Related papers: Comparing Morse Complexes Using Optimal Transport:…
We consider approximating distributions within the framework of optimal mass transport and specialize to the problem of clustering data sets. Distances between distributions are measured in the Wasserstein metric. The main problem we…
We introduce COPT, a novel distance metric between graphs defined via an optimization routine, computing a coordinated pair of optimal transport maps simultaneously. This gives an unsupervised way to learn general-purpose graph…
Understanding city-scale vehicular mobility and trip patterns is essential to addressing many problems, from transportation and pollution to public safety, among others. Using spatio-temporal analysis of vehicular mobility, promising…
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…
This paper describes the adaptation of a well-scaling parallel algorithm for computing Morse-Smale segmentations based on path compression to a distributed computational setting. Additionally, we extend the algorithm to efficiently compute…
Representational similarity metrics typically force all units to be matched, making them susceptible to noise and outliers common in neural representations. We extend the soft-matching distance to a partial optimal transport setting that…
Sampling from multimodal distributions is a challenging task in scientific computing. When a distribution has an exact symmetry between the modes, direct jumps among them can accelerate the samplings significantly. However, the…
A non-zero mutual information between morphology of a galaxy and its large-scale environment is known to exist in SDSS upto a few tens of Mpc. It is important to test the statistical significance of these mutual information if any. We…
This paper introduces the induced matching distance, a novel topological metric designed to compare discrete structures represented by a symmetric non-negative function. We apply this notion to analyze agent trajectories over time. We use…
Optimal transport has been one of the most exciting subjects in mathematics, starting from the 18th century. As a powerful tool to transport between two probability measures, optimal transport methods have been reinvigorated nowadays in a…
Determining the interaction partners among protein/domain families poses hard computational problems, in particular in the presence of paralogous proteins. Available approaches aim to identify interaction partners among protein/domain…
Although distance measures are used in many machine learning algorithms, the literature on the context-independent selection and evaluation of distance measures is limited in the sense that prior knowledge is used. In cluster analysis,…
Optimal transport (OT) is a widely used technique in machine learning, graphics, and vision that aligns two distributions or datasets using their relative geometry. In symmetry-rich settings, however, OT alignments based solely on pairwise…
We consider random i.i.d. samples of absolutely continuous measures on bounded connected domains. We prove an upper bound on the $\infty$-transportation distance between the measure and the empirical measure of the sample. The bound is…
In the current book I suggest an off-road path to the subject of optimal transport. I tried to avoid prior knowledge of analysis, PDE theory and functional analysis, as much as possible. Thus I concentrate on discrete and semi-discrete…
In this paper we examine the use of topological methods for multivariate statistics. Using persistent homology from computational algebraic topology, a random sample is used to construct estimators of persistent homology. This estimation…
When a vehicle observes another one, the two vehicles' poses are correlated by this spatial relative observation, which can be used in cooperative localization for further increasing localization accuracy and precision. To use spatial…
Optimal transportation distances are a fundamental family of parameterized distances for histograms. Despite their appealing theoretical properties, excellent performance in retrieval tasks and intuitive formulation, their computation…
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…
Merge trees are fundamental structures in topological data analysis. Interleaving distance is a widely accepted metric for comparing merge trees, with applications in visualization and scientific computing. While a greedy algorithm exists…