Related papers: An Explicit Formulation of the Earth Movers Distan…
Land remote sensing analysis is a crucial research in earth science. In this work, we focus on a challenging task of land analysis, i.e., automatic extraction of traffic roads from remote sensing data, which has widespread applications in…
Electric vehicles (EVs) are being rapidly adopted due to their economic and societal benefits. Autonomous mobility-on-demand (AMoD) systems also embrace this trend. However, the long charging time and high recharging frequency of EVs pose…
We introduce the proximal optimal transport divergence, a novel discrepancy measure that interpolates between information divergences and optimal transport distances via an infimal convolution formulation. This divergence provides a…
Metric data plays an important role in various settings such as metric-based indexing, clustering, classification, and approximation algorithms in general. Due to measurement error, noise, or an inability to completely gather all the data,…
The empirical mode decomposition (EMD) method and its variants have been extensively employed in the load and renewable forecasting literature. Using this multiresolution decomposition, time series (TS) related to the historical load and…
Comparing probability distributions is a fundamental problem in data sciences. Simple norms and divergences such as the total variation and the relative entropy only compare densities in a point-wise manner and fail to capture the geometric…
In this paper, we introduce a metric to evaluate the equity in mobility and a routing framework to enhance the metric within multi-modal intelligent transportation systems. The mobility equity metric (MEM) simultaneously accounts for…
The Pairwise Einstein Model (PEM) of steps not only justifies the use of the Generalized Wigner Distribution (GWD) for Terrace Width Distributions (TWDs), it also predicts a specific form for the Step Position Distribution (SPD), i.e., the…
Human motion prediction is essential for the safe and smooth operation of mobile service robots and intelligent vehicles around people. Commonly used neural network-based approaches often require large amounts of complete trajectories to…
The Expectation--Maximization (EM) algorithm is a simple meta-algorithm that has been used for many years as a methodology for statistical inference when there are missing measurements in the observed data or when the data is composed of…
Discrepancy measures between probability distributions are at the core of statistical inference and machine learning. In many applications, distributions of interest are supported on different spaces, and yet a meaningful correspondence…
This paper presents a unified framework for smooth convex regularization of discrete optimal transport problems. In this context, the regularized optimal transport turns out to be equivalent to a matrix nearness problem with respect to…
The optimal transport (OT) map is a geometry-driven transformation between high-dimensional probability distributions which underpins a wide range of tasks in statistics, applied probability, and machine learning. However, existing…
Many problems in machine learning involve calculating correspondences between sets of objects, such as point clouds or images. Discrete optimal transport provides a natural and successful approach to such tasks whenever the two sets of…
It is very important to understand urban mobility patterns because most trips are concentrated in urban areas. In the paper, a new model is proposed to model collective human mobility in urban areas. The model can be applied to predict…
We consider the problem of finding an optimal transport plan between an absolutely continuous measure $\mu$ on $\mathcal{X} \subset \mathbb{R}^d$ and a finitely supported measure $\nu$ on $\mathbb{R}^d$ when the transport cost is the…
The research objectives are exploring characteristics of human mobility patterns, subsequently modelling them mathematically depending on inter-event time and traveled distances parameters using CDRs (Call Detailed Records). The…
Transport in crowded, complex environments occurs across many spatial scales. Geometric restrictions can hinder the motion of individuals and, combined with crowding between individuals, can have drastic effects on global transport…
Multidimensional scaling (MDS) is a popular technique for mapping a finite metric space into a low-dimensional Euclidean space in a way that best preserves pairwise distances. We study a notion of MDS on infinite metric measure spaces,…
We prove that the distortion of any embedding into $L_1$ of the transportation cost space or earth mover distance over a $d$-dimensional grid $\{1,\dots m\}^d$ is $\Omega(\log N)$, where $N$ is the number of vertices and the implicit…