Related papers: Comparing Morse Complexes Using Optimal Transport:…
Optimal Transport (OT) has recently emerged as a powerful framework for learning minimal-displacement maps between distributions. The predominant approach involves a neural parametrization of the Monge formulation of OT, typically assuming…
When planning motions in a configuration space that has underlying symmetries (e.g. when manipulating one or multiple symmetric objects), the ideal planning algorithm should take advantage of those symmetries to produce shorter…
An explicit isomorphism between Morse homology and singular homology is constructed via the technique of pseudo-cycles. Given a Morse cycle as a formal sum of critical points of a Morse function, the unstable manifolds for the negative…
Concepts such as energy dependence, random deployment, dynamic topological update, self-organization, varying large number of nodes are among many factors that make WSNs a type of complex system. However, when analyzing WSNs properties…
Map matching is a common task when analysing GPS tracks, such as vehicle trajectories. The goal is to match a recorded noisy polygonal curve to a path on the map, usually represented as a geometric graph. The Fr\'echet distance is a…
Important data mining problems such as nearest-neighbor search and clustering admit theoretical guarantees when restricted to objects embedded in a metric space. Graphs are ubiquitous, and clustering and classification over graphs arise in…
We consider the problem of classifying trajectories on a discrete or discretised 2-dimensional manifold modelled by a simplicial complex. Previous works have proposed to project the trajectories into the harmonic eigenspace of the Hodge…
Measuring the distance between data points is fundamental to many statistical techniques, such as dimension reduction or clustering algorithms. However, improvements in data collection technologies has led to a growing versatility of…
Among the several topological properties of complex networks, the shortest path represents a particularly important characteristic because of its potential impact not only on other topological properties, but mainly for its influence on…
Cross-correlation is a popular signal processing technique used in numerous location tracking systems for obtaining reliable range information. However, its efficient design and practical implementation has not yet been achieved on mote…
We obtain a series of results in the global theory of free boundary minimal surfaces, which in particular provide a rather complete picture for the way different complexity criteria, such as area, topology and Morse index compare, beyond…
Many community detection algorithms require the introduction of a measure on the set of nodes. Previously, a lot of efforts have been made to find the top-performing measures. In most cases, experiments were conducted on several datasets or…
This paper explores the controllability and state tracking of ensembles from the perspective of optimal transport theory. Ensembles, characterized as collections of systems evolving under the same dynamics but with varying initial…
Optimal transport (OT) is a powerful tool in mathematics and data science but faces severe computational and statistical challenges in high dimensions. We propose convex relaxation approaches based on marginal and cluster moment relaxations…
The classical approach to the study of dynamical systems consists in representing the dynamics of the system in the form of a "source-sink", that means identifying an attractor-repeller pair, which are attractor-repellent sets for all other…
The modeling of phenomenological structure is a crucial aspect in inverse imaging problems. One emerging modeling tool in computational imaging is the optimal transport framework. Its ability to model geometric displacements across an…
We consider the optimal mass transportation problem in $\RR^d$ with measurably parameterized marginals, for general cost functions and under conditions ensuring the existence of a unique optimal transport map. We prove a joint measurability…
To improve our understanding of connected systems, different tools derived from statistics, signal processing, information theory and statistical physics have been developed in the last decade. Here, we will focus on the graph comparison…
Distance metric learning algorithms aim to appropriately measure similarities and distances between data points. In the context of clustering, metric learning is typically applied with the assist of side-information provided by experts,…
Optimal mass transport is described by an approximation of transport cost via semi-discrete costs. The notions of optimal partition and optimal strong partition are given as well. We also suggest an algorithm for computation of Optimal…