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We define a novel class of distances between statistical multivariate distributions by modeling an optimal transport problem on their marginals with respect to a ground distance defined on their conditionals. These new distances are metrics…
In literature, scientists describe human mobility in a range of granularities by several different models. Using frameworks like MATSIM, VehiLux, or Sumo, they often derive individual human movement indicators in their most detail. However,…
This paper is devoted to the study of the Monge-Kantorovich theory of optimal mass transport and its applications, in the special case of one-dimensional and circular distributions. More precisely, we study the Monge-Kantorovich distances…
What is the shortest path between two data points lying in a high-dimensional space? While the answer is trivial in Euclidean geometry, it becomes significantly more complex when the data lies on a curved manifold -- requiring a Riemannian…
The increasing congestion in the near-Earth space environment has amplified the need for robust and efficient conjunction analysis techniques including the computation of the minimum distance between orbital paths in the presence of…
Human mobility is a fundamental process underpinning socioeconomic life and urban structure. Classic theories, such as egocentric activity spaces and central place theory, provide crucial insights into specific facets of movement, like…
Optimal transport (OT) is a versatile framework for comparing probability measures, with many applications to statistics, machine learning, and applied mathematics. However, OT distances suffer from computational and statistical scalability…
In the present paper we focus on the coherence properties of general random Euclidean distance matrices, which are very closely related to the respective matrix completion problem. This problem is of great interest in several applications…
Driving risk assessment is crucial for both autonomous vehicles and human-driven vehicles. The driving risk can be quantified as the product of the probability that an event (such as collision) will occur and the consequence of that event.…
Mixture modelling using elliptical distributions promises enhanced robustness, flexibility and stability over the widely employed Gaussian mixture model (GMM). However, existing studies based on the elliptical mixture model (EMM) are…
Trip flow between areas is a fundamental metric for human mobility research. Given its identification with travel demand and its relevance for transportation and urban planning, many models have been developed for its estimation. These…
A unit spherical Euclidean distance matrix (EDM) D is a matrix whose entries can be realized as the interpoint (squared) Euclidean distances of n points on a unit sphere. In this paper, given such a D and 1 \leq k < l \leq n, we present a…
We study the unbalanced optimal transport (UOT) problem, where the marginal constraints are enforced using Maximum Mean Discrepancy (MMD) regularization. Our work is motivated by the observation that the literature on UOT is focused on…
The optimal transport (OT) problem has gained significant traction in modern machine learning for its ability to: (1) provide versatile metrics, such as Wasserstein distances and their variants, and (2) determine optimal couplings between…
This report presents a new, algorithmic approach to the distributions of the distance between two points distributed uniformly at random in various polygons, based on the extended Kinematic Measure (KM) from integral geometry. We first…
Realistic metric spaces (such as road/transportation networks) tend to be much more algorithmically tractable than general metrics. In an attempt to formalize this intuition, Abraham et~al.\ (SODA 2010, JACM 2016) introduced the notion of…
We lay out the phenomenological behavior of event-shape observables evaluated by solving optimal transport problems between collider events and reference geometries -- which we name 'manifold distances' -- to provide guidance regarding…
The unit Euclidean distance degree and the generic Euclidean distance degree are two well-studied invariants of projective varieties. These quantities measure the algebraic complexity of nearest-point problems on a variety, and in many…
Both the weighted and unweighted Unifrac distances have been very successfully employed to assess if two communities differ, but do not give any information about how two communities differ. We take advantage of recent observations that the…
Optimal transport distances (OT) have been widely used in recent work in Machine Learning as ways to compare probability distributions. These are costly to compute when the data lives in high dimension. Recent work by Paty et al., 2019,…