Related papers: Comparing Morse Complexes Using Optimal Transport:…
The traffic flow through a light signal is explored by using the optimal velocity model and its improvement known as full velocity differences model. The simulations consider a single line of identical cars, equally spaced, and with no…
Complex networks have attracted increasing interest from various fields of science. It has been demonstrated that each complex network model presents specific topological structures which characterize its connectivity and dynamics. Complex…
We propose the use of Flat Metric to assess the performance of reconstruction methods for single-molecule localization microscopy (SMLM) in scenarios where the ground-truth is available. Flat Metric is intimately related to the concept of…
Sparse data approximation has become a popular research topic in signal processing. However, in most cases only a single measurement vector (SMV) is considered. In applications, the multiple measurement vector (MMV) case is more usual,…
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,…
We study multi-marginal optimal transport (MOT) problems where the underlying cost has a graphical structure. These graphical multi-marginal optimal transport problems have found applications in several domains including traffic flow…
We study the properties of several proximity measures for the vertices of weighted multigraphs and multidigraphs. Unlike the classical distance for the vertices of connected graphs, these proximity measures are applicable to weighted…
We investigate the problem of efficiently computing optimal transport (OT) distances, which is equivalent to the node-capacitated minimum cost maximum flow problem in a bipartite graph. We compare runtimes in computing OT distances on data…
In this work, we propose a novel method for quantifying distances between Toeplitz structured covariance matrices. By exploiting the spectral representation of Toeplitz matrices, the proposed distance measure is defined based on an optimal…
Optimal transport (OT) distances between probability distributions are parameterized by the ground metric they use between observations. Their relevance for real-life applications strongly hinges on whether that ground metric parameter is…
Recently there has been much interest in graph-based learning, with applications in collaborative filtering for recommender networks, link prediction for social networks and fraud detection. These networks can consist of millions of…
We develop a new class of distances for objects including lines, hyperplanes, and trajectories, based on the distance to a set of landmarks. These distances easily and interpretably map objects to a Euclidean space, are simple to compute,…
Optimal transport provides a metric which quantifies the dissimilarity between probability measures. For measures supported in discrete metric spaces, finding the optimal transport distance has cubic time complexity in the size of the…
The present paper mainly presents, for example, explicit classifications of compact smooth manifolds having non-empty boundaries and simple structures where the dimensions are general. Studies of this type is fundamental and important. They…
Graph comparison deals with identifying similarities and dissimilarities between graphs. A major obstacle is the unknown alignment of graphs, as well as the lack of accurate and inexpensive comparison metrics. In this work we introduce the…
Optimal Morse matchings reveal essential structures of cell complexes which lead to powerful tools to study discrete geometrical objects, in particular discrete 3-manifolds. However, such matchings are known to be NP-hard to compute on…
Rising electricity demand and the growing integration of renewables are intensifying congestion in transmission grids. Grid topology optimization through busbar splitting (BuS) and optimal transmission switching can alleviate grid…
The concept of natural pseudo-distance has proven to be a powerful tool for measuring the dissimilarity between topological spaces endowed with continuous real-valued functions. Roughly speaking, the natural pseudo-distance is defined as…
Optimal transport (OT) is a powerful geometric tool used to compare and align probability measures following the least effort principle. Despite its widespread use in machine learning (ML), OT problem still bears its computational burden,…
Though analyzing a single scalar field using Morse complexes is well studied, there are few techniques for visualizing a collection of Morse complexes. We focus on analyses that are enabled by looking at a Morse complex as an embedded…