Applications of metric dimension include discovering the source of a spread in a network,…
Differential equations are pivotal in modeling and understanding the dynamics of various systems, offering insights into their future states through parameter estimation fitted to time series data. In fields such as economy, politics, and…